categories
string | doi
string | id
string | year
float64 | venue
string | link
string | updated
string | published
string | title
string | abstract
string | authors
sequence |
|---|---|---|---|---|---|---|---|---|---|---|
cs.LG | null | 1104.4664 | null | null | http://arxiv.org/pdf/1104.4664v1 | 2011-04-24T22:59:24Z | 2011-04-24T22:59:24Z | Temporal Second Difference Traces | Q-learning is a reliable but inefficient off-policy temporal-difference
method, backing up reward only one step at a time. Replacing traces, using a
recency heuristic, are more efficient but less reliable. In this work, we
introduce model-free, off-policy temporal difference methods that make better
use of experience than Watkins' Q(\lambda). We introduce both Optimistic
Q(\lambda) and the temporal second difference trace (TSDT). TSDT is
particularly powerful in deterministic domains. TSDT uses neither recency nor
frequency heuristics, storing (s,a,r,s',\delta) so that off-policy updates can
be performed after apparently suboptimal actions have been taken. There are
additional advantages when using state abstraction, as in MAXQ. We demonstrate
that TSDT does significantly better than both Q-learning and Watkins'
Q(\lambda) in a deterministic cliff-walking domain. Results in a noisy
cliff-walking domain are less advantageous for TSDT, but demonstrate the
efficacy of Optimistic Q(\lambda), a replacing trace with some of the
advantages of TSDT.
| [
"Mitchell Keith Bloch",
"['Mitchell Keith Bloch']"
] |
cs.LG stat.ML | null | 1104.4803 | null | null | http://arxiv.org/pdf/1104.4803v4 | 2014-07-24T00:44:05Z | 2011-04-25T20:33:55Z | Clustering Partially Observed Graphs via Convex Optimization | This paper considers the problem of clustering a partially observed
unweighted graph---i.e., one where for some node pairs we know there is an edge
between them, for some others we know there is no edge, and for the remaining
we do not know whether or not there is an edge. We want to organize the nodes
into disjoint clusters so that there is relatively dense (observed)
connectivity within clusters, and sparse across clusters.
We take a novel yet natural approach to this problem, by focusing on finding
the clustering that minimizes the number of "disagreements"---i.e., the sum of
the number of (observed) missing edges within clusters, and (observed) present
edges across clusters. Our algorithm uses convex optimization; its basis is a
reduction of disagreement minimization to the problem of recovering an
(unknown) low-rank matrix and an (unknown) sparse matrix from their partially
observed sum. We evaluate the performance of our algorithm on the classical
Planted Partition/Stochastic Block Model. Our main theorem provides sufficient
conditions for the success of our algorithm as a function of the minimum
cluster size, edge density and observation probability; in particular, the
results characterize the tradeoff between the observation probability and the
edge density gap. When there are a constant number of clusters of equal size,
our results are optimal up to logarithmic factors.
| [
"Yudong Chen, Ali Jalali, Sujay Sanghavi and Huan Xu",
"['Yudong Chen' 'Ali Jalali' 'Sujay Sanghavi' 'Huan Xu']"
] |
cs.LG | null | 1104.5059 | null | null | http://arxiv.org/pdf/1104.5059v1 | 2011-04-27T00:58:52Z | 2011-04-27T00:58:52Z | Reducing Commitment to Tasks with Off-Policy Hierarchical Reinforcement
Learning | In experimenting with off-policy temporal difference (TD) methods in
hierarchical reinforcement learning (HRL) systems, we have observed unwanted
on-policy learning under reproducible conditions. Here we present modifications
to several TD methods that prevent unintentional on-policy learning from
occurring. These modifications create a tension between exploration and
learning. Traditional TD methods require commitment to finishing subtasks
without exploration in order to update Q-values for early actions with high
probability. One-step intra-option learning and temporal second difference
traces (TSDT) do not suffer from this limitation. We demonstrate that our HRL
system is efficient without commitment to completion of subtasks in a
cliff-walking domain, contrary to a widespread claim in the literature that it
is critical for efficiency of learning. Furthermore, decreasing commitment as
exploration progresses is shown to improve both online performance and the
resultant policy in the taxicab domain, opening a new avenue for research into
when it is more beneficial to continue with the current subtask or to replan.
| [
"Mitchell Keith Bloch",
"['Mitchell Keith Bloch']"
] |
math.OC cs.LG stat.ML | null | 1104.5061 | null | null | http://arxiv.org/pdf/1104.5061v2 | 2014-03-13T01:07:49Z | 2011-04-27T01:21:05Z | On Combining Machine Learning with Decision Making | We present a new application and covering number bound for the framework of
"Machine Learning with Operational Costs (MLOC)," which is an exploratory form
of decision theory. The MLOC framework incorporates knowledge about how a
predictive model will be used for a subsequent task, thus combining machine
learning with the decision that is made afterwards. In this work, we use the
MLOC framework to study a problem that has implications for power grid
reliability and maintenance, called the Machine Learning and Traveling
Repairman Problem ML&TRP. The goal of the ML&TRP is to determine a route for a
"repair crew," which repairs nodes on a graph. The repair crew aims to minimize
the cost of failures at the nodes, but as in many real situations, the failure
probabilities are not known and must be estimated. The MLOC framework allows us
to understand how this uncertainty influences the repair route. We also present
new covering number generalization bounds for the MLOC framework.
| [
"['Theja Tulabandhula' 'Cynthia Rudin']",
"Theja Tulabandhula, Cynthia Rudin"
] |
stat.ML cs.GT cs.LG | null | 1104.5070 | null | null | http://arxiv.org/pdf/1104.5070v1 | 2011-04-27T04:11:10Z | 2011-04-27T04:11:10Z | Online Learning: Stochastic and Constrained Adversaries | Learning theory has largely focused on two main learning scenarios. The first
is the classical statistical setting where instances are drawn i.i.d. from a
fixed distribution and the second scenario is the online learning, completely
adversarial scenario where adversary at every time step picks the worst
instance to provide the learner with. It can be argued that in the real world
neither of these assumptions are reasonable. It is therefore important to study
problems with a range of assumptions on data. Unfortunately, theoretical
results in this area are scarce, possibly due to absence of general tools for
analysis. Focusing on the regret formulation, we define the minimax value of a
game where the adversary is restricted in his moves. The framework captures
stochastic and non-stochastic assumptions on data. Building on the sequential
symmetrization approach, we define a notion of distribution-dependent
Rademacher complexity for the spectrum of problems ranging from i.i.d. to
worst-case. The bounds let us immediately deduce variation-type bounds. We then
consider the i.i.d. adversary and show equivalence of online and batch
learnability. In the supervised setting, we consider various hybrid assumptions
on the way that x and y variables are chosen. Finally, we consider smoothed
learning problems and show that half-spaces are online learnable in the
smoothed model. In fact, exponentially small noise added to adversary's
decisions turns this problem with infinite Littlestone's dimension into a
learnable problem.
| [
"Alexander Rakhlin, Karthik Sridharan, Ambuj Tewari",
"['Alexander Rakhlin' 'Karthik Sridharan' 'Ambuj Tewari']"
] |
cs.LG | null | 1104.5071 | null | null | http://arxiv.org/pdf/1104.5071v1 | 2011-04-27T04:12:47Z | 2011-04-27T04:12:47Z | Attacking and Defending Covert Channels and Behavioral Models | In this paper we present methods for attacking and defending $k$-gram
statistical analysis techniques that are used, for example, in network traffic
analysis and covert channel detection. The main new result is our demonstration
of how to use a behavior's or process' $k$-order statistics to build a
stochastic process that has those same $k$-order stationary statistics but
possesses different, deliberately designed, $(k+1)$-order statistics if
desired. Such a model realizes a "complexification" of the process or behavior
which a defender can use to monitor whether an attacker is shaping the
behavior. By deliberately introducing designed $(k+1)$-order behaviors, the
defender can check to see if those behaviors are present in the data. We also
develop constructs for source codes that respect the $k$-order statistics of a
process while encoding covert information. One fundamental consequence of these
results is that certain types of behavior analyses techniques come down to an
{\em arms race} in the sense that the advantage goes to the party that has more
computing resources applied to the problem.
| [
"Valentino Crespi and George Cybenko and Annarita Giani",
"['Valentino Crespi' 'George Cybenko' 'Annarita Giani']"
] |
cs.NI cs.LG | null | 1104.5150 | null | null | http://arxiv.org/pdf/1104.5150v1 | 2011-04-27T14:04:27Z | 2011-04-27T14:04:27Z | File Transfer Application For Sharing Femto Access | In wireless access network optimization, today's main challenges reside in
traffic offload and in the improvement of both capacity and coverage networks.
The operators are interested in solving their localized coverage and capacity
problems in areas where the macro network signal is not able to serve the
demand for mobile data. Thus, the major issue for operators is to find the best
solution at reasonable expanses. The femto cell seems to be the answer to this
problematic. In this work (This work is supported by the COMET project AWARE.
http://www.ftw.at/news/project-start-for-aware-ftw), we focus on the problem of
sharing femto access between a same mobile operator's customers. This problem
can be modeled as a game where service requesters customers (SRCs) and service
providers customers (SPCs) are the players.
This work addresses the sharing femto access problem considering only one SPC
using game theory tools. We consider that SRCs are static and have some similar
and regular connection behavior. We also note that the SPC and each SRC have a
software embedded respectively on its femto access, user equipment (UE).
After each connection requested by a SRC, its software will learn the
strategy increasing its gain knowing that no information about the other SRCs
strategies is given. The following article presents a distributed learning
algorithm with incomplete information running in SRCs software. We will then
answer the following questions for a game with $N$ SRCs and one SPC: how many
connections are necessary for each SRC in order to learn the strategy
maximizing its gain? Does this algorithm converge to a stable state? If yes,
does this state a Nash Equilibrium and is there any way to optimize the
learning process duration time triggered by SRCs software?
| [
"['Mariem Krichen' 'Johanne Cohen' 'Dominique Barth']",
"Mariem Krichen and Johanne Cohen and Dominique Barth"
] |
cs.AI cs.LG | null | 1104.5256 | null | null | http://arxiv.org/pdf/1104.5256v1 | 2011-04-27T21:40:09Z | 2011-04-27T21:40:09Z | Learning Undirected Graphical Models with Structure Penalty | In undirected graphical models, learning the graph structure and learning the
functions that relate the predictive variables (features) to the responses
given the structure are two topics that have been widely investigated in
machine learning and statistics. Learning graphical models in two stages will
have problems because graph structure may change after considering the
features. The main contribution of this paper is the proposed method that
learns the graph structure and functions on the graph at the same time. General
graphical models with binary outcomes conditioned on predictive variables are
proved to be equivalent to multivariate Bernoulli model. The reparameterization
of the potential functions in graphical model by conditional log odds ratios in
multivariate Bernoulli model offers advantage in the representation of the
conditional independence structure in the model. Additionally, we impose a
structure penalty on groups of conditional log odds ratios to learn the graph
structure. These groups of functions are designed with overlaps to enforce
hierarchical function selection. In this way, we are able to shrink higher
order interactions to obtain a sparse graph structure. Simulation studies show
that the method is able to recover the graph structure. The analysis of county
data from Census Bureau gives interesting relations between unemployment rate,
crime and others discovered by the model.
| [
"['Shilin Ding']",
"Shilin Ding"
] |
cs.LG cs.SY math.OC | null | 1104.5391 | null | null | http://arxiv.org/pdf/1104.5391v1 | 2011-04-28T13:55:27Z | 2011-04-28T13:55:27Z | On Optimality of Greedy Policy for a Class of Standard Reward Function
of Restless Multi-armed Bandit Problem | In this paper,we consider the restless bandit problem, which is one of the
most well-studied generalizations of the celebrated stochastic multi-armed
bandit problem in decision theory. However, it is known be PSPACE-Hard to
approximate to any non-trivial factor. Thus the optimality is very difficult to
obtain due to its high complexity. A natural method is to obtain the greedy
policy considering its stability and simplicity. However, the greedy policy
will result in the optimality loss for its intrinsic myopic behavior generally.
In this paper, by analyzing one class of so-called standard reward function, we
establish the closed-form condition about the discounted factor \beta such that
the optimality of the greedy policy is guaranteed under the discounted expected
reward criterion, especially, the condition \beta = 1 indicating the optimality
of the greedy policy under the average accumulative reward criterion. Thus, the
standard form of reward function can easily be used to judge the optimality of
the greedy policy without any complicated calculation. Some examples in
cognitive radio networks are presented to verify the effectiveness of the
mathematical result in judging the optimality of the greedy policy.
| [
"Quan Liu, Kehao Wang, Lin Chen",
"['Quan Liu' 'Kehao Wang' 'Lin Chen']"
] |
cs.LG math.ST stat.ML stat.TH | null | 1104.5466 | null | null | http://arxiv.org/pdf/1104.5466v1 | 2011-04-28T18:46:06Z | 2011-04-28T18:46:06Z | Notes on a New Philosophy of Empirical Science | This book presents a methodology and philosophy of empirical science based on
large scale lossless data compression. In this view a theory is scientific if
it can be used to build a data compression program, and it is valuable if it
can compress a standard benchmark database to a small size, taking into account
the length of the compressor itself. This methodology therefore includes an
Occam principle as well as a solution to the problem of demarcation. Because of
the fundamental difficulty of lossless compression, this type of research must
be empirical in nature: compression can only be achieved by discovering and
characterizing empirical regularities in the data. Because of this, the
philosophy provides a way to reformulate fields such as computer vision and
computational linguistics as empirical sciences: the former by attempting to
compress databases of natural images, the latter by attempting to compress
large text databases. The book argues that the rigor and objectivity of the
compression principle should set the stage for systematic progress in these
fields. The argument is especially strong in the context of computer vision,
which is plagued by chronic problems of evaluation.
The book also considers the field of machine learning. Here the traditional
approach requires that the models proposed to solve learning problems be
extremely simple, in order to avoid overfitting. However, the world may contain
intrinsically complex phenomena, which would require complex models to
understand. The compression philosophy can justify complex models because of
the large quantity of data being modeled (if the target database is 100 Gb, it
is easy to justify a 10 Mb model). The complex models and abstractions learned
on the basis of the raw data (images, language, etc) can then be reused to
solve any specific learning problem, such as face recognition or machine
translation.
| [
"Daniel Burfoot",
"['Daniel Burfoot']"
] |
cs.LG cs.AI | null | 1104.5601 | null | null | http://arxiv.org/pdf/1104.5601v1 | 2011-04-29T11:39:40Z | 2011-04-29T11:39:40Z | Mean-Variance Optimization in Markov Decision Processes | We consider finite horizon Markov decision processes under performance
measures that involve both the mean and the variance of the cumulative reward.
We show that either randomized or history-based policies can improve
performance. We prove that the complexity of computing a policy that maximizes
the mean reward under a variance constraint is NP-hard for some cases, and
strongly NP-hard for others. We finally offer pseudopolynomial exact and
approximation algorithms.
| [
"Shie Mannor and John Tsitsiklis",
"['Shie Mannor' 'John Tsitsiklis']"
] |
stat.ME cs.LG math.ST stat.TH | 10.1214/11-AOS940 | 1104.5617 | null | null | http://arxiv.org/abs/1104.5617v3 | 2012-05-29T13:02:17Z | 2011-04-29T12:57:10Z | Learning high-dimensional directed acyclic graphs with latent and
selection variables | We consider the problem of learning causal information between random
variables in directed acyclic graphs (DAGs) when allowing arbitrarily many
latent and selection variables. The FCI (Fast Causal Inference) algorithm has
been explicitly designed to infer conditional independence and causal
information in such settings. However, FCI is computationally infeasible for
large graphs. We therefore propose the new RFCI algorithm, which is much faster
than FCI. In some situations the output of RFCI is slightly less informative,
in particular with respect to conditional independence information. However, we
prove that any causal information in the output of RFCI is correct in the
asymptotic limit. We also define a class of graphs on which the outputs of FCI
and RFCI are identical. We prove consistency of FCI and RFCI in sparse
high-dimensional settings, and demonstrate in simulations that the estimation
performances of the algorithms are very similar. All software is implemented in
the R-package pcalg.
| [
"Diego Colombo, Marloes H. Maathuis, Markus Kalisch, Thomas S.\n Richardson",
"['Diego Colombo' 'Marloes H. Maathuis' 'Markus Kalisch'\n 'Thomas S. Richardson']"
] |
stat.ML cs.LG | null | 1104.5687 | null | null | http://arxiv.org/pdf/1104.5687v2 | 2011-06-29T14:06:42Z | 2011-04-29T17:45:50Z | Preference elicitation and inverse reinforcement learning | We state the problem of inverse reinforcement learning in terms of preference
elicitation, resulting in a principled (Bayesian) statistical formulation. This
generalises previous work on Bayesian inverse reinforcement learning and allows
us to obtain a posterior distribution on the agent's preferences, policy and
optionally, the obtained reward sequence, from observations. We examine the
relation of the resulting approach to other statistical methods for inverse
reinforcement learning via analysis and experimental results. We show that
preferences can be determined accurately, even if the observed agent's policy
is sub-optimal with respect to its own preferences. In that case, significantly
improved policies with respect to the agent's preferences are obtained,
compared to both other methods and to the performance of the demonstrated
policy.
| [
"Constantin Rothkopf and Christos Dimitrakakis",
"['Constantin Rothkopf' 'Christos Dimitrakakis']"
] |
cs.LG stat.ML | null | 1105.0382 | null | null | http://arxiv.org/pdf/1105.0382v1 | 2011-05-02T17:10:49Z | 2011-05-02T17:10:49Z | Rapid Learning with Stochastic Focus of Attention | We present a method to stop the evaluation of a decision making process when
the result of the full evaluation is obvious. This trait is highly desirable
for online margin-based machine learning algorithms where a classifier
traditionally evaluates all the features for every example. We observe that
some examples are easier to classify than others, a phenomenon which is
characterized by the event when most of the features agree on the class of an
example. By stopping the feature evaluation when encountering an easy to
classify example, the learning algorithm can achieve substantial gains in
computation. Our method provides a natural attention mechanism for learning
algorithms. By modifying Pegasos, a margin-based online learning algorithm, to
include our attentive method we lower the number of attributes computed from
$n$ to an average of $O(\sqrt{n})$ features without loss in prediction
accuracy. We demonstrate the effectiveness of Attentive Pegasos on MNIST data.
| [
"['Raphael Pelossof' 'Zhiliang Ying']",
"Raphael Pelossof and Zhiliang Ying"
] |
cs.LG | null | 1105.0471 | null | null | http://arxiv.org/pdf/1105.0471v1 | 2011-05-03T03:14:14Z | 2011-05-03T03:14:14Z | Suboptimal Solution Path Algorithm for Support Vector Machine | We consider a suboptimal solution path algorithm for the Support Vector
Machine. The solution path algorithm is an effective tool for solving a
sequence of a parametrized optimization problems in machine learning. The path
of the solutions provided by this algorithm are very accurate and they satisfy
the optimality conditions more strictly than other SVM optimization algorithms.
In many machine learning application, however, this strict optimality is often
unnecessary, and it adversely affects the computational efficiency. Our
algorithm can generate the path of suboptimal solutions within an arbitrary
user-specified tolerance level. It allows us to control the trade-off between
the accuracy of the solution and the computational cost. Moreover, We also show
that our suboptimal solutions can be interpreted as the solution of a
\emph{perturbed optimization problem} from the original one. We provide some
theoretical analyses of our algorithm based on this novel interpretation. The
experimental results also demonstrate the effectiveness of our algorithm.
| [
"['Masayuki Karasuyama' 'Ichiro Takeuchi']",
"Masayuki Karasuyama and Ichiro Takeuchi"
] |
stat.ML cs.LG | null | 1105.0540 | null | null | http://arxiv.org/pdf/1105.0540v2 | 2011-05-05T14:13:49Z | 2011-05-03T10:34:25Z | Pruning nearest neighbor cluster trees | Nearest neighbor (k-NN) graphs are widely used in machine learning and data
mining applications, and our aim is to better understand what they reveal about
the cluster structure of the unknown underlying distribution of points.
Moreover, is it possible to identify spurious structures that might arise due
to sampling variability?
Our first contribution is a statistical analysis that reveals how certain
subgraphs of a k-NN graph form a consistent estimator of the cluster tree of
the underlying distribution of points. Our second and perhaps most important
contribution is the following finite sample guarantee. We carefully work out
the tradeoff between aggressive and conservative pruning and are able to
guarantee the removal of all spurious cluster structures at all levels of the
tree while at the same time guaranteeing the recovery of salient clusters. This
is the first such finite sample result in the context of clustering.
| [
"Samory Kpotufe, Ulrike von Luxburg",
"['Samory Kpotufe' 'Ulrike von Luxburg']"
] |
cs.LG | null | 1105.0857 | null | null | http://arxiv.org/pdf/1105.0857v1 | 2011-05-04T15:50:44Z | 2011-05-04T15:50:44Z | Domain Adaptation: Overfitting and Small Sample Statistics | We study the prevalent problem when a test distribution differs from the
training distribution. We consider a setting where our training set consists of
a small number of sample domains, but where we have many samples in each
domain. Our goal is to generalize to a new domain. For example, we may want to
learn a similarity function using only certain classes of objects, but we
desire that this similarity function be applicable to object classes not
present in our training sample (e.g. we might seek to learn that "dogs are
similar to dogs" even though images of dogs were absent from our training set).
Our theoretical analysis shows that we can select many more features than
domains while avoiding overfitting by utilizing data-dependent variance
properties. We present a greedy feature selection algorithm based on using
T-statistics. Our experiments validate this theory showing that our T-statistic
based greedy feature selection is more robust at avoiding overfitting than the
classical greedy procedure.
| [
"['Dean Foster' 'Sham Kakade' 'Ruslan Salakhutdinov']",
"Dean Foster and Sham Kakade and Ruslan Salakhutdinov"
] |
cs.LG cs.AI stat.ML | null | 1105.0972 | null | null | http://arxiv.org/pdf/1105.0972v1 | 2011-05-05T04:02:35Z | 2011-05-05T04:02:35Z | Rapid Feature Learning with Stacked Linear Denoisers | We investigate unsupervised pre-training of deep architectures as feature
generators for "shallow" classifiers. Stacked Denoising Autoencoders (SdA),
when used as feature pre-processing tools for SVM classification, can lead to
significant improvements in accuracy - however, at the price of a substantial
increase in computational cost. In this paper we create a simple algorithm
which mimics the layer by layer training of SdAs. However, in contrast to SdAs,
our algorithm requires no training through gradient descent as the parameters
can be computed in closed-form. It can be implemented in less than 20 lines of
MATLABTMand reduces the computation time from several hours to mere seconds. We
show that our feature transformation reliably improves the results of SVM
classification significantly on all our data sets - often outperforming SdAs
and even deep neural networks in three out of four deep learning benchmarks.
| [
"['Zhixiang Eddie Xu' 'Kilian Q. Weinberger' 'Fei Sha']",
"Zhixiang Eddie Xu, Kilian Q. Weinberger, Fei Sha"
] |
cs.LG | null | 1105.1033 | null | null | http://arxiv.org/pdf/1105.1033v2 | 2011-06-25T21:54:08Z | 2011-05-05T11:03:03Z | Adaptively Learning the Crowd Kernel | We introduce an algorithm that, given n objects, learns a similarity matrix
over all n^2 pairs, from crowdsourced data alone. The algorithm samples
responses to adaptively chosen triplet-based relative-similarity queries. Each
query has the form "is object 'a' more similar to 'b' or to 'c'?" and is chosen
to be maximally informative given the preceding responses. The output is an
embedding of the objects into Euclidean space (like MDS); we refer to this as
the "crowd kernel." SVMs reveal that the crowd kernel captures prominent and
subtle features across a number of domains, such as "is striped" among neckties
and "vowel vs. consonant" among letters.
| [
"['Omer Tamuz' 'Ce Liu' 'Serge Belongie' 'Ohad Shamir' 'Adam Tauman Kalai']",
"Omer Tamuz, Ce Liu, Serge Belongie, Ohad Shamir, Adam Tauman Kalai"
] |
cs.LG cs.DS stat.ML | null | 1105.1178 | null | null | http://arxiv.org/pdf/1105.1178v1 | 2011-05-05T21:24:37Z | 2011-05-05T21:24:37Z | Interpreting Graph Cuts as a Max-Product Algorithm | The maximum a posteriori (MAP) configuration of binary variable models with
submodular graph-structured energy functions can be found efficiently and
exactly by graph cuts. Max-product belief propagation (MP) has been shown to be
suboptimal on this class of energy functions by a canonical counterexample
where MP converges to a suboptimal fixed point (Kulesza & Pereira, 2008).
In this work, we show that under a particular scheduling and damping scheme,
MP is equivalent to graph cuts, and thus optimal. We explain the apparent
contradiction by showing that with proper scheduling and damping, MP always
converges to an optimal fixed point. Thus, the canonical counterexample only
shows the suboptimality of MP with a particular suboptimal choice of schedule
and damping. With proper choices, MP is optimal.
| [
"Daniel Tarlow, Inmar E. Givoni, Richard S. Zemel, Brendan J. Frey",
"['Daniel Tarlow' 'Inmar E. Givoni' 'Richard S. Zemel' 'Brendan J. Frey']"
] |
nlin.AO cs.LG stat.ML | null | 1105.1951 | null | null | http://arxiv.org/pdf/1105.1951v2 | 2011-09-05T11:54:46Z | 2011-05-10T14:01:41Z | Self-configuration from a Machine-Learning Perspective | The goal of machine learning is to provide solutions which are trained by
data or by experience coming from the environment. Many training algorithms
exist and some brilliant successes were achieved. But even in structured
environments for machine learning (e.g. data mining or board games), most
applications beyond the level of toy problems need careful hand-tuning or human
ingenuity (i.e. detection of interesting patterns) or both. We discuss several
aspects how self-configuration can help to alleviate these problems. One aspect
is the self-configuration by tuning of algorithms, where recent advances have
been made in the area of SPO (Sequen- tial Parameter Optimization). Another
aspect is the self-configuration by pattern detection or feature construction.
Forming multiple features (e.g. random boolean functions) and using algorithms
(e.g. random forests) which easily digest many fea- tures can largely increase
learning speed. However, a full-fledged theory of feature construction is not
yet available and forms a current barrier in machine learning. We discuss
several ideas for systematic inclusion of feature construction. This may lead
to partly self-configuring machine learning solutions which show robustness,
flexibility, and fast learning in potentially changing environments.
| [
"['Wolfgang Konen']",
"Wolfgang Konen"
] |
cs.LG stat.ML | null | 1105.2054 | null | null | http://arxiv.org/pdf/1105.2054v2 | 2012-02-14T06:33:18Z | 2011-05-10T21:02:58Z | Generalized Boosting Algorithms for Convex Optimization | Boosting is a popular way to derive powerful learners from simpler hypothesis
classes. Following previous work (Mason et al., 1999; Friedman, 2000) on
general boosting frameworks, we analyze gradient-based descent algorithms for
boosting with respect to any convex objective and introduce a new measure of
weak learner performance into this setting which generalizes existing work. We
present the weak to strong learning guarantees for the existing gradient
boosting work for strongly-smooth, strongly-convex objectives under this new
measure of performance, and also demonstrate that this work fails for
non-smooth objectives. To address this issue, we present new algorithms which
extend this boosting approach to arbitrary convex loss functions and give
corresponding weak to strong convergence results. In addition, we demonstrate
experimental results that support our analysis and demonstrate the need for the
new algorithms we present.
| [
"['Alexander Grubb' 'J. Andrew Bagnell']",
"Alexander Grubb and J. Andrew Bagnell"
] |
math.OC cs.IT cs.LG cs.SY math.IT | null | 1105.2176 | null | null | http://arxiv.org/pdf/1105.2176v1 | 2011-05-11T13:03:13Z | 2011-05-11T13:03:13Z | A Framework for Optimization under Limited Information | In many real world problems, optimization decisions have to be made with
limited information. The decision maker may have no a priori or posteriori data
about the often nonconvex objective function except from on a limited number of
points that are obtained over time through costly observations. This paper
presents an optimization framework that takes into account the information
collection (observation), estimation (regression), and optimization
(maximization) aspects in a holistic and structured manner. Explicitly
quantifying the information acquired at each optimization step using the
entropy measure from information theory, the (nonconvex) objective function to
be optimized (maximized) is modeled and estimated by adopting a Bayesian
approach and using Gaussian processes as a state-of-the-art regression method.
The resulting iterative scheme allows the decision maker to solve the problem
by expressing preferences for each aspect quantitatively and concurrently.
| [
"['Tansu Alpcan']",
"Tansu Alpcan"
] |
math.OC cs.IT cs.LG cs.SY math.IT | null | 1105.2211 | null | null | http://arxiv.org/pdf/1105.2211v1 | 2011-05-11T14:45:25Z | 2011-05-11T14:45:25Z | Dual Control with Active Learning using Gaussian Process Regression | In many real world problems, control decisions have to be made with limited
information. The controller may have no a priori (or even posteriori) data on
the nonlinear system, except from a limited number of points that are obtained
over time. This is either due to high cost of observation or the highly
non-stationary nature of the system. The resulting conflict between information
collection (identification, exploration) and control (optimization,
exploitation) necessitates an active learning approach for iteratively
selecting the control actions which concurrently provide the data points for
system identification. This paper presents a dual control approach where the
information acquired at each control step is quantified using the entropy
measure from information theory and serves as the training input to a
state-of-the-art Gaussian process regression (Bayesian learning) method. The
explicit quantification of the information obtained from each data point allows
for iterative optimization of both identification and control objectives. The
approach developed is illustrated with two examples: control of logistic map as
a chaotic system and position control of a cart with inverted pendulum.
| [
"['Tansu Alpcan']",
"Tansu Alpcan"
] |
cs.LG cs.DC | null | 1105.2274 | null | null | http://arxiv.org/pdf/1105.2274v1 | 2011-05-11T18:59:13Z | 2011-05-11T18:59:13Z | Data-Distributed Weighted Majority and Online Mirror Descent | In this paper, we focus on the question of the extent to which online
learning can benefit from distributed computing. We focus on the setting in
which $N$ agents online-learn cooperatively, where each agent only has access
to its own data. We propose a generic data-distributed online learning
meta-algorithm. We then introduce the Distributed Weighted Majority and
Distributed Online Mirror Descent algorithms, as special cases. We show, using
both theoretical analysis and experiments, that compared to a single agent:
given the same computation time, these distributed algorithms achieve smaller
generalization errors; and given the same generalization errors, they can be
$N$ times faster.
| [
"['Hua Ouyang' 'Alexander Gray']",
"Hua Ouyang, Alexander Gray"
] |
cs.LG stat.ML | null | 1105.2416 | null | null | http://arxiv.org/pdf/1105.2416v2 | 2011-05-19T17:04:35Z | 2011-05-12T10:40:19Z | PAC-Bayesian Analysis of Martingales and Multiarmed Bandits | We present two alternative ways to apply PAC-Bayesian analysis to sequences
of dependent random variables. The first is based on a new lemma that enables
to bound expectations of convex functions of certain dependent random variables
by expectations of the same functions of independent Bernoulli random
variables. This lemma provides an alternative tool to Hoeffding-Azuma
inequality to bound concentration of martingale values. Our second approach is
based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis.
We also introduce a way to apply PAC-Bayesian analysis in situation of limited
feedback. We combine the new tools to derive PAC-Bayesian generalization and
regret bounds for the multiarmed bandit problem. Although our regret bound is
not yet as tight as state-of-the-art regret bounds based on other
well-established techniques, our results significantly expand the range of
potential applications of PAC-Bayesian analysis and introduce a new analysis
tool to reinforcement learning and many other fields, where martingales and
limited feedback are encountered.
| [
"Yevgeny Seldin and Fran\\c{c}ois Laviolette and John Shawe-Taylor and\n Jan Peters and Peter Auer",
"['Yevgeny Seldin' 'François Laviolette' 'John Shawe-Taylor' 'Jan Peters'\n 'Peter Auer']"
] |
cs.LG | null | 1105.2550 | null | null | http://arxiv.org/pdf/1105.2550v3 | 2011-07-25T13:01:20Z | 2011-05-12T19:29:21Z | A Maximal Large Deviation Inequality for Sub-Gaussian Variables | In this short note we prove a maximal concentration lemma for sub-Gaussian
random variables stating that for independent sub-Gaussian random variables we
have \[P<(\max_{1\le i\le N}S_{i}>\epsilon>)
\le\exp<(-\frac{1}{N^2}\sum_{i=1}^{N}\frac{\epsilon^{2}}{2\sigma_{i}^{2}}>), \]
where $S_i$ is the sum of $i$ zero mean independent sub-Gaussian random
variables and $\sigma_i$ is the variance of the $i$th random variable.
| [
"Dotan Di Castro, Claudio Gentile, and Shie Mannor",
"['Dotan Di Castro' 'Claudio Gentile' 'Shie Mannor']"
] |
math.CO cs.LG | null | 1105.2651 | null | null | http://arxiv.org/pdf/1105.2651v1 | 2011-05-13T08:32:09Z | 2011-05-13T08:32:09Z | A Note on the Entropy/Influence Conjecture | The entropy/influence conjecture, raised by Friedgut and Kalai in 1996, seeks
to relate two different measures of concentration of the Fourier coefficients
of a Boolean function. Roughly saying, it claims that if the Fourier spectrum
is "smeared out", then the Fourier coefficients are concentrated on "high"
levels. In this note we generalize the conjecture to biased product measures on
the discrete cube, and prove a variant of the conjecture for functions with an
extremely low Fourier weight on the "high" levels.
| [
"['Nathan Keller' 'Elchanan Mossel' 'Tomer Schlank']",
"Nathan Keller, Elchanan Mossel, and Tomer Schlank"
] |
cs.LG cs.AI | null | 1105.2868 | null | null | http://arxiv.org/pdf/1105.2868v1 | 2011-05-14T07:13:25Z | 2011-05-14T07:13:25Z | Semantic Vector Machines | We first present our work in machine translation, during which we used
aligned sentences to train a neural network to embed n-grams of different
languages into an $d$-dimensional space, such that n-grams that are the
translation of each other are close with respect to some metric. Good n-grams
to n-grams translation results were achieved, but full sentences translation is
still problematic. We realized that learning semantics of sentences and
documents was the key for solving a lot of natural language processing
problems, and thus moved to the second part of our work: sentence compression.
We introduce a flexible neural network architecture for learning embeddings of
words and sentences that extract their semantics, propose an efficient
implementation in the Torch framework and present embedding results comparable
to the ones obtained with classical neural language models, while being more
powerful.
| [
"Etter Vincent",
"['Etter Vincent']"
] |
cs.LG cs.AI | 10.1016/j.neucom.2012.01.013 | 1105.2943 | null | null | http://arxiv.org/abs/1105.2943v1 | 2011-05-15T12:35:56Z | 2011-05-15T12:35:56Z | Feature Selection for MAUC-Oriented Classification Systems | Feature selection is an important pre-processing step for many pattern
classification tasks. Traditionally, feature selection methods are designed to
obtain a feature subset that can lead to high classification accuracy. However,
classification accuracy has recently been shown to be an inappropriate
performance metric of classification systems in many cases. Instead, the Area
Under the receiver operating characteristic Curve (AUC) and its multi-class
extension, MAUC, have been proved to be better alternatives. Hence, the target
of classification system design is gradually shifting from seeking a system
with the maximum classification accuracy to obtaining a system with the maximum
AUC/MAUC. Previous investigations have shown that traditional feature selection
methods need to be modified to cope with this new objective. These methods most
often are restricted to binary classification problems only. In this study, a
filter feature selection method, namely MAUC Decomposition based Feature
Selection (MDFS), is proposed for multi-class classification problems. To the
best of our knowledge, MDFS is the first method specifically designed to select
features for building classification systems with maximum MAUC. Extensive
empirical results demonstrate the advantage of MDFS over several compared
feature selection methods.
| [
"Rui Wang, Ke Tang",
"['Rui Wang' 'Ke Tang']"
] |
cs.IT cs.LG math.IT | 10.1088/1751-8113/45/3/032003 | 1105.3259 | null | null | http://arxiv.org/abs/1105.3259v1 | 2011-05-17T02:05:32Z | 2011-05-17T02:05:32Z | On R\'enyi and Tsallis entropies and divergences for exponential
families | Many common probability distributions in statistics like the Gaussian,
multinomial, Beta or Gamma distributions can be studied under the unified
framework of exponential families. In this paper, we prove that both R\'enyi
and Tsallis divergences of distributions belonging to the same exponential
family admit a generic closed form expression. Furthermore, we show that
R\'enyi and Tsallis entropies can also be calculated in closed-form for
sub-families including the Gaussian or exponential distributions, among others.
| [
"Frank Nielsen and Richard Nock",
"['Frank Nielsen' 'Richard Nock']"
] |
cs.LG math.NA stat.ML | null | 1105.3931 | null | null | http://arxiv.org/pdf/1105.3931v1 | 2011-05-19T16:54:39Z | 2011-05-19T16:54:39Z | Behavior of Graph Laplacians on Manifolds with Boundary | In manifold learning, algorithms based on graph Laplacians constructed from
data have received considerable attention both in practical applications and
theoretical analysis. In particular, the convergence of graph Laplacians
obtained from sampled data to certain continuous operators has become an active
research topic recently. Most of the existing work has been done under the
assumption that the data is sampled from a manifold without boundary or that
the functions of interests are evaluated at a point away from the boundary.
However, the question of boundary behavior is of considerable practical and
theoretical interest. In this paper we provide an analysis of the behavior of
graph Laplacians at a point near or on the boundary, discuss their convergence
rates and their implications and provide some numerical results. It turns out
that while points near the boundary occupy only a small part of the total
volume of a manifold, the behavior of graph Laplacian there has different
scaling properties from its behavior elsewhere on the manifold, with global
effects on the whole manifold, an observation with potentially important
implications for the general problem of learning on manifolds.
| [
"['Xueyuan Zhou' 'Mikhail Belkin']",
"Xueyuan Zhou and Mikhail Belkin"
] |
stat.ML cs.LG math.ST stat.TH | null | 1105.4042 | null | null | http://arxiv.org/pdf/1105.4042v4 | 2019-01-16T13:01:19Z | 2011-05-20T09:14:03Z | Adaptive and optimal online linear regression on $\ell^1$-balls | We consider the problem of online linear regression on individual sequences.
The goal in this paper is for the forecaster to output sequential predictions
which are, after $T$ time rounds, almost as good as the ones output by the best
linear predictor in a given $\ell^1$-ball in $\\R^d$. We consider both the
cases where the dimension~$d$ is small and large relative to the time horizon
$T$. We first present regret bounds with optimal dependencies on $d$, $T$, and
on the sizes $U$, $X$ and $Y$ of the $\ell^1$-ball, the input data and the
observations. The minimax regret is shown to exhibit a regime transition around
the point $d = \sqrt{T} U X / (2 Y)$. Furthermore, we present efficient
algorithms that are adaptive, \ie, that do not require the knowledge of $U$,
$X$, $Y$, and $T$, but still achieve nearly optimal regret bounds.
| [
"['Sébastien Gerchinovitz' 'Jia Yuan Yu']",
"S\\'ebastien Gerchinovitz (DMA, CLASSIC), Jia Yuan Yu"
] |
cs.LG | null | 1105.4272 | null | null | http://arxiv.org/pdf/1105.4272v1 | 2011-05-21T17:28:12Z | 2011-05-21T17:28:12Z | Calibration with Changing Checking Rules and Its Application to
Short-Term Trading | We provide a natural learning process in which a financial trader without a
risk receives a gain in case when Stock Market is inefficient. In this process,
the trader rationally choose his gambles using a prediction made by a
randomized calibrated algorithm. Our strategy is based on Dawid's notion of
calibration with more general changing checking rules and on some modification
of Kakade and Foster's randomized algorithm for computing calibrated forecasts.
| [
"['Vladimir Trunov' \"Vladimir V'yugin\"]",
"Vladimir Trunov and Vladimir V'yugin"
] |
cs.LG stat.AP stat.CO stat.ML | null | 1105.4385 | null | null | http://arxiv.org/pdf/1105.4385v1 | 2011-05-23T01:56:24Z | 2011-05-23T01:56:24Z | b-Bit Minwise Hashing for Large-Scale Linear SVM | In this paper, we propose to (seamlessly) integrate b-bit minwise hashing
with linear SVM to substantially improve the training (and testing) efficiency
using much smaller memory, with essentially no loss of accuracy. Theoretically,
we prove that the resemblance matrix, the minwise hashing matrix, and the b-bit
minwise hashing matrix are all positive definite matrices (kernels).
Interestingly, our proof for the positive definiteness of the b-bit minwise
hashing kernel naturally suggests a simple strategy to integrate b-bit hashing
with linear SVM. Our technique is particularly useful when the data can not fit
in memory, which is an increasingly critical issue in large-scale machine
learning. Our preliminary experimental results on a publicly available webspam
dataset (350K samples and 16 million dimensions) verified the effectiveness of
our algorithm. For example, the training time was reduced to merely a few
seconds. In addition, our technique can be easily extended to many other linear
and nonlinear machine learning applications such as logistic regression.
| [
"['Ping Li' 'Joshua Moore' 'Christian Konig']",
"Ping Li and Joshua Moore and Christian Konig"
] |
cs.LG stat.ML | null | 1105.4585 | null | null | http://arxiv.org/pdf/1105.4585v1 | 2011-05-23T19:10:03Z | 2011-05-23T19:10:03Z | PAC-Bayesian Analysis of the Exploration-Exploitation Trade-off | We develop a coherent framework for integrative simultaneous analysis of the
exploration-exploitation and model order selection trade-offs. We improve over
our preceding results on the same subject (Seldin et al., 2011) by combining
PAC-Bayesian analysis with Bernstein-type inequality for martingales. Such a
combination is also of independent interest for studies of multiple
simultaneously evolving martingales.
| [
"Yevgeny Seldin, Nicol\\`o Cesa-Bianchi, Fran\\c{c}ois Laviolette, Peter\n Auer, John Shawe-Taylor, Jan Peters",
"['Yevgeny Seldin' 'Nicolò Cesa-Bianchi' 'François Laviolette' 'Peter Auer'\n 'John Shawe-Taylor' 'Jan Peters']"
] |
cs.LG | null | 1105.4618 | null | null | http://arxiv.org/pdf/1105.4618v1 | 2011-05-23T20:04:16Z | 2011-05-23T20:04:16Z | Bounding the Fat Shattering Dimension of a Composition Function Class
Built Using a Continuous Logic Connective | We begin this report by describing the Probably Approximately Correct (PAC)
model for learning a concept class, consisting of subsets of a domain, and a
function class, consisting of functions from the domain to the unit interval.
Two combinatorial parameters, the Vapnik-Chervonenkis (VC) dimension and its
generalization, the Fat Shattering dimension of scale e, are explained and a
few examples of their calculations are given with proofs. We then explain
Sauer's Lemma, which involves the VC dimension and is used to prove the
equivalence of a concept class being distribution-free PAC learnable and it
having finite VC dimension.
As the main new result of our research, we explore the construction of a new
function class, obtained by forming compositions with a continuous logic
connective, a uniformly continuous function from the unit hypercube to the unit
interval, from a collection of function classes. Vidyasagar had proved that
such a composition function class has finite Fat Shattering dimension of all
scales if the classes in the original collection do; however, no estimates of
the dimension were known. Using results by Mendelson-Vershynin and Talagrand,
we bound the Fat Shattering dimension of scale e of this new function class in
terms of the Fat Shattering dimensions of the collection's classes.
We conclude this report by providing a few open questions and future research
topics involving the PAC learning model.
| [
"Hubert Haoyang Duan",
"['Hubert Haoyang Duan']"
] |
cs.LG | null | 1105.4701 | null | null | http://arxiv.org/pdf/1105.4701v3 | 2011-09-08T04:14:53Z | 2011-05-24T07:58:30Z | Online Learning, Stability, and Stochastic Gradient Descent | In batch learning, stability together with existence and uniqueness of the
solution corresponds to well-posedness of Empirical Risk Minimization (ERM)
methods; recently, it was proved that CV_loo stability is necessary and
sufficient for generalization and consistency of ERM. In this note, we
introduce CV_on stability, which plays a similar note in online learning. We
show that stochastic gradient descent (SDG) with the usual hypotheses is CVon
stable and we then discuss the implications of CV_on stability for convergence
of SGD.
| [
"['Tomaso Poggio' 'Stephen Voinea' 'Lorenzo Rosasco']",
"Tomaso Poggio, Stephen Voinea, Lorenzo Rosasco"
] |
math.ST cs.LG stat.TH | null | 1105.4995 | null | null | http://arxiv.org/pdf/1105.4995v3 | 2012-02-15T14:38:47Z | 2011-05-25T11:19:05Z | Robust approachability and regret minimization in games with partial
monitoring | Approachability has become a standard tool in analyzing earning algorithms in
the adversarial online learning setup. We develop a variant of approachability
for games where there is ambiguity in the obtained reward that belongs to a
set, rather than being a single vector. Using this variant we tackle the
problem of approachability in games with partial monitoring and develop simple
and efficient algorithms (i.e., with constant per-step complexity) for this
setup. We finally consider external regret and internal regret in repeated
games with partial monitoring and derive regret-minimizing strategies based on
approachability theory.
| [
"['Shie Mannor' 'Vianney Perchet' 'Gilles Stoltz']",
"Shie Mannor (EE-Technion), Vianney Perchet (CMLA), Gilles Stoltz (DMA,\n GREGH, INRIA Paris - Rocquencourt)"
] |
cs.LG | null | 1105.5196 | null | null | http://arxiv.org/pdf/1105.5196v1 | 2011-05-26T03:41:47Z | 2011-05-26T03:41:47Z | Large-Scale Music Annotation and Retrieval: Learning to Rank in Joint
Semantic Spaces | Music prediction tasks range from predicting tags given a song or clip of
audio, predicting the name of the artist, or predicting related songs given a
song, clip, artist name or tag. That is, we are interested in every semantic
relationship between the different musical concepts in our database. In
realistically sized databases, the number of songs is measured in the hundreds
of thousands or more, and the number of artists in the tens of thousands or
more, providing a considerable challenge to standard machine learning
techniques. In this work, we propose a method that scales to such datasets
which attempts to capture the semantic similarities between the database items
by modeling audio, artist names, and tags in a single low-dimensional semantic
space. This choice of space is learnt by optimizing the set of prediction tasks
of interest jointly using multi-task learning. Our method both outperforms
baseline methods and, in comparison to them, is faster and consumes less
memory. We then demonstrate how our method learns an interpretable model, where
the semantic space captures well the similarities of interest.
| [
"['Jason Weston' 'Samy Bengio' 'Philippe Hamel']",
"Jason Weston, Samy Bengio, Philippe Hamel"
] |
cs.LG cs.IT math.IT | null | 1105.5379 | null | null | http://arxiv.org/pdf/1105.5379v1 | 2011-05-26T19:19:30Z | 2011-05-26T19:19:30Z | Parallel Coordinate Descent for L1-Regularized Loss Minimization | We propose Shotgun, a parallel coordinate descent algorithm for minimizing
L1-regularized losses. Though coordinate descent seems inherently sequential,
we prove convergence bounds for Shotgun which predict linear speedups, up to a
problem-dependent limit. We present a comprehensive empirical study of Shotgun
for Lasso and sparse logistic regression. Our theoretical predictions on the
potential for parallelism closely match behavior on real data. Shotgun
outperforms other published solvers on a range of large problems, proving to be
one of the most scalable algorithms for L1.
| [
"['Joseph K. Bradley' 'Aapo Kyrola' 'Danny Bickson' 'Carlos Guestrin']",
"Joseph K. Bradley, Aapo Kyrola, Danny Bickson and Carlos Guestrin"
] |
cs.LG cs.AI | 10.1613/jair.587 | 1105.5464 | null | null | http://arxiv.org/abs/1105.5464v1 | 2011-05-27T01:54:11Z | 2011-05-27T01:54:11Z | Learning to Order Things | There are many applications in which it is desirable to order rather than
classify instances. Here we consider the problem of learning how to order
instances given feedback in the form of preference judgments, i.e., statements
to the effect that one instance should be ranked ahead of another. We outline a
two-stage approach in which one first learns by conventional means a binary
preference function indicating whether it is advisable to rank one instance
before another. Here we consider an on-line algorithm for learning preference
functions that is based on Freund and Schapire's 'Hedge' algorithm. In the
second stage, new instances are ordered so as to maximize agreement with the
learned preference function. We show that the problem of finding the ordering
that agrees best with a learned preference function is NP-complete.
Nevertheless, we describe simple greedy algorithms that are guaranteed to find
a good approximation. Finally, we show how metasearch can be formulated as an
ordering problem, and present experimental results on learning a combination of
'search experts', each of which is a domain-specific query expansion strategy
for a web search engine.
| [
"W. W. Cohen, R. E. Schapire, Y. Singer",
"['W. W. Cohen' 'R. E. Schapire' 'Y. Singer']"
] |
cs.LG | null | 1105.5592 | null | null | http://arxiv.org/pdf/1105.5592v1 | 2011-05-27T15:56:11Z | 2011-05-27T15:56:11Z | Kernel Belief Propagation | We propose a nonparametric generalization of belief propagation, Kernel
Belief Propagation (KBP), for pairwise Markov random fields. Messages are
represented as functions in a reproducing kernel Hilbert space (RKHS), and
message updates are simple linear operations in the RKHS. KBP makes none of the
assumptions commonly required in classical BP algorithms: the variables need
not arise from a finite domain or a Gaussian distribution, nor must their
relations take any particular parametric form. Rather, the relations between
variables are represented implicitly, and are learned nonparametrically from
training data. KBP has the advantage that it may be used on any domain where
kernels are defined (Rd, strings, groups), even where explicit parametric
models are not known, or closed form expressions for the BP updates do not
exist. The computational cost of message updates in KBP is polynomial in the
training data size. We also propose a constant time approximate message update
procedure by representing messages using a small number of basis functions. In
experiments, we apply KBP to image denoising, depth prediction from still
images, and protein configuration prediction: KBP is faster than competing
classical and nonparametric approaches (by orders of magnitude, in some cases),
while providing significantly more accurate results.
| [
"Le Song, Arthur Gretton, Danny Bickson, Yucheng Low, Carlos Guestrin",
"['Le Song' 'Arthur Gretton' 'Danny Bickson' 'Yucheng Low'\n 'Carlos Guestrin']"
] |
cs.LG cs.IT math.IT | 10.3390/e13061076 | 1105.5721 | null | null | http://arxiv.org/abs/1105.5721v1 | 2011-05-28T15:07:16Z | 2011-05-28T15:07:16Z | A Philosophical Treatise of Universal Induction | Understanding inductive reasoning is a problem that has engaged mankind for
thousands of years. This problem is relevant to a wide range of fields and is
integral to the philosophy of science. It has been tackled by many great minds
ranging from philosophers to scientists to mathematicians, and more recently
computer scientists. In this article we argue the case for Solomonoff
Induction, a formal inductive framework which combines algorithmic information
theory with the Bayesian framework. Although it achieves excellent theoretical
results and is based on solid philosophical foundations, the requisite
technical knowledge necessary for understanding this framework has caused it to
remain largely unknown and unappreciated in the wider scientific community. The
main contribution of this article is to convey Solomonoff induction and its
related concepts in a generally accessible form with the aim of bridging this
current technical gap. In the process we examine the major historical
contributions that have led to the formulation of Solomonoff Induction as well
as criticisms of Solomonoff and induction in general. In particular we examine
how Solomonoff induction addresses many issues that have plagued other
inductive systems, such as the black ravens paradox and the confirmation
problem, and compare this approach with other recent approaches.
| [
"['Samuel Rathmanner' 'Marcus Hutter']",
"Samuel Rathmanner and Marcus Hutter"
] |
stat.CO cs.LG stat.AP | null | 1105.5887 | null | null | http://arxiv.org/pdf/1105.5887v1 | 2011-05-30T07:31:01Z | 2011-05-30T07:31:01Z | Efficient sampling of high-dimensional Gaussian fields: the
non-stationary / non-sparse case | This paper is devoted to the problem of sampling Gaussian fields in high
dimension. Solutions exist for two specific structures of inverse covariance :
sparse and circulant. The proposed approach is valid in a more general case and
especially as it emerges in inverse problems. It relies on a
perturbation-optimization principle: adequate stochastic perturbation of a
criterion and optimization of the perturbed criterion. It is shown that the
criterion minimizer is a sample of the target density. The motivation in
inverse problems is related to general (non-convolutive) linear observation
models and their resolution in a Bayesian framework implemented through
sampling algorithms when existing samplers are not feasible. It finds a direct
application in myopic and/or unsupervised inversion as well as in some
non-Gaussian inversion. An illustration focused on hyperparameter estimation
for super-resolution problems assesses the effectiveness of the proposed
approach.
| [
"F. Orieux, and O. F\\'eron, and J.-F. Giovannelli",
"['F. Orieux' 'O. Féron' 'J. -F. Giovannelli']"
] |
cs.LG | null | 1105.6041 | null | null | http://arxiv.org/pdf/1105.6041v1 | 2011-05-30T17:02:09Z | 2011-05-30T17:02:09Z | The Perceptron with Dynamic Margin | The classical perceptron rule provides a varying upper bound on the maximum
margin, namely the length of the current weight vector divided by the total
number of updates up to that time. Requiring that the perceptron updates its
internal state whenever the normalized margin of a pattern is found not to
exceed a certain fraction of this dynamic upper bound we construct a new
approximate maximum margin classifier called the perceptron with dynamic margin
(PDM). We demonstrate that PDM converges in a finite number of steps and derive
an upper bound on them. We also compare experimentally PDM with other
perceptron-like algorithms and support vector machines on hard margin tasks
involving linear kernels which are equivalent to 2-norm soft margin.
| [
"['Constantinos Panagiotakopoulos' 'Petroula Tsampouka']",
"Constantinos Panagiotakopoulos and Petroula Tsampouka"
] |
cs.LG cs.AI cs.NE | 10.1613/jair.613 | 1106.0221 | null | null | http://arxiv.org/abs/1106.0221v1 | 2011-06-01T16:16:14Z | 2011-06-01T16:16:14Z | Evolutionary Algorithms for Reinforcement Learning | There are two distinct approaches to solving reinforcement learning problems,
namely, searching in value function space and searching in policy space.
Temporal difference methods and evolutionary algorithms are well-known examples
of these approaches. Kaelbling, Littman and Moore recently provided an
informative survey of temporal difference methods. This article focuses on the
application of evolutionary algorithms to the reinforcement learning problem,
emphasizing alternative policy representations, credit assignment methods, and
problem-specific genetic operators. Strengths and weaknesses of the
evolutionary approach to reinforcement learning are presented, along with a
survey of representative applications.
| [
"['J. J. Grefenstette' 'D. E. Moriarty' 'A. C. Schultz']",
"J. J. Grefenstette, D. E. Moriarty, A. C. Schultz"
] |
cs.LG cs.AI cs.CV | null | 1106.0357 | null | null | http://arxiv.org/pdf/1106.0357v1 | 2011-06-02T02:31:04Z | 2011-06-02T02:31:04Z | Learning Hierarchical Sparse Representations using Iterative Dictionary
Learning and Dimension Reduction | This paper introduces an elemental building block which combines Dictionary
Learning and Dimension Reduction (DRDL). We show how this foundational element
can be used to iteratively construct a Hierarchical Sparse Representation (HSR)
of a sensory stream. We compare our approach to existing models showing the
generality of our simple prescription. We then perform preliminary experiments
using this framework, illustrating with the example of an object recognition
task using standard datasets. This work introduces the very first steps towards
an integrated framework for designing and analyzing various computational tasks
from learning to attention to action. The ultimate goal is building a
mathematically rigorous, integrated theory of intelligence.
| [
"['Mohamad Tarifi' 'Meera Sitharam' 'Jeffery Ho']",
"Mohamad Tarifi, Meera Sitharam, Jeffery Ho"
] |
cs.AI cs.LG | null | 1106.0483 | null | null | http://arxiv.org/pdf/1106.0483v1 | 2011-06-02T18:48:59Z | 2011-06-02T18:48:59Z | Learning unbelievable marginal probabilities | Loopy belief propagation performs approximate inference on graphical models
with loops. One might hope to compensate for the approximation by adjusting
model parameters. Learning algorithms for this purpose have been explored
previously, and the claim has been made that every set of locally consistent
marginals can arise from belief propagation run on a graphical model. On the
contrary, here we show that many probability distributions have marginals that
cannot be reached by belief propagation using any set of model parameters or
any learning algorithm. We call such marginals `unbelievable.' This problem
occurs whenever the Hessian of the Bethe free energy is not positive-definite
at the target marginals. All learning algorithms for belief propagation
necessarily fail in these cases, producing beliefs or sets of beliefs that may
even be worse than the pre-learning approximation. We then show that averaging
inaccurate beliefs, each obtained from belief propagation using model
parameters perturbed about some learned mean values, can achieve the
unbelievable marginals.
| [
"Xaq Pitkow, Yashar Ahmadian, Ken D. Miller",
"['Xaq Pitkow' 'Yashar Ahmadian' 'Ken D. Miller']"
] |
cs.LG cs.CC cs.GT | null | 1106.0518 | null | null | http://arxiv.org/pdf/1106.0518v2 | 2011-06-13T14:32:55Z | 2011-06-02T21:30:50Z | Submodular Functions Are Noise Stable | We show that all non-negative submodular functions have high {\em
noise-stability}. As a consequence, we obtain a polynomial-time learning
algorithm for this class with respect to any product distribution on
$\{-1,1\}^n$ (for any constant accuracy parameter $\epsilon$). Our algorithm
also succeeds in the agnostic setting. Previous work on learning submodular
functions required either query access or strong assumptions about the types of
submodular functions to be learned (and did not hold in the agnostic setting).
| [
"Mahdi Cheraghchi, Adam Klivans, Pravesh Kothari, Homin K. Lee",
"['Mahdi Cheraghchi' 'Adam Klivans' 'Pravesh Kothari' 'Homin K. Lee']"
] |
cs.AI cs.LG | 10.1613/jair.807 | 1106.0666 | null | null | http://arxiv.org/abs/1106.0666v2 | 2019-11-14T04:58:31Z | 2011-06-03T14:52:26Z | Experiments with Infinite-Horizon, Policy-Gradient Estimation | In this paper, we present algorithms that perform gradient ascent of the
average reward in a partially observable Markov decision process (POMDP). These
algorithms are based on GPOMDP, an algorithm introduced in a companion paper
(Baxter and Bartlett, this volume), which computes biased estimates of the
performance gradient in POMDPs. The algorithm's chief advantages are that it
uses only one free parameter beta, which has a natural interpretation in terms
of bias-variance trade-off, it requires no knowledge of the underlying state,
and it can be applied to infinite state, control and observation spaces. We
show how the gradient estimates produced by GPOMDP can be used to perform
gradient ascent, both with a traditional stochastic-gradient algorithm, and
with an algorithm based on conjugate-gradients that utilizes gradient
information to bracket maxima in line searches. Experimental results are
presented illustrating both the theoretical results of (Baxter and Bartlett,
this volume) on a toy problem, and practical aspects of the algorithms on a
number of more realistic problems.
| [
"J. Baxter, P. L. Bartlett, L. Weaver",
"['J. Baxter' 'P. L. Bartlett' 'L. Weaver']"
] |
cs.LG cs.AI | 10.1613/jair.859 | 1106.0676 | null | null | http://arxiv.org/abs/1106.0676v1 | 2011-06-03T14:55:23Z | 2011-06-03T14:55:23Z | Optimizing Dialogue Management with Reinforcement Learning: Experiments
with the NJFun System | Designing the dialogue policy of a spoken dialogue system involves many
nontrivial choices. This paper presents a reinforcement learning approach for
automatically optimizing a dialogue policy, which addresses the technical
challenges in applying reinforcement learning to a working dialogue system with
human users. We report on the design, construction and empirical evaluation of
NJFun, an experimental spoken dialogue system that provides users with access
to information about fun things to do in New Jersey. Our results show that by
optimizing its performance via reinforcement learning, NJFun measurably
improves system performance.
| [
"['M. Kearns' 'D. Litman' 'S. Singh' 'M. Walker']",
"M. Kearns, D. Litman, S. Singh, M. Walker"
] |
cs.LG cs.AI | 10.1613/jair.898 | 1106.0681 | null | null | http://arxiv.org/abs/1106.0681v1 | 2011-06-03T14:57:02Z | 2011-06-03T14:57:02Z | Accelerating Reinforcement Learning through Implicit Imitation | Imitation can be viewed as a means of enhancing learning in multiagent
environments. It augments an agent's ability to learn useful behaviors by
making intelligent use of the knowledge implicit in behaviors demonstrated by
cooperative teachers or other more experienced agents. We propose and study a
formal model of implicit imitation that can accelerate reinforcement learning
dramatically in certain cases. Roughly, by observing a mentor, a
reinforcement-learning agent can extract information about its own capabilities
in, and the relative value of, unvisited parts of the state space. We study two
specific instantiations of this model, one in which the learning agent and the
mentor have identical abilities, and one designed to deal with agents and
mentors with different action sets. We illustrate the benefits of implicit
imitation by integrating it with prioritized sweeping, and demonstrating
improved performance and convergence through observation of single and multiple
mentors. Though we make some stringent assumptions regarding observability and
possible interactions, we briefly comment on extensions of the model that relax
these restricitions.
| [
"['C. Boutilier' 'B. Price']",
"C. Boutilier, B. Price"
] |
cs.LG cs.AI | 10.1613/jair.946 | 1106.0707 | null | null | http://arxiv.org/abs/1106.0707v1 | 2011-06-03T16:44:06Z | 2011-06-03T16:44:06Z | Efficient Reinforcement Learning Using Recursive Least-Squares Methods | The recursive least-squares (RLS) algorithm is one of the most well-known
algorithms used in adaptive filtering, system identification and adaptive
control. Its popularity is mainly due to its fast convergence speed, which is
considered to be optimal in practice. In this paper, RLS methods are used to
solve reinforcement learning problems, where two new reinforcement learning
algorithms using linear value function approximators are proposed and analyzed.
The two algorithms are called RLS-TD(lambda) and Fast-AHC (Fast Adaptive
Heuristic Critic), respectively. RLS-TD(lambda) can be viewed as the extension
of RLS-TD(0) from lambda=0 to general lambda within interval [0,1], so it is a
multi-step temporal-difference (TD) learning algorithm using RLS methods. The
convergence with probability one and the limit of convergence of RLS-TD(lambda)
are proved for ergodic Markov chains. Compared to the existing LS-TD(lambda)
algorithm, RLS-TD(lambda) has advantages in computation and is more suitable
for online learning. The effectiveness of RLS-TD(lambda) is analyzed and
verified by learning prediction experiments of Markov chains with a wide range
of parameter settings. The Fast-AHC algorithm is derived by applying the
proposed RLS-TD(lambda) algorithm in the critic network of the adaptive
heuristic critic method. Unlike conventional AHC algorithm, Fast-AHC makes use
of RLS methods to improve the learning-prediction efficiency in the critic.
Learning control experiments of the cart-pole balancing and the acrobot
swing-up problems are conducted to compare the data efficiency of Fast-AHC with
conventional AHC. From the experimental results, it is shown that the data
efficiency of learning control can also be improved by using RLS methods in the
learning-prediction process of the critic. The performance of Fast-AHC is also
compared with that of the AHC method using LS-TD(lambda). Furthermore, it is
demonstrated in the experiments that different initial values of the variance
matrix in RLS-TD(lambda) are required to get better performance not only in
learning prediction but also in learning control. The experimental results are
analyzed based on the existing theoretical work on the transient phase of
forgetting factor RLS methods.
| [
"['H. He' 'D. Hu' 'X. Xu']",
"H. He, D. Hu, X. Xu"
] |
stat.ML cs.LG | null | 1106.0730 | null | null | http://arxiv.org/pdf/1106.0730v2 | 2017-05-22T22:40:23Z | 2011-06-03T19:09:31Z | Rademacher complexity of stationary sequences | We show how to control the generalization error of time series models wherein
past values of the outcome are used to predict future values. The results are
based on a generalization of standard i.i.d. concentration inequalities to
dependent data without the mixing assumptions common in the time series
setting. Our proof and the result are simpler than previous analyses with
dependent data or stochastic adversaries which use sequential Rademacher
complexities rather than the expected Rademacher complexity for i.i.d.
processes. We also derive empirical Rademacher results without mixing
assumptions resulting in fully calculable upper bounds.
| [
"Daniel J. McDonald and Cosma Rohilla Shalizi",
"['Daniel J. McDonald' 'Cosma Rohilla Shalizi']"
] |
stat.ML cs.LG | null | 1106.0800 | null | null | http://arxiv.org/pdf/1106.0800v3 | 2011-10-14T15:01:11Z | 2011-06-04T08:14:59Z | Optimal Reinforcement Learning for Gaussian Systems | The exploration-exploitation trade-off is among the central challenges of
reinforcement learning. The optimal Bayesian solution is intractable in
general. This paper studies to what extent analytic statements about optimal
learning are possible if all beliefs are Gaussian processes. A first order
approximation of learning of both loss and dynamics, for nonlinear,
time-varying systems in continuous time and space, subject to a relatively weak
restriction on the dynamics, is described by an infinite-dimensional partial
differential equation. An approximate finite-dimensional projection gives an
impression for how this result may be helpful.
| [
"['Philipp Hennig']",
"Philipp Hennig"
] |
stat.ML cs.LG | null | 1106.0967 | null | null | http://arxiv.org/pdf/1106.0967v1 | 2011-06-06T06:38:20Z | 2011-06-06T06:38:20Z | Hashing Algorithms for Large-Scale Learning | In this paper, we first demonstrate that b-bit minwise hashing, whose
estimators are positive definite kernels, can be naturally integrated with
learning algorithms such as SVM and logistic regression. We adopt a simple
scheme to transform the nonlinear (resemblance) kernel into linear (inner
product) kernel; and hence large-scale problems can be solved extremely
efficiently. Our method provides a simple effective solution to large-scale
learning in massive and extremely high-dimensional datasets, especially when
data do not fit in memory.
We then compare b-bit minwise hashing with the Vowpal Wabbit (VW) algorithm
(which is related the Count-Min (CM) sketch). Interestingly, VW has the same
variances as random projections. Our theoretical and empirical comparisons
illustrate that usually $b$-bit minwise hashing is significantly more accurate
(at the same storage) than VW (and random projections) in binary data.
Furthermore, $b$-bit minwise hashing can be combined with VW to achieve further
improvements in terms of training speed, especially when $b$ is large.
| [
"Ping Li, Anshumali Shrivastava, Joshua Moore, Arnd Christian Konig",
"['Ping Li' 'Anshumali Shrivastava' 'Joshua Moore' 'Arnd Christian Konig']"
] |
cs.LG cs.AI cs.CG cs.CV | null | 1106.0987 | null | null | http://arxiv.org/pdf/1106.0987v1 | 2011-06-06T08:32:16Z | 2011-06-06T08:32:16Z | Nearest Prime Simplicial Complex for Object Recognition | The structure representation of data distribution plays an important role in
understanding the underlying mechanism of generating data. In this paper, we
propose nearest prime simplicial complex approaches (NSC) by utilizing
persistent homology to capture such structures. Assuming that each class is
represented with a prime simplicial complex, we classify unlabeled samples
based on the nearest projection distances from the samples to the simplicial
complexes. We also extend the extrapolation ability of these complexes with a
projection constraint term. Experiments in simulated and practical datasets
indicate that compared with several published algorithms, the proposed NSC
approaches achieve promising performance without losing the structure
representation.
| [
"Junping Zhang and Ziyu Xie and Stan Z. Li",
"['Junping Zhang' 'Ziyu Xie' 'Stan Z. Li']"
] |
cs.LG cs.DM | null | 1106.1113 | null | null | http://arxiv.org/pdf/1106.1113v1 | 2011-06-06T16:25:58Z | 2011-06-06T16:25:58Z | Complexity Analysis of Vario-eta through Structure | Graph-based representations of images have recently acquired an important
role for classification purposes within the context of machine learning
approaches. The underlying idea is to consider that relevant information of an
image is implicitly encoded into the relationships between more basic entities
that compose by themselves the whole image. The classification problem is then
reformulated in terms of an optimization problem usually solved by a
gradient-based search procedure. Vario-eta through structure is an approximate
second order stochastic optimization technique that achieves a good trade-off
between speed of convergence and the computational effort required. However,
the robustness of this technique for large scale problems has not been yet
assessed. In this paper we firstly provide a theoretical justification of the
assumptions made by this optimization procedure. Secondly, a complexity
analysis of the algorithm is performed to prove its suitability for large scale
learning problems.
| [
"['Alejandro Chinea' 'Elka Korutcheva']",
"Alejandro Chinea, Elka Korutcheva"
] |
cs.LG cs.AI stat.ML | null | 1106.1157 | null | null | http://arxiv.org/pdf/1106.1157v3 | 2012-08-17T04:15:40Z | 2011-06-06T19:24:44Z | Bayesian and L1 Approaches to Sparse Unsupervised Learning | The use of L1 regularisation for sparse learning has generated immense
research interest, with successful application in such diverse areas as signal
acquisition, image coding, genomics and collaborative filtering. While existing
work highlights the many advantages of L1 methods, in this paper we find that
L1 regularisation often dramatically underperforms in terms of predictive
performance when compared with other methods for inferring sparsity. We focus
on unsupervised latent variable models, and develop L1 minimising factor
models, Bayesian variants of "L1", and Bayesian models with a stronger L0-like
sparsity induced through spike-and-slab distributions. These spike-and-slab
Bayesian factor models encourage sparsity while accounting for uncertainty in a
principled manner and avoiding unnecessary shrinkage of non-zero values. We
demonstrate on a number of data sets that in practice spike-and-slab Bayesian
methods outperform L1 minimisation, even on a computational budget. We thus
highlight the need to re-assess the wide use of L1 methods in sparsity-reliant
applications, particularly when we care about generalising to previously unseen
data, and provide an alternative that, over many varying conditions, provides
improved generalisation performance.
| [
"['Shakir Mohamed' 'Katherine Heller' 'Zoubin Ghahramani']",
"Shakir Mohamed, Katherine Heller and Zoubin Ghahramani"
] |
cs.LG stat.ML | null | 1106.1216 | null | null | http://arxiv.org/pdf/1106.1216v2 | 2011-06-15T01:17:56Z | 2011-06-06T23:55:00Z | Using More Data to Speed-up Training Time | In many recent applications, data is plentiful. By now, we have a rather
clear understanding of how more data can be used to improve the accuracy of
learning algorithms. Recently, there has been a growing interest in
understanding how more data can be leveraged to reduce the required training
runtime. In this paper, we study the runtime of learning as a function of the
number of available training examples, and underscore the main high-level
techniques. We provide some initial positive results showing that the runtime
can decrease exponentially while only requiring a polynomial growth of the
number of examples, and spell-out several interesting open problems.
| [
"['Shai Shalev-Shwartz' 'Ohad Shamir' 'Eran Tromer']",
"Shai Shalev-Shwartz and Ohad Shamir and Eran Tromer"
] |
cs.LG | null | 1106.1379 | null | null | http://arxiv.org/pdf/1106.1379v4 | 2016-05-28T21:58:42Z | 2011-06-07T15:52:39Z | A Unified Framework for Approximating and Clustering Data | Given a set $F$ of $n$ positive functions over a ground set $X$, we consider
the problem of computing $x^*$ that minimizes the expression $\sum_{f\in
F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we
wish to approximate a set $P$ of $n$ elements (say, points) by a shape $x$ from
a (possibly infinite) family $X$ of shapes. Here, each point $p\in P$
corresponds to a function $f$ such that $f(x)$ is the distance from $p$ to $x$,
and we seek a shape $x$ that minimizes the sum of distances from each point in
$P$. In the $k$-clustering variant, each $x\in X$ is a tuple of $k$ shapes, and
$f(x)$ is the distance from $p$ to its closest shape in $x$.
Our main result is a unified framework for constructing {\em coresets} and
{\em approximate clustering} for such general sets of functions. To achieve our
results, we forge a link between the classic and well defined notion of
$\varepsilon$-approximations from the theory of PAC Learning and VC dimension,
to the relatively new (and not so consistent) paradigm of coresets, which are
some kind of "compressed representation" of the input set $F$. Using
traditional techniques, a coreset usually implies an LTAS (linear time
approximation scheme) for the corresponding optimization problem, which can be
computed in parallel, via one pass over the data, and using only
polylogarithmic space (i.e, in the streaming model).
We show how to generalize the results of our framework for squared distances
(as in $k$-mean), distances to the $q$th power, and deterministic
constructions.
| [
"Dan Feldman, Michael Langberg",
"['Dan Feldman' 'Michael Langberg']"
] |
cs.LG stat.ML | null | 1106.1622 | null | null | http://arxiv.org/pdf/1106.1622v1 | 2011-06-08T19:07:09Z | 2011-06-08T19:07:09Z | Large-Scale Convex Minimization with a Low-Rank Constraint | We address the problem of minimizing a convex function over the space of
large matrices with low rank. While this optimization problem is hard in
general, we propose an efficient greedy algorithm and derive its formal
approximation guarantees. Each iteration of the algorithm involves
(approximately) finding the left and right singular vectors corresponding to
the largest singular value of a certain matrix, which can be calculated in
linear time. This leads to an algorithm which can scale to large matrices
arising in several applications such as matrix completion for collaborative
filtering and robust low rank matrix approximation.
| [
"['Shai Shalev-Shwartz' 'Alon Gonen' 'Ohad Shamir']",
"Shai Shalev-Shwartz and Alon Gonen and Ohad Shamir"
] |
cs.IT cs.LG cs.SY math.IT math.OC | null | 1106.1651 | null | null | http://arxiv.org/pdf/1106.1651v1 | 2011-06-08T20:01:17Z | 2011-06-08T20:01:17Z | Sparse Principal Component of a Rank-deficient Matrix | We consider the problem of identifying the sparse principal component of a
rank-deficient matrix. We introduce auxiliary spherical variables and prove
that there exists a set of candidate index-sets (that is, sets of indices to
the nonzero elements of the vector argument) whose size is polynomially
bounded, in terms of rank, and contains the optimal index-set, i.e. the
index-set of the nonzero elements of the optimal solution. Finally, we develop
an algorithm that computes the optimal sparse principal component in polynomial
time for any sparsity degree.
| [
"['Megasthenis Asteris' 'Dimitris S. Papailiopoulos' 'George N. Karystinos']",
"Megasthenis Asteris, Dimitris S. Papailiopoulos, and George N.\n Karystinos"
] |
cs.LG | null | 1106.1684 | null | null | http://arxiv.org/pdf/1106.1684v1 | 2011-06-08T23:03:47Z | 2011-06-08T23:03:47Z | Max-Margin Stacking and Sparse Regularization for Linear Classifier
Combination and Selection | The main principle of stacked generalization (or Stacking) is using a
second-level generalizer to combine the outputs of base classifiers in an
ensemble. In this paper, we investigate different combination types under the
stacking framework; namely weighted sum (WS), class-dependent weighted sum
(CWS) and linear stacked generalization (LSG). For learning the weights, we
propose using regularized empirical risk minimization with the hinge loss. In
addition, we propose using group sparsity for regularization to facilitate
classifier selection. We performed experiments using two different ensemble
setups with differing diversities on 8 real-world datasets. Results show the
power of regularized learning with the hinge loss function. Using sparse
regularization, we are able to reduce the number of selected classifiers of the
diverse ensemble without sacrificing accuracy. With the non-diverse ensembles,
we even gain accuracy on average by using sparse regularization.
| [
"['Mehmet Umut Sen' 'Hakan Erdogan']",
"Mehmet Umut Sen and Hakan Erdogan"
] |
cs.LG | null | 1106.1770 | null | null | http://arxiv.org/pdf/1106.1770v3 | 2011-10-04T06:02:16Z | 2011-06-09T10:40:08Z | Reinforcement learning based sensing policy optimization for energy
efficient cognitive radio networks | This paper introduces a machine learning based collaborative multi-band
spectrum sensing policy for cognitive radios. The proposed sensing policy
guides secondary users to focus the search of unused radio spectrum to those
frequencies that persistently provide them high data rate. The proposed policy
is based on machine learning, which makes it adaptive with the temporally and
spatially varying radio spectrum. Furthermore, there is no need for dynamic
modeling of the primary activity since it is implicitly learned over time.
Energy efficiency is achieved by minimizing the number of assigned sensors per
each subband under a constraint on miss detection probability. It is important
to control the missed detections because they cause collisions with primary
transmissions and lead to retransmissions at both the primary and secondary
user. Simulations show that the proposed machine learning based sensing policy
improves the overall throughput of the secondary network and improves the
energy efficiency while controlling the miss detection probability.
| [
"Jan Oksanen, Jarmo Lund\\'en, Visa Koivunen",
"['Jan Oksanen' 'Jarmo Lundén' 'Visa Koivunen']"
] |
cs.LG | null | 1106.1887 | null | null | http://arxiv.org/pdf/1106.1887v4 | 2012-05-01T04:30:11Z | 2011-06-09T19:34:29Z | Learning the Dependence Graph of Time Series with Latent Factors | This paper considers the problem of learning, from samples, the dependency
structure of a system of linear stochastic differential equations, when some of
the variables are latent. In particular, we observe the time evolution of some
variables, and never observe other variables; from this, we would like to find
the dependency structure between the observed variables - separating out the
spurious interactions caused by the (marginalizing out of the) latent
variables' time series. We develop a new method, based on convex optimization,
to do so in the case when the number of latent variables is smaller than the
number of observed ones. For the case when the dependency structure between the
observed variables is sparse, we theoretically establish a high-dimensional
scaling result for structure recovery. We verify our theoretical result with
both synthetic and real data (from the stock market).
| [
"Ali Jalali and Sujay Sanghavi",
"['Ali Jalali' 'Sujay Sanghavi']"
] |
stat.ML cs.IR cs.LG | null | 1106.1925 | null | null | http://arxiv.org/pdf/1106.1925v2 | 2011-06-14T00:11:51Z | 2011-06-09T21:57:27Z | Ranking via Sinkhorn Propagation | It is of increasing importance to develop learning methods for ranking. In
contrast to many learning objectives, however, the ranking problem presents
difficulties due to the fact that the space of permutations is not smooth. In
this paper, we examine the class of rank-linear objective functions, which
includes popular metrics such as precision and discounted cumulative gain. In
particular, we observe that expectations of these gains are completely
characterized by the marginals of the corresponding distribution over
permutation matrices. Thus, the expectations of rank-linear objectives can
always be described through locations in the Birkhoff polytope, i.e.,
doubly-stochastic matrices (DSMs). We propose a technique for learning
DSM-based ranking functions using an iterative projection operator known as
Sinkhorn normalization. Gradients of this operator can be computed via
backpropagation, resulting in an algorithm we call Sinkhorn propagation, or
SinkProp. This approach can be combined with a wide range of gradient-based
approaches to rank learning. We demonstrate the utility of SinkProp on several
information retrieval data sets.
| [
"Ryan Prescott Adams, Richard S. Zemel",
"['Ryan Prescott Adams' 'Richard S. Zemel']"
] |
cs.GT cs.LG cs.SY math.OC | null | 1106.1933 | null | null | http://arxiv.org/pdf/1106.1933v2 | 2012-04-23T18:19:52Z | 2011-06-09T23:55:58Z | Lyapunov stochastic stability and control of robust dynamic coalitional
games with transferable utilities | This paper considers a dynamic game with transferable utilities (TU), where
the characteristic function is a continuous-time bounded mean ergodic process.
A central planner interacts continuously over time with the players by choosing
the instantaneous allocations subject to budget constraints. Before the game
starts, the central planner knows the nature of the process (bounded mean
ergodic), the bounded set from which the coalitions' values are sampled, and
the long run average coalitions' values. On the other hand, he has no knowledge
of the underlying probability function generating the coalitions' values. Our
goal is to find allocation rules that use a measure of the extra reward that a
coalition has received up to the current time by re-distributing the budget
among the players. The objective is two-fold: i) guaranteeing convergence of
the average allocations to the core (or a specific point in the core) of the
average game, ii) driving the coalitions' excesses to an a priori given cone.
The resulting allocation rules are robust as they guarantee the aforementioned
convergence properties despite the uncertain and time-varying nature of the
coaltions' values. We highlight three main contributions. First, we design an
allocation rule based on full observation of the extra reward so that the
average allocation approaches a specific point in the core of the average game,
while the coalitions' excesses converge to an a priori given direction. Second,
we design a new allocation rule based on partial observation on the extra
reward so that the average allocation converges to the core of the average
game, while the coalitions' excesses converge to an a priori given cone. And
third, we establish connections to approachability theory and attainability
theory.
| [
"['Dario Bauso' 'Puduru Viswanadha Reddy' 'Tamer Basar']",
"Dario Bauso, Puduru Viswanadha Reddy and Tamer Basar"
] |
cs.LG cs.CV cs.SI stat.ML | 10.1109/TSP.2012.2212886 | 1106.2233 | null | null | http://arxiv.org/abs/1106.2233v1 | 2011-06-11T12:43:18Z | 2011-06-11T12:43:18Z | Clustering with Multi-Layer Graphs: A Spectral Perspective | Observational data usually comes with a multimodal nature, which means that
it can be naturally represented by a multi-layer graph whose layers share the
same set of vertices (users) with different edges (pairwise relationships). In
this paper, we address the problem of combining different layers of the
multi-layer graph for improved clustering of the vertices compared to using
layers independently. We propose two novel methods, which are based on joint
matrix factorization and graph regularization framework respectively, to
efficiently combine the spectrum of the multiple graph layers, namely the
eigenvectors of the graph Laplacian matrices. In each case, the resulting
combination, which we call a "joint spectrum" of multiple graphs, is used for
clustering the vertices. We evaluate our approaches by simulations with several
real world social network datasets. Results demonstrate the superior or
competitive performance of the proposed methods over state-of-the-art technique
and common baseline methods, such as co-regularization and summation of
information from individual graphs.
| [
"['Xiaowen Dong' 'Pascal Frossard' 'Pierre Vandergheynst' 'Nikolai Nefedov']",
"Xiaowen Dong, Pascal Frossard, Pierre Vandergheynst and Nikolai\n Nefedov"
] |
math.ST cs.AI cs.LG stat.ML stat.TH | null | 1106.2363 | null | null | http://arxiv.org/pdf/1106.2363v2 | 2014-03-25T02:16:11Z | 2011-06-13T01:08:48Z | Random design analysis of ridge regression | This work gives a simultaneous analysis of both the ordinary least squares
estimator and the ridge regression estimator in the random design setting under
mild assumptions on the covariate/response distributions. In particular, the
analysis provides sharp results on the ``out-of-sample'' prediction error, as
opposed to the ``in-sample'' (fixed design) error. The analysis also reveals
the effect of errors in the estimated covariance structure, as well as the
effect of modeling errors, neither of which effects are present in the fixed
design setting. The proofs of the main results are based on a simple
decomposition lemma combined with concentration inequalities for random vectors
and matrices.
| [
"['Daniel Hsu' 'Sham M. Kakade' 'Tong Zhang']",
"Daniel Hsu, Sham M. Kakade, Tong Zhang"
] |
cs.LG cs.AI stat.ML | null | 1106.2369 | null | null | http://arxiv.org/pdf/1106.2369v1 | 2011-06-13T01:57:52Z | 2011-06-13T01:57:52Z | Efficient Optimal Learning for Contextual Bandits | We address the problem of learning in an online setting where the learner
repeatedly observes features, selects among a set of actions, and receives
reward for the action taken. We provide the first efficient algorithm with an
optimal regret. Our algorithm uses a cost sensitive classification learner as
an oracle and has a running time $\mathrm{polylog}(N)$, where $N$ is the number
of classification rules among which the oracle might choose. This is
exponentially faster than all previous algorithms that achieve optimal regret
in this setting. Our formulation also enables us to create an algorithm with
regret that is additive rather than multiplicative in feedback delay as in all
previous work.
| [
"Miroslav Dudik, Daniel Hsu, Satyen Kale, Nikos Karampatziakis, John\n Langford, Lev Reyzin, Tong Zhang",
"['Miroslav Dudik' 'Daniel Hsu' 'Satyen Kale' 'Nikos Karampatziakis'\n 'John Langford' 'Lev Reyzin' 'Tong Zhang']"
] |
cs.LG stat.ML | null | 1106.2429 | null | null | http://arxiv.org/pdf/1106.2429v4 | 2013-09-11T10:55:26Z | 2011-06-13T12:30:05Z | Efficient Transductive Online Learning via Randomized Rounding | Most traditional online learning algorithms are based on variants of mirror
descent or follow-the-leader. In this paper, we present an online algorithm
based on a completely different approach, tailored for transductive settings,
which combines "random playout" and randomized rounding of loss subgradients.
As an application of our approach, we present the first computationally
efficient online algorithm for collaborative filtering with trace-norm
constrained matrices. As a second application, we solve an open question
linking batch learning and transductive online learning
| [
"['Nicolò Cesa-Bianchi' 'Ohad Shamir']",
"Nicol\\`o Cesa-Bianchi and Ohad Shamir"
] |
cs.LG stat.ML | null | 1106.2436 | null | null | http://arxiv.org/pdf/1106.2436v3 | 2011-10-25T15:55:47Z | 2011-06-13T13:11:33Z | From Bandits to Experts: On the Value of Side-Observations | We consider an adversarial online learning setting where a decision maker can
choose an action in every stage of the game. In addition to observing the
reward of the chosen action, the decision maker gets side observations on the
reward he would have obtained had he chosen some of the other actions. The
observation structure is encoded as a graph, where node i is linked to node j
if sampling i provides information on the reward of j. This setting naturally
interpolates between the well-known "experts" setting, where the decision maker
can view all rewards, and the multi-armed bandits setting, where the decision
maker can only view the reward of the chosen action. We develop practical
algorithms with provable regret guarantees, which depend on non-trivial
graph-theoretic properties of the information feedback structure. We also
provide partially-matching lower bounds.
| [
"Shie Mannor and Ohad Shamir",
"['Shie Mannor' 'Ohad Shamir']"
] |
cs.LG cs.AI cs.GT cs.MA | 10.1109/MCOM.2011.5978427 | 1106.2662 | null | null | http://arxiv.org/abs/1106.2662v1 | 2011-06-14T09:58:36Z | 2011-06-14T09:58:36Z | Learning Equilibria with Partial Information in Decentralized Wireless
Networks | In this article, a survey of several important equilibrium concepts for
decentralized networks is presented. The term decentralized is used here to
refer to scenarios where decisions (e.g., choosing a power allocation policy)
are taken autonomously by devices interacting with each other (e.g., through
mutual interference). The iterative long-term interaction is characterized by
stable points of the wireless network called equilibria. The interest in these
equilibria stems from the relevance of network stability and the fact that they
can be achieved by letting radio devices to repeatedly interact over time. To
achieve these equilibria, several learning techniques, namely, the best
response dynamics, fictitious play, smoothed fictitious play, reinforcement
learning algorithms, and regret matching, are discussed in terms of information
requirements and convergence properties. Most of the notions introduced here,
for both equilibria and learning schemes, are illustrated by a simple case
study, namely, an interference channel with two transmitter-receiver pairs.
| [
"Luca Rose, Samir M. Perlaza, Samson Lasaulce, M\\'erouane Debbah",
"['Luca Rose' 'Samir M. Perlaza' 'Samson Lasaulce' 'Mérouane Debbah']"
] |
q-fin.GN cs.LG | null | 1106.2882 | null | null | http://arxiv.org/pdf/1106.2882v1 | 2011-06-15T06:04:25Z | 2011-06-15T06:04:25Z | Learning, investments and derivatives | The recent crisis and the following flight to simplicity put most derivative
businesses around the world under considerable pressure. We argue that the
traditional modeling techniques must be extended to include product design. We
propose a quantitative framework for creating products which meet the challenge
of being optimal from the investors point of view while remaining relatively
simple and transparent.
| [
"Andrei N. Soklakov",
"['Andrei N. Soklakov']"
] |
cs.LG | 10.1239/jap/1346955334 | 1106.3355 | null | null | http://arxiv.org/abs/1106.3355v2 | 2012-03-05T21:36:51Z | 2011-06-16T21:32:26Z | On epsilon-optimality of the pursuit learning algorithm | Estimator algorithms in learning automata are useful tools for adaptive,
real-time optimization in computer science and engineering applications. This
paper investigates theoretical convergence properties for a special case of
estimator algorithms: the pursuit learning algorithm. In this note, we identify
and fill a gap in existing proofs of probabilistic convergence for pursuit
learning. It is tradition to take the pursuit learning tuning parameter to be
fixed in practical applications, but our proof sheds light on the importance of
a vanishing sequence of tuning parameters in a theoretical convergence
analysis.
| [
"Ryan Martin, Omkar Tilak",
"['Ryan Martin' 'Omkar Tilak']"
] |
cs.LG | null | 1106.3395 | null | null | http://arxiv.org/pdf/1106.3395v1 | 2011-06-17T06:53:47Z | 2011-06-17T06:53:47Z | Decoding finger movements from ECoG signals using switching linear
models | One of the major challenges of ECoG-based Brain-Machine Interfaces is the
movement prediction of a human subject. Several methods exist to predict an arm
2-D trajectory. The fourth BCI Competition gives a dataset in which the aim is
to predict individual finger movements (5-D trajectory). The difficulty lies in
the fact that there is no simple relation between ECoG signals and finger
movement. We propose in this paper to decode finger flexions using switching
models. This method permits to simplify the system as it is now described as an
ensemble of linear models depending on an internal state. We show that an
interesting accuracy prediction can be obtained by such a model.
| [
"R\\'emi Flamary (LITIS), Alain Rakotomamonjy (LITIS)",
"['Rémi Flamary' 'Alain Rakotomamonjy']"
] |
cs.LG | 10.1109/ICASSP.2010.5495281 | 1106.3396 | null | null | http://arxiv.org/abs/1106.3396v1 | 2011-06-17T06:54:35Z | 2011-06-17T06:54:35Z | Large margin filtering for signal sequence labeling | Signal Sequence Labeling consists in predicting a sequence of labels given an
observed sequence of samples. A naive way is to filter the signal in order to
reduce the noise and to apply a classification algorithm on the filtered
samples. We propose in this paper to jointly learn the filter with the
classifier leading to a large margin filtering for classification. This method
allows to learn the optimal cutoff frequency and phase of the filter that may
be different from zero. Two methods are proposed and tested on a toy dataset
and on a real life BCI dataset from BCI Competition III.
| [
"['Rémi Flamary' 'Benjamin Labbé' 'Alain Rakotomamonjy']",
"R\\'emi Flamary (LITIS), Benjamin Labb\\'e (LITIS), Alain Rakotomamonjy\n (LITIS)"
] |
cs.LG | null | 1106.3397 | null | null | http://arxiv.org/pdf/1106.3397v1 | 2011-06-17T06:55:24Z | 2011-06-17T06:55:24Z | Handling uncertainties in SVM classification | This paper addresses the pattern classification problem arising when
available target data include some uncertainty information. Target data
considered here is either qualitative (a class label) or quantitative (an
estimation of the posterior probability). Our main contribution is a SVM
inspired formulation of this problem allowing to take into account class label
through a hinge loss as well as probability estimates using epsilon-insensitive
cost function together with a minimum norm (maximum margin) objective. This
formulation shows a dual form leading to a quadratic problem and allows the use
of a representer theorem and associated kernel. The solution provided can be
used for both decision and posterior probability estimation. Based on empirical
evidence our method outperforms regular SVM in terms of probability predictions
and classification performances.
| [
"Emilie Niaf (CREATIS), R\\'emi Flamary (LITIS), Carole Lartizien\n (CREATIS), St\\'ephane Canu (LITIS)",
"['Emilie Niaf' 'Rémi Flamary' 'Carole Lartizien' 'Stéphane Canu']"
] |
cs.LG stat.ML | null | 1106.3651 | null | null | http://arxiv.org/pdf/1106.3651v2 | 2011-11-11T14:14:12Z | 2011-06-18T14:39:58Z | Robust Bayesian reinforcement learning through tight lower bounds | In the Bayesian approach to sequential decision making, exact calculation of
the (subjective) utility is intractable. This extends to most special cases of
interest, such as reinforcement learning problems. While utility bounds are
known to exist for this problem, so far none of them were particularly tight.
In this paper, we show how to efficiently calculate a lower bound, which
corresponds to the utility of a near-optimal memoryless policy for the decision
problem, which is generally different from both the Bayes-optimal policy and
the policy which is optimal for the expected MDP under the current belief. We
then show how these can be applied to obtain robust exploration policies in a
Bayesian reinforcement learning setting.
| [
"['Christos Dimitrakakis']",
"Christos Dimitrakakis"
] |
nlin.AO cs.AI cs.IT cs.LG cs.SY math.IT q-bio.QM stat.ME | null | 1106.3703 | null | null | http://arxiv.org/pdf/1106.3703v2 | 2015-01-16T06:53:24Z | 2011-06-19T04:20:16Z | Prediction and Modularity in Dynamical Systems | Identifying and understanding modular organizations is centrally important in
the study of complex systems. Several approaches to this problem have been
advanced, many framed in information-theoretic terms. Our treatment starts from
the complementary point of view of statistical modeling and prediction of
dynamical systems. It is known that for finite amounts of training data,
simpler models can have greater predictive power than more complex ones. We use
the trade-off between model simplicity and predictive accuracy to generate
optimal multiscale decompositions of dynamical networks into weakly-coupled,
simple modules. State-dependent and causal versions of our method are also
proposed.
| [
"Artemy Kolchinsky, Luis M. Rocha",
"['Artemy Kolchinsky' 'Luis M. Rocha']"
] |
cs.DB cs.LG | null | 1106.3725 | null | null | http://arxiv.org/pdf/1106.3725v3 | 2012-04-20T20:28:35Z | 2011-06-19T09:29:54Z | Learning XML Twig Queries | We investigate the problem of learning XML queries, path queries and tree
pattern queries, from examples given by the user. A learning algorithm takes on
the input a set of XML documents with nodes annotated by the user and returns a
query that selects the nodes in a manner consistent with the annotation. We
study two learning settings that differ with the types of annotations. In the
first setting the user may only indicate required nodes that the query must
return. In the second, more general, setting, the user may also indicate
forbidden nodes that the query must not return. The query may or may not return
any node with no annotation. We formalize what it means for a class of queries
to be \emph{learnable}. One requirement is the existence of a learning
algorithm that is sound i.e., always returns a query consistent with the
examples given by the user. Furthermore, the learning algorithm should be
complete i.e., able to produce every query with a sufficiently rich example.
Other requirements involve tractability of learning and its robustness to
nonessential examples. We show that the classes of simple path queries and
path-subsumption-free tree queries are learnable from positive examples. The
learnability of the full class of tree pattern queries (and the full class of
path queries) remains an open question. We show also that adding negative
examples to the picture renders the learning unfeasible.
Published in ICDT 2012, Berlin.
| [
"S{\\l}awomir Staworko, Piotr Wieczorek",
"['Sławomir Staworko' 'Piotr Wieczorek']"
] |
cs.LG | null | 1106.4064 | null | null | http://arxiv.org/pdf/1106.4064v2 | 2011-11-09T19:45:30Z | 2011-06-21T00:37:23Z | Algorithmic Programming Language Identification | Motivated by the amount of code that goes unidentified on the web, we
introduce a practical method for algorithmically identifying the programming
language of source code. Our work is based on supervised learning and
intelligent statistical features. We also explored, but abandoned, a
grammatical approach. In testing, our implementation greatly outperforms that
of an existing tool that relies on a Bayesian classifier. Code is written in
Python and available under an MIT license.
| [
"David Klein, Kyle Murray and Simon Weber",
"['David Klein' 'Kyle Murray' 'Simon Weber']"
] |
math.FA cs.LG | null | 1106.4075 | null | null | http://arxiv.org/pdf/1106.4075v1 | 2011-06-21T02:49:12Z | 2011-06-21T02:49:12Z | On the Inclusion Relation of Reproducing Kernel Hilbert Spaces | To help understand various reproducing kernels used in applied sciences, we
investigate the inclusion relation of two reproducing kernel Hilbert spaces.
Characterizations in terms of feature maps of the corresponding reproducing
kernels are established. A full table of inclusion relations among widely-used
translation invariant kernels is given. Concrete examples for Hilbert-Schmidt
kernels are presented as well. We also discuss the preservation of such a
relation under various operations of reproducing kernels. Finally, we briefly
discuss the special inclusion with a norm equivalence.
| [
"['Haizhang Zhang' 'Liang Zhao']",
"Haizhang Zhang, Liang Zhao"
] |
cs.LG stat.ML | null | 1106.4251 | null | null | http://arxiv.org/pdf/1106.4251v1 | 2011-06-21T16:16:24Z | 2011-06-21T16:16:24Z | Learning with the Weighted Trace-norm under Arbitrary Sampling
Distributions | We provide rigorous guarantees on learning with the weighted trace-norm under
arbitrary sampling distributions. We show that the standard weighted trace-norm
might fail when the sampling distribution is not a product distribution (i.e.
when row and column indexes are not selected independently), present a
corrected variant for which we establish strong learning guarantees, and
demonstrate that it works better in practice. We provide guarantees when
weighting by either the true or empirical sampling distribution, and suggest
that even if the true distribution is known (or is uniform), weighting by the
empirical distribution may be beneficial.
| [
"Rina Foygel, Ruslan Salakhutdinov, Ohad Shamir, and Nathan Srebro",
"['Rina Foygel' 'Ruslan Salakhutdinov' 'Ohad Shamir' 'Nathan Srebro']"
] |
stat.ML cs.LG | null | 1106.4355 | null | null | http://arxiv.org/pdf/1106.4355v3 | 2011-10-18T02:16:55Z | 2011-06-22T00:45:59Z | Tight Measurement Bounds for Exact Recovery of Structured Sparse Signals | Standard compressive sensing results state that to exactly recover an s
sparse signal in R^p, one requires O(s. log(p)) measurements. While this bound
is extremely useful in practice, often real world signals are not only sparse,
but also exhibit structure in the sparsity pattern. We focus on
group-structured patterns in this paper. Under this model, groups of signal
coefficients are active (or inactive) together. The groups are predefined, but
the particular set of groups that are active (i.e., in the signal support) must
be learned from measurements. We show that exploiting knowledge of groups can
further reduce the number of measurements required for exact signal recovery,
and derive universal bounds for the number of measurements needed. The bound is
universal in the sense that it only depends on the number of groups under
consideration, and not the particulars of the groups (e.g., compositions,
sizes, extents, overlaps, etc.). Experiments show that our result holds for a
variety of overlapping group configurations.
| [
"['Nikhil Rao' 'Benjamin Recht' 'Robert Nowak']",
"Nikhil Rao, Benjamin Recht and Robert Nowak"
] |
cs.AI cs.LG | 10.1613/jair.1050 | 1106.4572 | null | null | http://arxiv.org/abs/1106.4572v1 | 2011-06-22T20:58:18Z | 2011-06-22T20:58:18Z | Specific-to-General Learning for Temporal Events with Application to
Learning Event Definitions from Video | We develop, analyze, and evaluate a novel, supervised, specific-to-general
learner for a simple temporal logic and use the resulting algorithm to learn
visual event definitions from video sequences. First, we introduce a simple,
propositional, temporal, event-description language called AMA that is
sufficiently expressive to represent many events yet sufficiently restrictive
to support learning. We then give algorithms, along with lower and upper
complexity bounds, for the subsumption and generalization problems for AMA
formulas. We present a positive-examples--only specific-to-general learning
method based on these algorithms. We also present a polynomial-time--computable
``syntactic'' subsumption test that implies semantic subsumption without being
equivalent to it. A generalization algorithm based on syntactic subsumption can
be used in place of semantic generalization to improve the asymptotic
complexity of the resulting learning algorithm. Finally, we apply this
algorithm to the task of learning relational event definitions from video and
show that it yields definitions that are competitive with hand-coded ones.
| [
"A. Fern, R. Givan, J. M. Siskind",
"['A. Fern' 'R. Givan' 'J. M. Siskind']"
] |
cs.LG | null | 1106.4574 | null | null | http://arxiv.org/pdf/1106.4574v1 | 2011-06-22T20:59:20Z | 2011-06-22T20:59:20Z | Better Mini-Batch Algorithms via Accelerated Gradient Methods | Mini-batch algorithms have been proposed as a way to speed-up stochastic
convex optimization problems. We study how such algorithms can be improved
using accelerated gradient methods. We provide a novel analysis, which shows
how standard gradient methods may sometimes be insufficient to obtain a
significant speed-up and propose a novel accelerated gradient algorithm, which
deals with this deficiency, enjoys a uniformly superior guarantee and works
well in practice.
| [
"Andrew Cotter, Ohad Shamir, Nathan Srebro, Karthik Sridharan",
"['Andrew Cotter' 'Ohad Shamir' 'Nathan Srebro' 'Karthik Sridharan']"
] |
cs.LG stat.ML | null | 1106.5236 | null | null | http://arxiv.org/pdf/1106.5236v1 | 2011-06-26T17:03:44Z | 2011-06-26T17:03:44Z | A General Framework for Structured Sparsity via Proximal Optimization | We study a generalized framework for structured sparsity. It extends the
well-known methods of Lasso and Group Lasso by incorporating additional
constraints on the variables as part of a convex optimization problem. This
framework provides a straightforward way of favouring prescribed sparsity
patterns, such as orderings, contiguous regions and overlapping groups, among
others. Existing optimization methods are limited to specific constraint sets
and tend to not scale well with sample size and dimensionality. We propose a
novel first order proximal method, which builds upon results on fixed points
and successive approximations. The algorithm can be applied to a general class
of conic and norm constraints sets and relies on a proximity operator
subproblem which can be computed explicitly. Experiments on different
regression problems demonstrate the efficiency of the optimization algorithm
and its scalability with the size of the problem. They also demonstrate state
of the art statistical performance, which improves over Lasso and StructOMP.
| [
"Andreas Argyriou and Luca Baldassarre and Jean Morales and\n Massimiliano Pontil",
"['Andreas Argyriou' 'Luca Baldassarre' 'Jean Morales'\n 'Massimiliano Pontil']"
] |
cs.LG | 10.1613/jair.1190 | 1106.5267 | null | null | http://arxiv.org/abs/1106.5267v1 | 2011-06-26T21:07:01Z | 2011-06-26T21:07:01Z | Potential-Based Shaping and Q-Value Initialization are Equivalent | Shaping has proven to be a powerful but precarious means of improving
reinforcement learning performance. Ng, Harada, and Russell (1999) proposed the
potential-based shaping algorithm for adding shaping rewards in a way that
guarantees the learner will learn optimal behavior. In this note, we prove
certain similarities between this shaping algorithm and the initialization step
required for several reinforcement learning algorithms. More specifically, we
prove that a reinforcement learner with initial Q-values based on the shaping
algorithm's potential function make the same updates throughout learning as a
learner receiving potential-based shaping rewards. We further prove that under
a broad category of policies, the behavior of these two learners are
indistinguishable. The comparison provides intuition on the theoretical
properties of the shaping algorithm as well as a suggestion for a simpler
method for capturing the algorithm's benefit. In addition, the equivalence
raises previously unaddressed issues concerning the efficiency of learning with
potential-based shaping.
| [
"['E. Wiewiora']",
"E. Wiewiora"
] |
cs.LO cs.GT cs.LG | null | 1106.5294 | null | null | http://arxiv.org/pdf/1106.5294v1 | 2011-06-27T04:55:23Z | 2011-06-27T04:55:23Z | Set systems: order types, continuous nondeterministic deformations, and
quasi-orders | By reformulating a learning process of a set system L as a game between
Teacher and Learner, we define the order type of L to be the order type of the
game tree, if the tree is well-founded. The features of the order type of L
(dim L in symbol) are (1) We can represent any well-quasi-order (wqo for short)
by the set system L of the upper-closed sets of the wqo such that the maximal
order type of the wqo is equal to dim L. (2) dim L is an upper bound of the
mind-change complexity of L. dim L is defined iff L has a finite elasticity (fe
for short), where, according to computational learning theory, if an indexed
family of recursive languages has fe then it is learnable by an algorithm from
positive data. Regarding set systems as subspaces of Cantor spaces, we prove
that fe of set systems is preserved by any continuous function which is
monotone with respect to the set-inclusion. By it, we prove that finite
elasticity is preserved by various (nondeterministic) language operators
(Kleene-closure, shuffle-closure, union, product, intersection,. . ..) The
monotone continuous functions represent nondeterministic computations. If a
monotone continuous function has a computation tree with each node followed by
at most n immediate successors and the order type of a set system L is
{\alpha}, then the direct image of L is a set system of order type at most
n-adic diagonal Ramsey number of {\alpha}. Furthermore, we provide an
order-type-preserving contravariant embedding from the category of quasi-orders
and finitely branching simulations between them, into the complete category of
subspaces of Cantor spaces and monotone continuous functions having Girard's
linearity between them. Keyword: finite elasticity, shuffle-closure
| [
"Yohji Akama",
"['Yohji Akama']"
] |
cs.CV cs.AI cs.LG | null | 1106.5341 | null | null | http://arxiv.org/pdf/1106.5341v1 | 2011-06-27T09:47:28Z | 2011-06-27T09:47:28Z | Pose Estimation from a Single Depth Image for Arbitrary Kinematic
Skeletons | We present a method for estimating pose information from a single depth image
given an arbitrary kinematic structure without prior training. For an arbitrary
skeleton and depth image, an evolutionary algorithm is used to find the optimal
kinematic configuration to explain the observed image. Results show that our
approach can correctly estimate poses of 39 and 78 degree-of-freedom models
from a single depth image, even in cases of significant self-occlusion.
| [
"Daniel L. Ly and Ashutosh Saxena and Hod Lipson",
"['Daniel L. Ly' 'Ashutosh Saxena' 'Hod Lipson']"
] |
math.OC cs.LG | null | 1106.5730 | null | null | http://arxiv.org/pdf/1106.5730v2 | 2011-11-11T15:59:15Z | 2011-06-28T17:23:42Z | HOGWILD!: A Lock-Free Approach to Parallelizing Stochastic Gradient
Descent | Stochastic Gradient Descent (SGD) is a popular algorithm that can achieve
state-of-the-art performance on a variety of machine learning tasks. Several
researchers have recently proposed schemes to parallelize SGD, but all require
performance-destroying memory locking and synchronization. This work aims to
show using novel theoretical analysis, algorithms, and implementation that SGD
can be implemented without any locking. We present an update scheme called
HOGWILD! which allows processors access to shared memory with the possibility
of overwriting each other's work. We show that when the associated optimization
problem is sparse, meaning most gradient updates only modify small parts of the
decision variable, then HOGWILD! achieves a nearly optimal rate of convergence.
We demonstrate experimentally that HOGWILD! outperforms alternative schemes
that use locking by an order of magnitude.
| [
"Feng Niu, Benjamin Recht, Christopher Re, Stephen J. Wright",
"['Feng Niu' 'Benjamin Recht' 'Christopher Re' 'Stephen J. Wright']"
] |
cs.LG math.ST stat.ML stat.TH | null | 1106.5826 | null | null | http://arxiv.org/pdf/1106.5826v1 | 2011-06-29T00:53:15Z | 2011-06-29T00:53:15Z | A Dirty Model for Multiple Sparse Regression | Sparse linear regression -- finding an unknown vector from linear
measurements -- is now known to be possible with fewer samples than variables,
via methods like the LASSO. We consider the multiple sparse linear regression
problem, where several related vectors -- with partially shared support sets --
have to be recovered. A natural question in this setting is whether one can use
the sharing to further decrease the overall number of samples required. A line
of recent research has studied the use of \ell_1/\ell_q norm
block-regularizations with q>1 for such problems; however these could actually
perform worse in sample complexity -- vis a vis solving each problem separately
ignoring sharing -- depending on the level of sharing.
We present a new method for multiple sparse linear regression that can
leverage support and parameter overlap when it exists, but not pay a penalty
when it does not. A very simple idea: we decompose the parameters into two
components and regularize these differently. We show both theoretically and
empirically, our method strictly and noticeably outperforms both \ell_1 or
\ell_1/\ell_q methods, over the entire range of possible overlaps (except at
boundary cases, where we match the best method). We also provide theoretical
guarantees that the method performs well under high-dimensional scaling.
| [
"Ali Jalali and Pradeep Ravikumar and Sujay Sanghavi",
"['Ali Jalali' 'Pradeep Ravikumar' 'Sujay Sanghavi']"
] |
math.OC cs.LG cs.SY math.PR math.ST stat.TH | null | 1106.6104 | null | null | http://arxiv.org/pdf/1106.6104v3 | 2013-03-09T20:17:17Z | 2011-06-30T02:12:32Z | Deterministic Sequencing of Exploration and Exploitation for Multi-Armed
Bandit Problems | In the Multi-Armed Bandit (MAB) problem, there is a given set of arms with
unknown reward models. At each time, a player selects one arm to play, aiming
to maximize the total expected reward over a horizon of length T. An approach
based on a Deterministic Sequencing of Exploration and Exploitation (DSEE) is
developed for constructing sequential arm selection policies. It is shown that
for all light-tailed reward distributions, DSEE achieves the optimal
logarithmic order of the regret, where regret is defined as the total expected
reward loss against the ideal case with known reward models. For heavy-tailed
reward distributions, DSEE achieves O(T^1/p) regret when the moments of the
reward distributions exist up to the pth order for 1<p<=2 and O(T^1/(1+p/2))
for p>2. With the knowledge of an upperbound on a finite moment of the
heavy-tailed reward distributions, DSEE offers the optimal logarithmic regret
order. The proposed DSEE approach complements existing work on MAB by providing
corresponding results for general reward distributions. Furthermore, with a
clearly defined tunable parameter-the cardinality of the exploration sequence,
the DSEE approach is easily extendable to variations of MAB, including MAB with
various objectives, decentralized MAB with multiple players and incomplete
reward observations under collisions, MAB with unknown Markov dynamics, and
combinatorial MAB with dependent arms that often arise in network optimization
problems such as the shortest path, the minimum spanning, and the dominating
set problems under unknown random weights.
| [
"Sattar Vakili, Keqin Liu, Qing Zhao",
"['Sattar Vakili' 'Keqin Liu' 'Qing Zhao']"
] |
cs.LG | null | 1106.6186 | null | null | http://arxiv.org/pdf/1106.6186v1 | 2011-06-30T11:08:35Z | 2011-06-30T11:08:35Z | IBSEAD: - A Self-Evolving Self-Obsessed Learning Algorithm for Machine
Learning | We present IBSEAD or distributed autonomous entity systems based Interaction
- a learning algorithm for the computer to self-evolve in a self-obsessed
manner. This learning algorithm will present the computer to look at the
internal and external environment in series of independent entities, which will
interact with each other, with and/or without knowledge of the computer's
brain. When a learning algorithm interacts, it does so by detecting and
understanding the entities in the human algorithm. However, the problem with
this approach is that the algorithm does not consider the interaction of the
third party or unknown entities, which may be interacting with each other.
These unknown entities in their interaction with the non-computer entities make
an effect in the environment that influences the information and the behaviour
of the computer brain. Such details and the ability to process the dynamic and
unsettling nature of these interactions are absent in the current learning
algorithm such as the decision tree learning algorithm. IBSEAD is able to
evaluate and consider such algorithms and thus give us a better accuracy in
simulation of the highly evolved nature of the human brain. Processes such as
dreams, imagination and novelty, that exist in humans are not fully simulated
by the existing learning algorithms. Also, Hidden Markov models (HMM) are
useful in finding "hidden" entities, which may be known or unknown. However,
this model fails to consider the case of unknown entities which maybe unclear
or unknown. IBSEAD is better because it considers three types of entities-
known, unknown and invisible. We present our case with a comparison of existing
algorithms in known environments and cases and present the results of the
experiments using dry run of the simulated runs of the existing machine
learning algorithms versus IBSEAD.
| [
"Jitesh Dundas and David Chik",
"['Jitesh Dundas' 'David Chik']"
] |
cs.LG | null | 1106.6258 | null | null | http://arxiv.org/pdf/1106.6258v2 | 2014-05-12T19:40:40Z | 2011-06-30T15:03:58Z | A Note on Improved Loss Bounds for Multiple Kernel Learning | In this paper, we correct an upper bound, presented in~\cite{hs-11}, on the
generalisation error of classifiers learned through multiple kernel learning.
The bound in~\cite{hs-11} uses Rademacher complexity and has an\emph{additive}
dependence on the logarithm of the number of kernels and the margin achieved by
the classifier. However, there are some errors in parts of the proof which are
corrected in this paper. Unfortunately, the final result turns out to be a risk
bound which has a \emph{multiplicative} dependence on the logarithm of the
number of kernels and the margin achieved by the classifier.
| [
"Zakria Hussain and John Shawe-Taylor and Mario Marchand",
"['Zakria Hussain' 'John Shawe-Taylor' 'Mario Marchand']"
] |
cs.AI cs.FL cs.LG | null | 1107.0434 | null | null | http://arxiv.org/pdf/1107.0434v1 | 2011-07-03T07:33:51Z | 2011-07-03T07:33:51Z | Abstraction Super-structuring Normal Forms: Towards a Theory of
Structural Induction | Induction is the process by which we obtain predictive laws or theories or
models of the world. We consider the structural aspect of induction. We answer
the question as to whether we can find a finite and minmalistic set of
operations on structural elements in terms of which any theory can be
expressed. We identify abstraction (grouping similar entities) and
super-structuring (combining topologically e.g., spatio-temporally close
entities) as the essential structural operations in the induction process. We
show that only two more structural operations, namely, reverse abstraction and
reverse super-structuring (the duals of abstraction and super-structuring
respectively) suffice in order to exploit the full power of Turing-equivalent
generative grammars in induction. We explore the implications of this theorem
with respect to the nature of hidden variables, radical positivism and the
2-century old claim of David Hume about the principles of connexion among
ideas.
| [
"Adrian Silvescu and Vasant Honavar",
"['Adrian Silvescu' 'Vasant Honavar']"
] |
nlin.AO cs.LG | null | 1107.0674 | null | null | http://arxiv.org/pdf/1107.0674v3 | 2015-10-07T13:57:56Z | 2011-07-04T16:18:04Z | "Memory foam" approach to unsupervised learning | We propose an alternative approach to construct an artificial learning
system, which naturally learns in an unsupervised manner. Its mathematical
prototype is a dynamical system, which automatically shapes its vector field in
response to the input signal. The vector field converges to a gradient of a
multi-dimensional probability density distribution of the input process, taken
with negative sign. The most probable patterns are represented by the stable
fixed points, whose basins of attraction are formed automatically. The
performance of this system is illustrated with musical signals.
| [
"Natalia B. Janson and Christopher J. Marsden",
"['Natalia B. Janson' 'Christopher J. Marsden']"
] |
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