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A new order theory of set systems and better quasi-orderings | math.CO cs.LG | By reformulating a learning process of a set system L as a game between
Teacher (presenter of data) and Learner (updater of the abstract independent
set), we define the order type dim L of L to be the order type of the game
tree. The theory of this new order type and continuous, monotone function
between set systems corresponds to the theory of well quasi-orderings (WQOs).
As Nash-Williams developed the theory of WQOs to the theory of better
quasi-orderings (BQOs), we introduce a set system that has order type and
corresponds to a BQO. We prove that the class of set systems corresponding to
BQOs is closed by any monotone function. In (Shinohara and Arimura. "Inductive
inference of unbounded unions of pattern languages from positive data."
Theoretical Computer Science, pp. 191-209, 2000), for any set system L, they
considered the class of arbitrary (finite) unions of members of L. From
viewpoint of WQOs and BQOs, we characterize the set systems L such that the
class of arbitrary (finite) unions of members of L has order type. The
characterization shows that the order structure of the set system L with
respect to the set-inclusion is not important for the resulting set system
having order type. We point out continuous, monotone function of set systems is
similar to positive reduction to Jockusch-Owings' weakly semirecursive sets.
| Yohji Akama | null | 1112.2801 | null | null |
Analysis and Extension of Arc-Cosine Kernels for Large Margin
Classification | cs.LG | We investigate a recently proposed family of positive-definite kernels that
mimic the computation in large neural networks. We examine the properties of
these kernels using tools from differential geometry; specifically, we analyze
the geometry of surfaces in Hilbert space that are induced by these kernels.
When this geometry is described by a Riemannian manifold, we derive results for
the metric, curvature, and volume element. Interestingly, though, we find that
the simplest kernel in this family does not admit such an interpretation. We
explore two variations of these kernels that mimic computation in neural
networks with different activation functions. We experiment with these new
kernels on several data sets and highlight their general trends in performance
for classification.
| Youngmin Cho and Lawrence K. Saul | null | 1112.3712 | null | null |
Nonnegative Matrix Factorization for Semi-supervised Dimensionality
Reduction | cs.LG | We show how to incorporate information from labeled examples into nonnegative
matrix factorization (NMF), a popular unsupervised learning algorithm for
dimensionality reduction. In addition to mapping the data into a space of lower
dimensionality, our approach aims to preserve the nonnegative components of the
data that are important for classification. We identify these components from
the support vectors of large-margin classifiers and derive iterative updates to
preserve them in a semi-supervised version of NMF. These updates have a simple
multiplicative form like their unsupervised counterparts; they are also
guaranteed at each iteration to decrease their loss function---a weighted sum
of I-divergences that captures the trade-off between unsupervised and
supervised learning. We evaluate these updates for dimensionality reduction
when they are used as a precursor to linear classification. In this role, we
find that they yield much better performance than their unsupervised
counterparts. We also find one unexpected benefit of the low dimensional
representations discovered by our approach: often they yield more accurate
classifiers than both ordinary and transductive SVMs trained in the original
input space.
| Youngmin Cho and Lawrence K. Saul | null | 1112.3714 | null | null |
Strongly Convex Programming for Exact Matrix Completion and Robust
Principal Component Analysis | cs.IT cs.LG math.IT | The common task in matrix completion (MC) and robust principle component
analysis (RPCA) is to recover a low-rank matrix from a given data matrix. These
problems gained great attention from various areas in applied sciences
recently, especially after the publication of the pioneering works of Cand`es
et al.. One fundamental result in MC and RPCA is that nuclear norm based convex
optimizations lead to the exact low-rank matrix recovery under suitable
conditions. In this paper, we extend this result by showing that strongly
convex optimizations can guarantee the exact low-rank matrix recovery as well.
The result in this paper not only provides sufficient conditions under which
the strongly convex models lead to the exact low-rank matrix recovery, but also
guides us on how to choose suitable parameters in practical algorithms.
| Hui Zhang, Jian-Feng Cai, Lizhi Cheng, Jubo Zhu | null | 1112.3946 | null | null |
Clustering and Latent Semantic Indexing Aspects of the Nonnegative
Matrix Factorization | cs.LG | This paper provides a theoretical support for clustering aspect of the
nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker
optimality conditions, we show that NMF objective is equivalent to graph
clustering objective, so clustering aspect of the NMF has a solid
justification. Different from previous approaches which usually discard the
nonnegativity constraints, our approach guarantees the stationary point being
used in deriving the equivalence is located on the feasible region in the
nonnegative orthant. Additionally, since clustering capability of a matrix
decomposition technique can sometimes imply its latent semantic indexing (LSI)
aspect, we will also evaluate LSI aspect of the NMF by showing its capability
in solving the synonymy and polysemy problems in synthetic datasets. And more
extensive evaluation will be conducted by comparing LSI performances of the NMF
and the singular value decomposition (SVD), the standard LSI method, using some
standard datasets.
| Andri Mirzal | null | 1112.4020 | null | null |
epsilon-Samples of Kernels | cs.CG cs.DS cs.LG | We study the worst case error of kernel density estimates via subset
approximation. A kernel density estimate of a distribution is the convolution
of that distribution with a fixed kernel (e.g. Gaussian kernel). Given a subset
(i.e. a point set) of the input distribution, we can compare the kernel density
estimates of the input distribution with that of the subset and bound the worst
case error. If the maximum error is eps, then this subset can be thought of as
an eps-sample (aka an eps-approximation) of the range space defined with the
input distribution as the ground set and the fixed kernel representing the
family of ranges. Interestingly, in this case the ranges are not binary, but
have a continuous range (for simplicity we focus on kernels with range of
[0,1]); these allow for smoother notions of range spaces.
It turns out, the use of this smoother family of range spaces has an added
benefit of greatly decreasing the size required for eps-samples. For instance,
in the plane the size is O((1/eps^{4/3}) log^{2/3}(1/eps)) for disks (based on
VC-dimension arguments) but is only O((1/eps) sqrt{log (1/eps)}) for Gaussian
kernels and for kernels with bounded slope that only affect a bounded domain.
These bounds are accomplished by studying the discrepancy of these "kernel"
range spaces, and here the improvement in bounds are even more pronounced. In
the plane, we show the discrepancy is O(sqrt{log n}) for these kernels, whereas
for balls there is a lower bound of Omega(n^{1/4}).
| Jeff M. Phillips | null | 1112.4105 | null | null |
Evaluation of Performance Measures for Classifiers Comparison | cs.LG | The selection of the best classification algorithm for a given dataset is a
very widespread problem, occuring each time one has to choose a classifier to
solve a real-world problem. It is also a complex task with many important
methodological decisions to make. Among those, one of the most crucial is the
choice of an appropriate measure in order to properly assess the classification
performance and rank the algorithms. In this article, we focus on this specific
task. We present the most popular measures and compare their behavior through
discrimination plots. We then discuss their properties from a more theoretical
perspective. It turns out several of them are equivalent for classifiers
comparison purposes. Futhermore. they can also lead to interpretation problems.
Among the numerous measures proposed over the years, it appears that the
classical overall success rate and marginal rates are the more suitable for
classifier comparison task.
| Vincent Labatut, Hocine Cherifi (Le2i) | null | 1112.4133 | null | null |
Online Learning for Classification of Low-rank Representation Features
and Its Applications in Audio Segment Classification | cs.LG cs.MM | In this paper, a novel framework based on trace norm minimization for audio
segment is proposed. In this framework, both the feature extraction and
classification are obtained by solving corresponding convex optimization
problem with trace norm regularization. For feature extraction, robust
principle component analysis (robust PCA) via minimization a combination of the
nuclear norm and the $\ell_1$-norm is used to extract low-rank features which
are robust to white noise and gross corruption for audio segments. These
low-rank features are fed to a linear classifier where the weight and bias are
learned by solving similar trace norm constrained problems. For this
classifier, most methods find the weight and bias in batch-mode learning, which
makes them inefficient for large-scale problems. In this paper, we propose an
online framework using accelerated proximal gradient method. This framework has
a main advantage in memory cost. In addition, as a result of the regularization
formulation of matrix classification, the Lipschitz constant was given
explicitly, and hence the step size estimation of general proximal gradient
method was omitted in our approach. Experiments on real data sets for
laugh/non-laugh and applause/non-applause classification indicate that this
novel framework is effective and noise robust.
| Ziqiang Shi and Jiqing Han and Tieran Zheng and Shiwen Deng | null | 1112.4243 | null | null |
A geometric analysis of subspace clustering with outliers | cs.IT cs.LG math.IT math.ST stat.ML stat.TH | This paper considers the problem of clustering a collection of unlabeled data
points assumed to lie near a union of lower-dimensional planes. As is common in
computer vision or unsupervised learning applications, we do not know in
advance how many subspaces there are nor do we have any information about their
dimensions. We develop a novel geometric analysis of an algorithm named sparse
subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern
Recognition, 2009. CVPR 2009 (2009) 2790-2797. IEEE], which significantly
broadens the range of problems where it is provably effective. For instance, we
show that SSC can recover multiple subspaces, each of dimension comparable to
the ambient dimension. We also prove that SSC can correctly cluster data points
even when the subspaces of interest intersect. Further, we develop an extension
of SSC that succeeds when the data set is corrupted with possibly
overwhelmingly many outliers. Underlying our analysis are clear geometric
insights, which may bear on other sparse recovery problems. A numerical study
complements our theoretical analysis and demonstrates the effectiveness of
these methods.
| Mahdi Soltanolkotabi, Emmanuel J. Cand\'es | 10.1214/12-AOS1034 | 1112.4258 | null | null |
Performance Analysis of Enhanced Clustering Algorithm for Gene
Expression Data | cs.LG cs.CE cs.DB | Microarrays are made it possible to simultaneously monitor the expression
profiles of thousands of genes under various experimental conditions. It is
used to identify the co-expressed genes in specific cells or tissues that are
actively used to make proteins. This method is used to analysis the gene
expression, an important task in bioinformatics research. Cluster analysis of
gene expression data has proved to be a useful tool for identifying
co-expressed genes, biologically relevant groupings of genes and samples. In
this paper we applied K-Means with Automatic Generations of Merge Factor for
ISODATA- AGMFI. Though AGMFI has been applied for clustering of Gene Expression
Data, this proposed Enhanced Automatic Generations of Merge Factor for ISODATA-
EAGMFI Algorithms overcome the drawbacks of AGMFI in terms of specifying the
optimal number of clusters and initialization of good cluster centroids.
Experimental results on Gene Expression Data show that the proposed EAGMFI
algorithms could identify compact clusters with perform well in terms of the
Silhouette Coefficients cluster measure.
| T.Chandrasekhar, K.Thangavel and E.Elayaraja | null | 1112.4261 | null | null |
A Scalable Multiclass Algorithm for Node Classification | cs.LG cs.GT | We introduce a scalable algorithm, MUCCA, for multiclass node classification
in weighted graphs. Unlike previously proposed methods for the same task, MUCCA
works in time linear in the number of nodes. Our approach is based on a
game-theoretic formulation of the problem in which the test labels are
expressed as a Nash Equilibrium of a certain game. However, in order to achieve
scalability, we find the equilibrium on a spanning tree of the original graph.
Experiments on real-world data reveal that MUCCA is much faster than its
competitors while achieving a similar predictive performance.
| Giovanni Zappella | null | 1112.4344 | null | null |
Additive Gaussian Processes | stat.ML cs.LG | We introduce a Gaussian process model of functions which are additive. An
additive function is one which decomposes into a sum of low-dimensional
functions, each depending on only a subset of the input variables. Additive GPs
generalize both Generalized Additive Models, and the standard GP models which
use squared-exponential kernels. Hyperparameter learning in this model can be
seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive
but tractable parameterization of the kernel function, which allows efficient
evaluation of all input interaction terms, whose number is exponential in the
input dimension. The additional structure discoverable by this model results in
increased interpretability, as well as state-of-the-art predictive power in
regression tasks.
| David Duvenaud, Hannes Nickisch, Carl Edward Rasmussen | null | 1112.4394 | null | null |
Alignment Based Kernel Learning with a Continuous Set of Base Kernels | cs.LG stat.ML | The success of kernel-based learning methods depend on the choice of kernel.
Recently, kernel learning methods have been proposed that use data to select
the most appropriate kernel, usually by combining a set of base kernels. We
introduce a new algorithm for kernel learning that combines a {\em continuous
set of base kernels}, without the common step of discretizing the space of base
kernels. We demonstrate that our new method achieves state-of-the-art
performance across a variety of real-world datasets. Furthermore, we explicitly
demonstrate the importance of combining the right dictionary of kernels, which
is problematic for methods based on a finite set of base kernels chosen a
priori. Our method is not the first approach to work with continuously
parameterized kernels. However, we show that our method requires substantially
less computation than previous such approaches, and so is more amenable to
multiple dimensional parameterizations of base kernels, which we demonstrate.
| Arash Afkanpour and Csaba Szepesvari and Michael Bowling | null | 1112.4607 | null | null |
Using Artificial Bee Colony Algorithm for MLP Training on Earthquake
Time Series Data Prediction | cs.NE cs.AI cs.LG | Nowadays, computer scientists have shown the interest in the study of social
insect's behaviour in neural networks area for solving different combinatorial
and statistical problems. Chief among these is the Artificial Bee Colony (ABC)
algorithm. This paper investigates the use of ABC algorithm that simulates the
intelligent foraging behaviour of a honey bee swarm. Multilayer Perceptron
(MLP) trained with the standard back propagation algorithm normally utilises
computationally intensive training algorithms. One of the crucial problems with
the backpropagation (BP) algorithm is that it can sometimes yield the networks
with suboptimal weights because of the presence of many local optima in the
solution space. To overcome ABC algorithm used in this work to train MLP
learning the complex behaviour of earthquake time series data trained by BP,
the performance of MLP-ABC is benchmarked against MLP training with the
standard BP. The experimental result shows that MLP-ABC performance is better
than MLP-BP for time series data.
| Habib Shah, Rozaida Ghazali, and Nazri Mohd Nawi | null | 1112.4628 | null | null |
Modeling transition dynamics in MDPs with RKHS embeddings of conditional
distributions | cs.LG | We propose a new, nonparametric approach to estimating the value function in
reinforcement learning. This approach makes use of a recently developed
representation of conditional distributions as functions in a reproducing
kernel Hilbert space. Such representations bypass the need for estimating
transition probabilities, and apply to any domain on which kernels can be
defined. Our approach avoids the need to approximate intractable integrals
since expectations are represented as RKHS inner products whose computation has
linear complexity in the sample size. Thus, we can efficiently perform value
function estimation in a wide variety of settings, including finite state
spaces, continuous states spaces, and partially observable tasks where only
sensor measurements are available. A second advantage of the approach is that
we learn the conditional distribution representation from a training sample,
and do not require an exhaustive exploration of the state space. We prove
convergence of our approach either to the optimal policy, or to the closest
projection of the optimal policy in our model class, under reasonable
assumptions. In experiments, we demonstrate the performance of our algorithm on
a learning task in a continuous state space (the under-actuated pendulum), and
on a navigation problem where only images from a sensor are observed. We
compare with least-squares policy iteration where a Gaussian process is used
for value function estimation. Our algorithm achieves better performance in
both tasks.
| Steffen Gr\"unew\"alder, Luca Baldassarre, Massimiliano Pontil, Arthur
Gretton, Guy Lever | null | 1112.4722 | null | null |
Combining One-Class Classifiers via Meta-Learning | cs.LG | Selecting the best classifier among the available ones is a difficult task,
especially when only instances of one class exist. In this work we examine the
notion of combining one-class classifiers as an alternative for selecting the
best classifier. In particular, we propose two new one-class classification
performance measures to weigh classifiers and show that a simple ensemble that
implements these measures can outperform the most popular one-class ensembles.
Furthermore, we propose a new one-class ensemble scheme, TUPSO, which uses
meta-learning to combine one-class classifiers. Our experiments demonstrate the
superiority of TUPSO over all other tested ensembles and show that the TUPSO
performance is statistically indistinguishable from that of the hypothetical
best classifier.
| Eitan Menahem, Lior Rokach and Yuval Elovici | null | 1112.5246 | null | null |
POWERPLAY: Training an Increasingly General Problem Solver by
Continually Searching for the Simplest Still Unsolvable Problem | cs.AI cs.LG | Most of computer science focuses on automatically solving given computational
problems. I focus on automatically inventing or discovering problems in a way
inspired by the playful behavior of animals and humans, to train a more and
more general problem solver from scratch in an unsupervised fashion. Consider
the infinite set of all computable descriptions of tasks with possibly
computable solutions. The novel algorithmic framework POWERPLAY (2011)
continually searches the space of possible pairs of new tasks and modifications
of the current problem solver, until it finds a more powerful problem solver
that provably solves all previously learned tasks plus the new one, while the
unmodified predecessor does not. Wow-effects are achieved by continually making
previously learned skills more efficient such that they require less time and
space. New skills may (partially) re-use previously learned skills. POWERPLAY's
search orders candidate pairs of tasks and solver modifications by their
conditional computational (time & space) complexity, given the stored
experience so far. The new task and its corresponding task-solving skill are
those first found and validated. The computational costs of validating new
tasks need not grow with task repertoire size. POWERPLAY's ongoing search for
novelty keeps breaking the generalization abilities of its present solver. This
is related to Goedel's sequence of increasingly powerful formal theories based
on adding formerly unprovable statements to the axioms without affecting
previously provable theorems. The continually increasing repertoire of problem
solving procedures can be exploited by a parallel search for solutions to
additional externally posed tasks. POWERPLAY may be viewed as a greedy but
practical implementation of basic principles of creativity. A first
experimental analysis can be found in separate papers [53,54].
| J\"urgen Schmidhuber | null | 1112.5309 | null | null |
Similarity-based Learning via Data Driven Embeddings | cs.LG stat.ML | We consider the problem of classification using similarity/distance functions
over data. Specifically, we propose a framework for defining the goodness of a
(dis)similarity function with respect to a given learning task and propose
algorithms that have guaranteed generalization properties when working with
such good functions. Our framework unifies and generalizes the frameworks
proposed by [Balcan-Blum ICML 2006] and [Wang et al ICML 2007]. An attractive
feature of our framework is its adaptability to data - we do not promote a
fixed notion of goodness but rather let data dictate it. We show, by giving
theoretical guarantees that the goodness criterion best suited to a problem can
itself be learned which makes our approach applicable to a variety of domains
and problems. We propose a landmarking-based approach to obtaining a classifier
from such learned goodness criteria. We then provide a novel diversity based
heuristic to perform task-driven selection of landmark points instead of random
selection. We demonstrate the effectiveness of our goodness criteria learning
method as well as the landmark selection heuristic on a variety of
similarity-based learning datasets and benchmark UCI datasets on which our
method consistently outperforms existing approaches by a significant margin.
| Purushottam Kar and Prateek Jain | null | 1112.5404 | null | null |
Finding Density Functionals with Machine Learning | physics.comp-ph cs.LG physics.chem-ph stat.ML | Machine learning is used to approximate density functionals. For the model
problem of the kinetic energy of non-interacting fermions in 1d, mean absolute
errors below 1 kcal/mol on test densities similar to the training set are
reached with fewer than 100 training densities. A predictor identifies if a
test density is within the interpolation region. Via principal component
analysis, a projected functional derivative finds highly accurate
self-consistent densities. Challenges for application of our method to real
electronic structure problems are discussed.
| John C. Snyder, Matthias Rupp, Katja Hansen, Klaus-Robert M\"uller,
and Kieron Burke | 10.1103/PhysRevLett.108.253002 | 1112.5441 | null | null |
A Study on Using Uncertain Time Series Matching Algorithms in MapReduce
Applications | cs.DC cs.AI cs.LG cs.PF | In this paper, we study CPU utilization time patterns of several Map-Reduce
applications. After extracting running patterns of several applications, the
patterns with their statistical information are saved in a reference database
to be later used to tweak system parameters to efficiently execute unknown
applications in future. To achieve this goal, CPU utilization patterns of new
applications along with its statistical information are compared with the
already known ones in the reference database to find/predict their most
probable execution patterns. Because of different patterns lengths, the Dynamic
Time Warping (DTW) is utilized for such comparison; a statistical analysis is
then applied to DTWs' outcomes to select the most suitable candidates.
Moreover, under a hypothesis, another algorithm is proposed to classify
applications under similar CPU utilization patterns. Three widely used text
processing applications (WordCount, Distributed Grep, and Terasort) and another
application (Exim Mainlog parsing) are used to evaluate our hypothesis in
tweaking system parameters in executing similar applications. Results were very
promising and showed effectiveness of our approach on 5-node Map-Reduce
platform
| Nikzad Babaii Rizvandi, Javid Taheri, Albert Y. Zomaya, Reza Moraveji | null | 1112.5505 | null | null |
Minimax Rates for Homology Inference | stat.ML cs.LG | Often, high dimensional data lie close to a low-dimensional submanifold and
it is of interest to understand the geometry of these submanifolds. The
homology groups of a manifold are important topological invariants that provide
an algebraic summary of the manifold. These groups contain rich topological
information, for instance, about the connected components, holes, tunnels and
sometimes the dimension of the manifold. In this paper, we consider the
statistical problem of estimating the homology of a manifold from noisy samples
under several different noise models. We derive upper and lower bounds on the
minimax risk for this problem. Our upper bounds are based on estimators which
are constructed from a union of balls of appropriate radius around carefully
selected points. In each case we establish complementary lower bounds using Le
Cam's lemma.
| Sivaraman Balakrishnan, Alessandro Rinaldo, Don Sheehy, Aarti Singh,
Larry Wasserman | null | 1112.5627 | null | null |
High-Rank Matrix Completion and Subspace Clustering with Missing Data | cs.IT cs.LG math.IT stat.ML | This paper considers the problem of completing a matrix with many missing
entries under the assumption that the columns of the matrix belong to a union
of multiple low-rank subspaces. This generalizes the standard low-rank matrix
completion problem to situations in which the matrix rank can be quite high or
even full rank. Since the columns belong to a union of subspaces, this problem
may also be viewed as a missing-data version of the subspace clustering
problem. Let X be an n x N matrix whose (complete) columns lie in a union of at
most k subspaces, each of rank <= r < n, and assume N >> kn. The main result of
the paper shows that under mild assumptions each column of X can be perfectly
recovered with high probability from an incomplete version so long as at least
CrNlog^2(n) entries of X are observed uniformly at random, with C>1 a constant
depending on the usual incoherence conditions, the geometrical arrangement of
subspaces, and the distribution of columns over the subspaces. The result is
illustrated with numerical experiments and an application to Internet distance
matrix completion and topology identification.
| Brian Eriksson and Laura Balzano and Robert Nowak | null | 1112.5629 | null | null |
Bayesian Active Learning for Classification and Preference Learning | stat.ML cs.LG | Information theoretic active learning has been widely studied for
probabilistic models. For simple regression an optimal myopic policy is easily
tractable. However, for other tasks and with more complex models, such as
classification with nonparametric models, the optimal solution is harder to
compute. Current approaches make approximations to achieve tractability. We
propose an approach that expresses information gain in terms of predictive
entropies, and apply this method to the Gaussian Process Classifier (GPC). Our
approach makes minimal approximations to the full information theoretic
objective. Our experimental performance compares favourably to many popular
active learning algorithms, and has equal or lower computational complexity. We
compare well to decision theoretic approaches also, which are privy to more
information and require much more computational time. Secondly, by developing
further a reformulation of binary preference learning to a classification
problem, we extend our algorithm to Gaussian Process preference learning.
| Neil Houlsby, Ferenc Husz\'ar, Zoubin Ghahramani, M\'at\'e Lengyel | null | 1112.5745 | null | null |
Building high-level features using large scale unsupervised learning | cs.LG | We consider the problem of building high-level, class-specific feature
detectors from only unlabeled data. For example, is it possible to learn a face
detector using only unlabeled images? To answer this, we train a 9-layered
locally connected sparse autoencoder with pooling and local contrast
normalization on a large dataset of images (the model has 1 billion
connections, the dataset has 10 million 200x200 pixel images downloaded from
the Internet). We train this network using model parallelism and asynchronous
SGD on a cluster with 1,000 machines (16,000 cores) for three days. Contrary to
what appears to be a widely-held intuition, our experimental results reveal
that it is possible to train a face detector without having to label images as
containing a face or not. Control experiments show that this feature detector
is robust not only to translation but also to scaling and out-of-plane
rotation. We also find that the same network is sensitive to other high-level
concepts such as cat faces and human bodies. Starting with these learned
features, we trained our network to obtain 15.8% accuracy in recognizing 20,000
object categories from ImageNet, a leap of 70% relative improvement over the
previous state-of-the-art.
| Quoc V. Le, Marc'Aurelio Ranzato, Rajat Monga, Matthieu Devin, Kai
Chen, Greg S. Corrado, Jeff Dean, Andrew Y. Ng | null | 1112.6209 | null | null |
Sparse Recovery from Nonlinear Measurements with Applications in Bad
Data Detection for Power Networks | cs.IT cs.LG cs.SY math.IT | In this paper, we consider the problem of sparse recovery from nonlinear
measurements, which has applications in state estimation and bad data detection
for power networks. An iterative mixed $\ell_1$ and $\ell_2$ convex program is
used to estimate the true state by locally linearizing the nonlinear
measurements. When the measurements are linear, through using the almost
Euclidean property for a linear subspace, we derive a new performance bound for
the state estimation error under sparse bad data and additive observation
noise. As a byproduct, in this paper we provide sharp bounds on the almost
Euclidean property of a linear subspace, using the "escape-through-the-mesh"
theorem from geometric functional analysis. When the measurements are
nonlinear, we give conditions under which the solution of the iterative
algorithm converges to the true state even though the locally linearized
measurements may not be the actual nonlinear measurements. We numerically
evaluate our iterative convex programming approach to perform bad data
detections in nonlinear electrical power networks problems. We are able to use
semidefinite programming to verify the conditions for convergence of the
proposed iterative sparse recovery algorithms from nonlinear measurements.
| Weiyu Xu, Meng Wang, Jianfeng Cai and Ao Tang | null | 1112.6234 | null | null |
Two-Manifold Problems | cs.LG | Recently, there has been much interest in spectral approaches to learning
manifolds---so-called kernel eigenmap methods. These methods have had some
successes, but their applicability is limited because they are not robust to
noise. To address this limitation, we look at two-manifold problems, in which
we simultaneously reconstruct two related manifolds, each representing a
different view of the same data. By solving these interconnected learning
problems together and allowing information to flow between them, two-manifold
algorithms are able to succeed where a non-integrated approach would fail: each
view allows us to suppress noise in the other, reducing bias in the same way
that an instrumental variable allows us to remove bias in a {linear}
dimensionality reduction problem. We propose a class of algorithms for
two-manifold problems, based on spectral decomposition of cross-covariance
operators in Hilbert space. Finally, we discuss situations where two-manifold
problems are useful, and demonstrate that solving a two-manifold problem can
aid in learning a nonlinear dynamical system from limited data.
| Byron Boots and Geoffrey J. Gordon | null | 1112.6399 | null | null |
High-dimensional Sparse Inverse Covariance Estimation using Greedy
Methods | cs.LG math.ST stat.ML stat.TH | In this paper we consider the task of estimating the non-zero pattern of the
sparse inverse covariance matrix of a zero-mean Gaussian random vector from a
set of iid samples. Note that this is also equivalent to recovering the
underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We
present two novel greedy approaches to solving this problem. The first
estimates the non-zero covariates of the overall inverse covariance matrix
using a series of global forward and backward greedy steps. The second
estimates the neighborhood of each node in the graph separately, again using
greedy forward and backward steps, and combines the intermediate neighborhoods
to form an overall estimate. The principal contribution of this paper is a
rigorous analysis of the sparsistency, or consistency in recovering the
sparsity pattern of the inverse covariance matrix. Surprisingly, we show that
both the local and global greedy methods learn the full structure of the model
with high probability given just $O(d\log(p))$ samples, which is a
\emph{significant} improvement over state of the art $\ell_1$-regularized
Gaussian MLE (Graphical Lasso) that requires $O(d^2\log(p))$ samples. Moreover,
the restricted eigenvalue and smoothness conditions imposed by our greedy
methods are much weaker than the strong irrepresentable conditions required by
the $\ell_1$-regularization based methods. We corroborate our results with
extensive simulations and examples, comparing our local and global greedy
methods to the $\ell_1$-regularized Gaussian MLE as well as the Neighborhood
Greedy method to that of nodewise $\ell_1$-regularized linear regression
(Neighborhood Lasso).
| Christopher C. Johnson, Ali Jalali and Pradeep Ravikumar | null | 1112.6411 | null | null |
T-Learning | cs.LG | Traditional Reinforcement Learning (RL) has focused on problems involving
many states and few actions, such as simple grid worlds. Most real world
problems, however, are of the opposite type, Involving Few relevant states and
many actions. For example, to return home from a conference, humans identify
only few subgoal states such as lobby, taxi, airport etc. Each valid behavior
connecting two such states can be viewed as an action, and there are trillions
of them. Assuming the subgoal identification problem is already solved, the
quality of any RL method---in real-world settings---depends less on how well it
scales with the number of states than on how well it scales with the number of
actions. This is where our new method T-Learning excels, by evaluating the
relatively few possible transits from one state to another in a
policy-independent way, rather than a huge number of state-action pairs, or
states in traditional policy-dependent ways. Illustrative experiments
demonstrate that performance improvements of T-Learning over Q-learning can be
arbitrarily large.
| Vincent Graziano, Faustino Gomez, Mark Ring, Juergen Schmidhuber | null | 1201.0292 | null | null |
Collaborative Filtering via Group-Structured Dictionary Learning | math.OC cs.LG math.ST stat.ML stat.TH | Structured sparse coding and the related structured dictionary learning
problems are novel research areas in machine learning. In this paper we present
a new application of structured dictionary learning for collaborative filtering
based recommender systems. Our extensive numerical experiments demonstrate that
the presented technique outperforms its state-of-the-art competitors and has
several advantages over approaches that do not put structured constraints on
the dictionary elements.
| Zoltan Szabo, Barnabas Poczos, Andras Lorincz | 10.1007/978-3-642-28551-6_31 | 1201.0341 | null | null |
Scikit-learn: Machine Learning in Python | cs.LG cs.MS | Scikit-learn is a Python module integrating a wide range of state-of-the-art
machine learning algorithms for medium-scale supervised and unsupervised
problems. This package focuses on bringing machine learning to non-specialists
using a general-purpose high-level language. Emphasis is put on ease of use,
performance, documentation, and API consistency. It has minimal dependencies
and is distributed under the simplified BSD license, encouraging its use in
both academic and commercial settings. Source code, binaries, and documentation
can be downloaded from http://scikit-learn.org.
| Fabian Pedregosa, Ga\"el Varoquaux, Alexandre Gramfort, Vincent
Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Andreas M\"uller,
Joel Nothman, Gilles Louppe, Peter Prettenhofer, Ron Weiss, Vincent Dubourg,
Jake Vanderplas, Alexandre Passos, David Cournapeau, Matthieu Brucher,
Matthieu Perrot, \'Edouard Duchesnay | null | 1201.0490 | null | null |
Random Forests for Metric Learning with Implicit Pairwise Position
Dependence | stat.ML cs.LG | Metric learning makes it plausible to learn distances for complex
distributions of data from labeled data. However, to date, most metric learning
methods are based on a single Mahalanobis metric, which cannot handle
heterogeneous data well. Those that learn multiple metrics throughout the space
have demonstrated superior accuracy, but at the cost of computational
efficiency. Here, we take a new angle to the metric learning problem and learn
a single metric that is able to implicitly adapt its distance function
throughout the feature space. This metric adaptation is accomplished by using a
random forest-based classifier to underpin the distance function and
incorporate both absolute pairwise position and standard relative position into
the representation. We have implemented and tested our method against state of
the art global and multi-metric methods on a variety of data sets. Overall, the
proposed method outperforms both types of methods in terms of accuracy
(consistently ranked first) and is an order of magnitude faster than state of
the art multi-metric methods (16x faster in the worst case).
| Caiming Xiong, David Johnson, Ran Xu and Jason J. Corso | null | 1201.0610 | null | null |
Sparse Nonparametric Graphical Models | stat.ML cs.LG stat.ME | We present some nonparametric methods for graphical modeling. In the discrete
case, where the data are binary or drawn from a finite alphabet, Markov random
fields are already essentially nonparametric, since the cliques can take only a
finite number of values. Continuous data are different. The Gaussian graphical
model is the standard parametric model for continuous data, but it makes
distributional assumptions that are often unrealistic. We discuss two
approaches to building more flexible graphical models. One allows arbitrary
graphs and a nonparametric extension of the Gaussian; the other uses kernel
density estimation and restricts the graphs to trees and forests. Examples of
both methods are presented. We also discuss possible future research directions
for nonparametric graphical modeling.
| John Lafferty, Han Liu, Larry Wasserman | 10.1214/12-STS391 | 1201.0794 | null | null |
A Topic Modeling Toolbox Using Belief Propagation | cs.LG | Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model
for probabilistic topic modeling, which attracts worldwide interests and
touches on many important applications in text mining, computer vision and
computational biology. This paper introduces a topic modeling toolbox (TMBP)
based on the belief propagation (BP) algorithms. TMBP toolbox is implemented by
MEX C++/Matlab/Octave for either Windows 7 or Linux. Compared with existing
topic modeling packages, the novelty of this toolbox lies in the BP algorithms
for learning LDA-based topic models. The current version includes BP algorithms
for latent Dirichlet allocation (LDA), author-topic models (ATM), relational
topic models (RTM), and labeled LDA (LaLDA). This toolbox is an ongoing project
and more BP-based algorithms for various topic models will be added in the near
future. Interested users may also extend BP algorithms for learning more
complicated topic models. The source codes are freely available under the GNU
General Public Licence, Version 1.0 at https://mloss.org/software/view/399/.
| Jia Zeng | null | 1201.0838 | null | null |
Constrained variable clustering and the best basis problem in functional
data analysis | stat.ML cs.LG | Functional data analysis involves data described by regular functions rather
than by a finite number of real valued variables. While some robust data
analysis methods can be applied directly to the very high dimensional vectors
obtained from a fine grid sampling of functional data, all methods benefit from
a prior simplification of the functions that reduces the redundancy induced by
the regularity. In this paper we propose to use a clustering approach that
targets variables rather than individual to design a piecewise constant
representation of a set of functions. The contiguity constraint induced by the
functional nature of the variables allows a polynomial complexity algorithm to
give the optimal solution.
| Fabrice Rossi (LTCI), Yves Lechevallier (INRIA Rocquencourt / INRIA
Sophia Antipolis) | 10.1007/978-3-642-13312-1_46 | 1201.0959 | null | null |
Clustering Dynamic Web Usage Data | stat.ML cs.LG | Most classification methods are based on the assumption that data conforms to
a stationary distribution. The machine learning domain currently suffers from a
lack of classification techniques that are able to detect the occurrence of a
change in the underlying data distribution. Ignoring possible changes in the
underlying concept, also known as concept drift, may degrade the performance of
the classification model. Often these changes make the model inconsistent and
regular updatings become necessary. Taking the temporal dimension into account
during the analysis of Web usage data is a necessity, since the way a site is
visited may indeed evolve due to modifications in the structure and content of
the site, or even due to changes in the behavior of certain user groups. One
solution to this problem, proposed in this article, is to update models using
summaries obtained by means of an evolutionary approach based on an intelligent
clustering approach. We carry out various clustering strategies that are
applied on time sub-periods. To validate our approach we apply two external
evaluation criteria which compare different partitions from the same data set.
Our experiments show that the proposed approach is efficient to detect the
occurrence of changes.
| Alzennyr Da Silva (INRIA Rocquencourt / INRIA Sophia Antipolis), Yves
Lechevallier (INRIA Rocquencourt / INRIA Sophia Antipolis), Fabrice Rossi
(INRIA Rocquencourt / INRIA Sophia Antipolis), Francisco De A. T. De Carvahlo
(CIn) | 10.1007/978-3-540-88045-5 | 1201.0963 | null | null |
A Thermodynamical Approach for Probability Estimation | cs.LG physics.data-an stat.ME | The issue of discrete probability estimation for samples of small size is
addressed in this study. The maximum likelihood method often suffers
over-fitting when insufficient data is available. Although the Bayesian
approach can avoid over-fitting by using prior distributions, it still has
problems with objective analysis. In response to these drawbacks, a new
theoretical framework based on thermodynamics, where energy and temperature are
introduced, was developed. Entropy and likelihood are placed at the center of
this method. The key principle of inference for probability mass functions is
the minimum free energy, which is shown to unify the two principles of maximum
likelihood and maximum entropy. Our method can robustly estimate probability
functions from small size data.
| Takashi Isozaki | null | 1201.1384 | null | null |
The Interaction of Entropy-Based Discretization and Sample Size: An
Empirical Study | stat.ML cs.LG | An empirical investigation of the interaction of sample size and
discretization - in this case the entropy-based method CAIM (Class-Attribute
Interdependence Maximization) - was undertaken to evaluate the impact and
potential bias introduced into data mining performance metrics due to variation
in sample size as it impacts the discretization process. Of particular interest
was the effect of discretizing within cross-validation folds averse to outside
discretization folds. Previous publications have suggested that discretizing
externally can bias performance results; however, a thorough review of the
literature found no empirical evidence to support such an assertion. This
investigation involved construction of over 117,000 models on seven distinct
datasets from the UCI (University of California-Irvine) Machine Learning
Library and multiple modeling methods across a variety of configurations of
sample size and discretization, with each unique "setup" being independently
replicated ten times. The analysis revealed a significant optimistic bias as
sample sizes decreased and discretization was employed. The study also revealed
that there may be a relationship between the interaction that produces such
bias and the numbers and types of predictor attributes, extending the "curse of
dimensionality" concept from feature selection into the discretization realm.
Directions for further exploration are laid out, as well some general
guidelines about the proper application of discretization in light of these
results.
| Casey Bennett | null | 1201.1450 | null | null |
Feature Selection via Regularized Trees | cs.LG stat.ME stat.ML | We propose a tree regularization framework, which enables many tree models to
perform feature selection efficiently. The key idea of the regularization
framework is to penalize selecting a new feature for splitting when its gain
(e.g. information gain) is similar to the features used in previous splits. The
regularization framework is applied on random forest and boosted trees here,
and can be easily applied to other tree models. Experimental studies show that
the regularized trees can select high-quality feature subsets with regard to
both strong and weak classifiers. Because tree models can naturally deal with
categorical and numerical variables, missing values, different scales between
variables, interactions and nonlinearities etc., the tree regularization
framework provides an effective and efficient feature selection solution for
many practical problems.
| Houtao Deng and George Runger | null | 1201.1587 | null | null |
Customers Behavior Modeling by Semi-Supervised Learning in Customer
Relationship Management | cs.LG | Leveraging the power of increasing amounts of data to analyze customer base
for attracting and retaining the most valuable customers is a major problem
facing companies in this information age. Data mining technologies extract
hidden information and knowledge from large data stored in databases or data
warehouses, thereby supporting the corporate decision making process. CRM uses
data mining (one of the elements of CRM) techniques to interact with customers.
This study investigates the use of a technique, semi-supervised learning, for
the management and analysis of customer-related data warehouse and information.
The idea of semi-supervised learning is to learn not only from the labeled
training data, but to exploit also the structural information in additionally
available unlabeled data. The proposed semi-supervised method is a model by
means of a feed-forward neural network trained by a back propagation algorithm
(multi-layer perceptron) in order to predict the category of an unknown
customer (potential customers). In addition, this technique can be used with
Rapid Miner tools for both labeled and unlabeled data.
| Siavash Emtiyaz, MohammadReza Keyvanpour | 10.4156/AISS.vol3.issue9.31 | 1201.1670 | null | null |
Adaptive Context Tree Weighting | cs.IT cs.LG math.IT | We describe an adaptive context tree weighting (ACTW) algorithm, as an
extension to the standard context tree weighting (CTW) algorithm. Unlike the
standard CTW algorithm, which weights all observations equally regardless of
the depth, ACTW gives increasing weight to more recent observations, aiming to
improve performance in cases where the input sequence is from a non-stationary
distribution. Data compression results show ACTW variants improving over CTW on
merged files from standard compression benchmark tests while never being
significantly worse on any individual file.
| Alexander O'Neill and Marcus Hutter and Wen Shao and Peter Sunehag | null | 1201.2056 | null | null |
Automatic Detection of Diabetes Diagnosis using Feature Weighted Support
Vector Machines based on Mutual Information and Modified Cuckoo Search | cs.LG | Diabetes is a major health problem in both developing and developed countries
and its incidence is rising dramatically. In this study, we investigate a novel
automatic approach to diagnose Diabetes disease based on Feature Weighted
Support Vector Machines (FW-SVMs) and Modified Cuckoo Search (MCS). The
proposed model consists of three stages: Firstly, PCA is applied to select an
optimal subset of features out of set of all the features. Secondly, Mutual
Information is employed to construct the FWSVM by weighting different features
based on their degree of importance. Finally, since parameter selection plays a
vital role in classification accuracy of SVMs, MCS is applied to select the
best parameter values. The proposed MI-MCS-FWSVM method obtains 93.58% accuracy
on UCI dataset. The experimental results demonstrate that our method
outperforms the previous methods by not only giving more accurate results but
also significantly speeding up the classification procedure.
| Davar Giveki, Hamid Salimi, GholamReza Bahmanyar, Younes Khademian | null | 1201.2173 | null | null |
Stochastic Low-Rank Kernel Learning for Regression | cs.LG | We present a novel approach to learn a kernel-based regression function. It
is based on the useof conical combinations of data-based parameterized kernels
and on a new stochastic convex optimization procedure of which we establish
convergence guarantees. The overall learning procedure has the nice properties
that a) the learned conical combination is automatically designed to perform
the regression task at hand and b) the updates implicated by the optimization
procedure are quite inexpensive. In order to shed light on the appositeness of
our learning strategy, we present empirical results from experiments conducted
on various benchmark datasets.
| Pierre Machart (LIF), Thomas Peel (LIF, LATP), Liva Ralaivola (LIF),
Sandrine Anthoine (LATP), Herv\'e Glotin (LSIS) | null | 1201.2416 | null | null |
Sparse Reward Processes | cs.LG stat.ML | We introduce a class of learning problems where the agent is presented with a
series of tasks. Intuitively, if there is relation among those tasks, then the
information gained during execution of one task has value for the execution of
another task. Consequently, the agent is intrinsically motivated to explore its
environment beyond the degree necessary to solve the current task it has at
hand. We develop a decision theoretic setting that generalises standard
reinforcement learning tasks and captures this intuition. More precisely, we
consider a multi-stage stochastic game between a learning agent and an
opponent. We posit that the setting is a good model for the problem of
life-long learning in uncertain environments, where while resources must be
spent learning about currently important tasks, there is also the need to
allocate effort towards learning about aspects of the world which are not
relevant at the moment. This is due to the fact that unpredictable future
events may lead to a change of priorities for the decision maker. Thus, in some
sense, the model "explains" the necessity of curiosity. Apart from introducing
the general formalism, the paper provides algorithms. These are evaluated
experimentally in some exemplary domains. In addition, performance bounds are
proven for some cases of this problem.
| Christos Dimitrakakis | null | 1201.2555 | null | null |
Joint Approximation of Information and Distributed Link-Scheduling
Decisions in Wireless Networks | cs.LG cs.NI | For a large multi-hop wireless network, nodes are preferable to make
distributed and localized link-scheduling decisions with only interactions
among a small number of neighbors. However, for a slowly decaying channel and
densely populated interferers, a small size neighborhood often results in
nontrivial link outages and is thus insufficient for making optimal scheduling
decisions. A question arises how to deal with the information outside a
neighborhood in distributed link-scheduling. In this work, we develop joint
approximation of information and distributed link scheduling. We first apply
machine learning approaches to model distributed link-scheduling with complete
information. We then characterize the information outside a neighborhood in
form of residual interference as a random loss variable. The loss variable is
further characterized by either a Mean Field approximation or a normal
distribution based on the Lyapunov central limit theorem. The approximated
information outside a neighborhood is incorporated in a factor graph. This
results in joint approximation and distributed link-scheduling in an iterative
fashion. Link-scheduling decisions are first made at each individual node based
on the approximated loss variables. Loss variables are then updated and used
for next link-scheduling decisions. The algorithm repeats between these two
phases until convergence. Interactive iterations among these variables are
implemented with a message-passing algorithm over a factor graph. Simulation
results show that using learned information outside a neighborhood jointly with
distributed link-scheduling reduces the outage probability close to zero even
for a small neighborhood.
| Sung-eok Jeon, and Chuanyi Ji | null | 1201.2575 | null | null |
Autonomous Cleaning of Corrupted Scanned Documents - A Generative
Modeling Approach | cs.CV cs.LG | We study the task of cleaning scanned text documents that are strongly
corrupted by dirt such as manual line strokes, spilled ink etc. We aim at
autonomously removing dirt from a single letter-size page based only on the
information the page contains. Our approach, therefore, has to learn character
representations without supervision and requires a mechanism to distinguish
learned representations from irregular patterns. To learn character
representations, we use a probabilistic generative model parameterizing pattern
features, feature variances, the features' planar arrangements, and pattern
frequencies. The latent variables of the model describe pattern class, pattern
position, and the presence or absence of individual pattern features. The model
parameters are optimized using a novel variational EM approximation. After
learning, the parameters represent, independently of their absolute position,
planar feature arrangements and their variances. A quality measure defined
based on the learned representation then allows for an autonomous
discrimination between regular character patterns and the irregular patterns
making up the dirt. The irregular patterns can thus be removed to clean the
document. For a full Latin alphabet we found that a single page does not
contain sufficiently many character examples. However, even if heavily
corrupted by dirt, we show that a page containing a lower number of character
types can efficiently and autonomously be cleaned solely based on the
structural regularity of the characters it contains. In different examples
using characters from different alphabets, we demonstrate generality of the
approach and discuss its implications for future developments.
| Zhenwen Dai and J\"org L\"ucke | 10.1109/TPAMI.2014.2313126 | 1201.2605 | null | null |
Acoustical Quality Assessment of the Classroom Environment | cs.LG | Teaching is one of the most important factors affecting any education system.
Many research efforts have been conducted to facilitate the presentation modes
used by instructors in classrooms as well as provide means for students to
review lectures through web browsers. Other studies have been made to provide
acoustical design recommendations for classrooms like room size and
reverberation times. However, using acoustical features of classrooms as a way
to provide education systems with feedback about the learning process was not
thoroughly investigated in any of these studies. We propose a system that
extracts different sound features of students and instructors, and then uses
machine learning techniques to evaluate the acoustical quality of any learning
environment. We infer conclusions about the students' satisfaction with the
quality of lectures. Using classifiers instead of surveys and other subjective
ways of measures can facilitate and speed such experiments which enables us to
perform them continuously. We believe our system enables education systems to
continuously review and improve their teaching strategies and acoustical
quality of classrooms.
| Marian George, Moustafa Youssef | null | 1201.2902 | null | null |
Combining Heterogeneous Classifiers for Relational Databases | cs.LG cs.DB | Most enterprise data is distributed in multiple relational databases with
expert-designed schema. Using traditional single-table machine learning
techniques over such data not only incur a computational penalty for converting
to a 'flat' form (mega-join), even the human-specified semantic information
present in the relations is lost. In this paper, we present a practical,
two-phase hierarchical meta-classification algorithm for relational databases
with a semantic divide and conquer approach. We propose a recursive, prediction
aggregation technique over heterogeneous classifiers applied on individual
database tables. The proposed algorithm was evaluated on three diverse
datasets, namely TPCH, PKDD and UCI benchmarks and showed considerable
reduction in classification time without any loss of prediction accuracy.
| Geetha Manjunatha, M Narasimha Murty, Dinkar Sitaram | null | 1201.2925 | null | null |
A Spiking Neural Learning Classifier System | cs.NE cs.LG cs.RO | Learning Classifier Systems (LCS) are population-based reinforcement learners
used in a wide variety of applications. This paper presents a LCS where each
traditional rule is represented by a spiking neural network, a type of network
with dynamic internal state. We employ a constructivist model of growth of both
neurons and dendrites that realise flexible learning by evolving structures of
sufficient complexity to solve a well-known problem involving continuous,
real-valued inputs. Additionally, we extend the system to enable temporal state
decomposition. By allowing our LCS to chain together sequences of heterogeneous
actions into macro-actions, it is shown to perform optimally in a problem where
traditional methods can fail to find a solution in a reasonable amount of time.
Our final system is tested on a simulated robotics platform.
| Gerard Howard and Larry Bull and Pier-Luca Lanzi | null | 1201.3249 | null | null |
Spike-and-Slab Sparse Coding for Unsupervised Feature Discovery | stat.ML cs.LG | We consider the problem of using a factor model we call {\em spike-and-slab
sparse coding} (S3C) to learn features for a classification task. The S3C model
resembles both the spike-and-slab RBM and sparse coding. Since exact inference
in this model is intractable, we derive a structured variational inference
procedure and employ a variational EM training algorithm. Prior work on
approximate inference for this model has not prioritized the ability to exploit
parallel architectures and scale to enormous problem sizes. We present an
inference procedure appropriate for use with GPUs which allows us to
dramatically increase both the training set size and the amount of latent
factors.
We demonstrate that this approach improves upon the supervised learning
capabilities of both sparse coding and the ssRBM on the CIFAR-10 dataset. We
evaluate our approach's potential for semi-supervised learning on subsets of
CIFAR-10. We demonstrate state-of-the art self-taught learning performance on
the STL-10 dataset and use our method to win the NIPS 2011 Workshop on
Challenges In Learning Hierarchical Models' Transfer Learning Challenge.
| Ian J. Goodfellow and Aaron Courville and Yoshua Bengio | null | 1201.3382 | null | null |
On the Lagrangian Biduality of Sparsity Minimization Problems | cs.CV cs.LG stat.ML | Recent results in Compressive Sensing have shown that, under certain
conditions, the solution to an underdetermined system of linear equations with
sparsity-based regularization can be accurately recovered by solving convex
relaxations of the original problem. In this work, we present a novel
primal-dual analysis on a class of sparsity minimization problems. We show that
the Lagrangian bidual (i.e., the Lagrangian dual of the Lagrangian dual) of the
sparsity minimization problems can be used to derive interesting convex
relaxations: the bidual of the $\ell_0$-minimization problem is the
$\ell_1$-minimization problem; and the bidual of the $\ell_{0,1}$-minimization
problem for enforcing group sparsity on structured data is the
$\ell_{1,\infty}$-minimization problem. The analysis provides a means to
compute per-instance non-trivial lower bounds on the (group) sparsity of the
desired solutions. In a real-world application, the bidual relaxation improves
the performance of a sparsity-based classification framework applied to robust
face recognition.
| Dheeraj Singaraju, Ehsan Elhamifar, Roberto Tron, Allen Y. Yang, S.
Shankar Sastry | null | 1201.3674 | null | null |
Adaptive Policies for Sequential Sampling under Incomplete Information
and a Cost Constraint | stat.ML cs.LG math.OC | We consider the problem of sequential sampling from a finite number of
independent statistical populations to maximize the expected infinite horizon
average outcome per period, under a constraint that the expected average
sampling cost does not exceed an upper bound. The outcome distributions are not
known. We construct a class of consistent adaptive policies, under which the
average outcome converges with probability 1 to the true value under complete
information for all distributions with finite means. We also compare the rate
of convergence for various policies in this class using simulation.
| Apostolos Burnetas and Odysseas Kanavetas | null | 1201.4002 | null | null |
A metric learning perspective of SVM: on the relation of SVM and LMNN | cs.LG stat.ML | Support Vector Machines, SVMs, and the Large Margin Nearest Neighbor
algorithm, LMNN, are two very popular learning algorithms with quite different
learning biases. In this paper we bring them into a unified view and show that
they have a much stronger relation than what is commonly thought. We analyze
SVMs from a metric learning perspective and cast them as a metric learning
problem, a view which helps us uncover the relations of the two algorithms. We
show that LMNN can be seen as learning a set of local SVM-like models in a
quadratic space. Along the way and inspired by the metric-based interpretation
of SVM s we derive a novel variant of SVMs, epsilon-SVM, to which LMNN is even
more similar. We give a unified view of LMNN and the different SVM variants.
Finally we provide some preliminary experiments on a number of benchmark
datasets in which show that epsilon-SVM compares favorably both with respect to
LMNN and SVM.
| Huyen Do, Alexandros Kalousis, Jun Wang and Adam Woznica | null | 1201.4714 | null | null |
A probabilistic methodology for multilabel classification | cs.AI cs.LG | Multilabel classification is a relatively recent subfield of machine
learning. Unlike to the classical approach, where instances are labeled with
only one category, in multilabel classification, an arbitrary number of
categories is chosen to label an instance. Due to the problem complexity (the
solution is one among an exponential number of alternatives), a very common
solution (the binary method) is frequently used, learning a binary classifier
for every category, and combining them all afterwards. The assumption taken in
this solution is not realistic, and in this work we give examples where the
decisions for all the labels are not taken independently, and thus, a
supervised approach should learn those existing relationships among categories
to make a better classification. Therefore, we show here a generic methodology
that can improve the results obtained by a set of independent probabilistic
binary classifiers, by using a combination procedure with a classifier trained
on the co-occurrences of the labels. We show an exhaustive experimentation in
three different standard corpora of labeled documents (Reuters-21578,
Ohsumed-23 and RCV1), which present noticeable improvements in all of them,
when using our methodology, in three probabilistic base classifiers.
| Alfonso E. Romero, Luis M. de Campos | null | 1201.4777 | null | null |
Adaptive Shortest-Path Routing under Unknown and Stochastically Varying
Link States | cs.NI cs.LG | We consider the adaptive shortest-path routing problem in wireless networks
under unknown and stochastically varying link states. In this problem, we aim
to optimize the quality of communication between a source and a destination
through adaptive path selection. Due to the randomness and uncertainties in the
network dynamics, the quality of each link varies over time according to a
stochastic process with unknown distributions. After a path is selected for
communication, the aggregated quality of all links on this path (e.g., total
path delay) is observed. The quality of each individual link is not observable.
We formulate this problem as a multi-armed bandit with dependent arms. We show
that by exploiting arm dependencies, a regret polynomial with network size can
be achieved while maintaining the optimal logarithmic order with time. This is
in sharp contrast with the exponential regret order with network size offered
by a direct application of the classic MAB policies that ignore arm
dependencies. Furthermore, our results are obtained under a general model of
link-quality distributions (including heavy-tailed distributions) and find
applications in cognitive radio and ad hoc networks with unknown and dynamic
communication environments.
| Keqin Liu, Qing Zhao | null | 1201.4906 | null | null |
Unsupervised Classification Using Immune Algorithm | cs.LG cs.AI | Unsupervised classification algorithm based on clonal selection principle
named Unsupervised Clonal Selection Classification (UCSC) is proposed in this
paper. The new proposed algorithm is data driven and self-adaptive, it adjusts
its parameters to the data to make the classification operation as fast as
possible. The performance of UCSC is evaluated by comparing it with the well
known K-means algorithm using several artificial and real-life data sets. The
experiments show that the proposed UCSC algorithm is more reliable and has high
classification precision comparing to traditional classification methods such
as K-means.
| M. T. Al-Muallim, R. El-Kouatly | 10.5120/677-952 | 1201.5217 | null | null |
An Efficient Primal-Dual Prox Method for Non-Smooth Optimization | cs.LG | We study the non-smooth optimization problems in machine learning, where both
the loss function and the regularizer are non-smooth functions. Previous
studies on efficient empirical loss minimization assume either a smooth loss
function or a strongly convex regularizer, making them unsuitable for
non-smooth optimization. We develop a simple yet efficient method for a family
of non-smooth optimization problems where the dual form of the loss function is
bilinear in primal and dual variables. We cast a non-smooth optimization
problem into a minimax optimization problem, and develop a primal dual prox
method that solves the minimax optimization problem at a rate of $O(1/T)$
{assuming that the proximal step can be efficiently solved}, significantly
faster than a standard subgradient descent method that has an $O(1/\sqrt{T})$
convergence rate. Our empirical study verifies the efficiency of the proposed
method for various non-smooth optimization problems that arise ubiquitously in
machine learning by comparing it to the state-of-the-art first order methods.
| Tianbao Yang, Mehrdad Mahdavi, Rong Jin, Shenghuo Zhu | null | 1201.5283 | null | null |
On Constrained Spectral Clustering and Its Applications | cs.LG stat.ML | Constrained clustering has been well-studied for algorithms such as $K$-means
and hierarchical clustering. However, how to satisfy many constraints in these
algorithmic settings has been shown to be intractable. One alternative to
encode many constraints is to use spectral clustering, which remains a
developing area. In this paper, we propose a flexible framework for constrained
spectral clustering. In contrast to some previous efforts that implicitly
encode Must-Link and Cannot-Link constraints by modifying the graph Laplacian
or constraining the underlying eigenspace, we present a more natural and
principled formulation, which explicitly encodes the constraints as part of a
constrained optimization problem. Our method offers several practical
advantages: it can encode the degree of belief in Must-Link and Cannot-Link
constraints; it guarantees to lower-bound how well the given constraints are
satisfied using a user-specified threshold; it can be solved deterministically
in polynomial time through generalized eigendecomposition. Furthermore, by
inheriting the objective function from spectral clustering and encoding the
constraints explicitly, much of the existing analysis of unconstrained spectral
clustering techniques remains valid for our formulation. We validate the
effectiveness of our approach by empirical results on both artificial and real
datasets. We also demonstrate an innovative use of encoding large number of
constraints: transfer learning via constraints.
| Xiang Wang, Buyue Qian, Ian Davidson | 10.1007/s10618-012-0291-9 | 1201.5338 | null | null |
Discrete and fuzzy dynamical genetic programming in the XCSF learning
classifier system | cs.AI cs.LG cs.NE cs.SY math.OC | A number of representation schemes have been presented for use within
learning classifier systems, ranging from binary encodings to neural networks.
This paper presents results from an investigation into using discrete and fuzzy
dynamical system representations within the XCSF learning classifier system. In
particular, asynchronous random Boolean networks are used to represent the
traditional condition-action production system rules in the discrete case and
asynchronous fuzzy logic networks in the continuous-valued case. It is shown
possible to use self-adaptive, open-ended evolution to design an ensemble of
such dynamical systems within XCSF to solve a number of well-known test
problems.
| Richard J. Preen and Larry Bull | 10.1007/s00500-013-1044-4 | 1201.5604 | null | null |
A Comparison Between Data Mining Prediction Algorithms for Fault
Detection(Case study: Ahanpishegan co.) | cs.LG | In the current competitive world, industrial companies seek to manufacture
products of higher quality which can be achieved by increasing reliability,
maintainability and thus the availability of products. On the other hand,
improvement in products lifecycle is necessary for achieving high reliability.
Typically, maintenance activities are aimed to reduce failures of industrial
machinery and minimize the consequences of such failures. So the industrial
companies try to improve their efficiency by using different fault detection
techniques. One strategy is to process and analyze previous generated data to
predict future failures. The purpose of this paper is to detect wasted parts
using different data mining algorithms and compare the accuracy of these
algorithms. A combination of thermal and physical characteristics has been used
and the algorithms were implemented on Ahanpishegan's current data to estimate
the availability of its produced parts.
Keywords: Data Mining, Fault Detection, Availability, Prediction Algorithms.
| Golriz Amooee, Behrouz Minaei-Bidgoli, Malihe Bagheri-Dehnavi | null | 1201.6053 | null | null |
Real-time jam-session support system | cs.HC cs.LG cs.SD | We propose a method for the problem of real time chord accompaniment of
improvised music. Our implementation can learn an underlying structure of the
musical performance and predict next chord. The system uses Hidden Markov Model
to find the most probable chord sequence for the played melody and then a
Variable Order Markov Model is used to a) learn the structure (if any) and b)
predict next chord. We implemented our system in Java and MAX/Msp and compared
and evaluated using objective (prediction accuracy) and subjective
(questionnaire) evaluation methods.
| Panagiotis Tigas | null | 1201.6251 | null | null |
Active Learning of Custering with Side Information Using $\eps$-Smooth
Relative Regret Approximations | cs.LG | Clustering is considered a non-supervised learning setting, in which the goal
is to partition a collection of data points into disjoint clusters. Often a
bound $k$ on the number of clusters is given or assumed by the practitioner.
Many versions of this problem have been defined, most notably $k$-means and
$k$-median.
An underlying problem with the unsupervised nature of clustering it that of
determining a similarity function. One approach for alleviating this difficulty
is known as clustering with side information, alternatively, semi-supervised
clustering. Here, the practitioner incorporates side information in the form of
"must be clustered" or "must be separated" labels for data point pairs. Each
such piece of information comes at a "query cost" (often involving human
response solicitation). The collection of labels is then incorporated in the
usual clustering algorithm as either strict or as soft constraints, possibly
adding a pairwise constraint penalty function to the chosen clustering
objective.
Our work is mostly related to clustering with side information. We ask how to
choose the pairs of data points. Our analysis gives rise to a method provably
better than simply choosing them uniformly at random. Roughly speaking, we show
that the distribution must be biased so as more weight is placed on pairs
incident to elements in smaller clusters in some optimal solution. Of course we
do not know the optimal solution, hence we don't know the bias. Using the
recently introduced method of $\eps$-smooth relative regret approximations of
Ailon, Begleiter and Ezra, we can show an iterative process that improves both
the clustering and the bias in tandem. The process provably converges to the
optimal solution faster (in terms of query cost) than an algorithm selecting
pairs uniformly.
| Nir Ailon and Ron Begleiter | null | 1201.6462 | null | null |
Random Feature Maps for Dot Product Kernels | cs.LG cs.CG math.FA stat.ML | Approximating non-linear kernels using feature maps has gained a lot of
interest in recent years due to applications in reducing training and testing
times of SVM classifiers and other kernel based learning algorithms. We extend
this line of work and present low distortion embeddings for dot product kernels
into linear Euclidean spaces. We base our results on a classical result in
harmonic analysis characterizing all dot product kernels and use it to define
randomized feature maps into explicit low dimensional Euclidean spaces in which
the native dot product provides an approximation to the dot product kernel with
high confidence.
| Purushottam Kar and Harish Karnick | null | 1201.6530 | null | null |
Empowerment for Continuous Agent-Environment Systems | cs.AI cs.LG | This paper develops generalizations of empowerment to continuous states.
Empowerment is a recently introduced information-theoretic quantity motivated
by hypotheses about the efficiency of the sensorimotor loop in biological
organisms, but also from considerations stemming from curiosity-driven
learning. Empowemerment measures, for agent-environment systems with stochastic
transitions, how much influence an agent has on its environment, but only that
influence that can be sensed by the agent sensors. It is an
information-theoretic generalization of joint controllability (influence on
environment) and observability (measurement by sensors) of the environment by
the agent, both controllability and observability being usually defined in
control theory as the dimensionality of the control/observation spaces. Earlier
work has shown that empowerment has various interesting and relevant
properties, e.g., it allows us to identify salient states using only the
dynamics, and it can act as intrinsic reward without requiring an external
reward. However, in this previous work empowerment was limited to the case of
small-scale and discrete domains and furthermore state transition probabilities
were assumed to be known. The goal of this paper is to extend empowerment to
the significantly more important and relevant case of continuous vector-valued
state spaces and initially unknown state transition probabilities. The
continuous state space is addressed by Monte-Carlo approximation; the unknown
transitions are addressed by model learning and prediction for which we apply
Gaussian processes regression with iterated forecasting. In a number of
well-known continuous control tasks we examine the dynamics induced by
empowerment and include an application to exploration and online model
learning.
| Tobias Jung and Daniel Polani and Peter Stone | null | 1201.6583 | null | null |
Gaussian Processes for Sample Efficient Reinforcement Learning with
RMAX-like Exploration | cs.AI cs.LG | We present an implementation of model-based online reinforcement learning
(RL) for continuous domains with deterministic transitions that is specifically
designed to achieve low sample complexity. To achieve low sample complexity,
since the environment is unknown, an agent must intelligently balance
exploration and exploitation, and must be able to rapidly generalize from
observations. While in the past a number of related sample efficient RL
algorithms have been proposed, to allow theoretical analysis, mainly
model-learners with weak generalization capabilities were considered. Here, we
separate function approximation in the model learner (which does require
samples) from the interpolation in the planner (which does not require
samples). For model-learning we apply Gaussian processes regression (GP) which
is able to automatically adjust itself to the complexity of the problem (via
Bayesian hyperparameter selection) and, in practice, often able to learn a
highly accurate model from very little data. In addition, a GP provides a
natural way to determine the uncertainty of its predictions, which allows us to
implement the "optimism in the face of uncertainty" principle used to
efficiently control exploration. Our method is evaluated on four common
benchmark domains.
| Tobias Jung and Peter Stone | null | 1201.6604 | null | null |
Feature Selection for Value Function Approximation Using Bayesian Model
Selection | cs.AI cs.LG | Feature selection in reinforcement learning (RL), i.e. choosing basis
functions such that useful approximations of the unkown value function can be
obtained, is one of the main challenges in scaling RL to real-world
applications. Here we consider the Gaussian process based framework GPTD for
approximate policy evaluation, and propose feature selection through marginal
likelihood optimization of the associated hyperparameters. Our approach has two
appealing benefits: (1) given just sample transitions, we can solve the policy
evaluation problem fully automatically (without looking at the learning task,
and, in theory, independent of the dimensionality of the state space), and (2)
model selection allows us to consider more sophisticated kernels, which in turn
enable us to identify relevant subspaces and eliminate irrelevant state
variables such that we can achieve substantial computational savings and
improved prediction performance.
| Tobias Jung and Peter Stone | null | 1201.6615 | null | null |
Learning RoboCup-Keepaway with Kernels | cs.AI cs.LG cs.MA | We apply kernel-based methods to solve the difficult reinforcement learning
problem of 3vs2 keepaway in RoboCup simulated soccer. Key challenges in
keepaway are the high-dimensionality of the state space (rendering conventional
discretization-based function approximation like tilecoding infeasible), the
stochasticity due to noise and multiple learning agents needing to cooperate
(meaning that the exact dynamics of the environment are unknown) and real-time
learning (meaning that an efficient online implementation is required). We
employ the general framework of approximate policy iteration with
least-squares-based policy evaluation. As underlying function approximator we
consider the family of regularization networks with subset of regressors
approximation. The core of our proposed solution is an efficient recursive
implementation with automatic supervised selection of relevant basis functions.
Simulation results indicate that the behavior learned through our approach
clearly outperforms the best results obtained earlier with tilecoding by Stone
et al. (2005).
| Tobias Jung and Daniel Polani | null | 1201.6626 | null | null |
Kernels on Sample Sets via Nonparametric Divergence Estimates | cs.LG stat.ML | Most machine learning algorithms, such as classification or regression, treat
the individual data point as the object of interest. Here we consider extending
machine learning algorithms to operate on groups of data points. We suggest
treating a group of data points as an i.i.d. sample set from an underlying
feature distribution for that group. Our approach employs kernel machines with
a kernel on i.i.d. sample sets of vectors. We define certain kernel functions
on pairs of distributions, and then use a nonparametric estimator to
consistently estimate those functions based on sample sets. The projection of
the estimated Gram matrix to the cone of symmetric positive semi-definite
matrices enables us to use kernel machines for classification, regression,
anomaly detection, and low-dimensional embedding in the space of distributions.
We present several numerical experiments both on real and simulated datasets to
demonstrate the advantages of our new approach.
| Danica J. Sutherland, Liang Xiong, Barnab\'as P\'oczos, and Jeff
Schneider | null | 1202.0302 | null | null |
Minimax Rates of Estimation for Sparse PCA in High Dimensions | stat.ML cs.LG math.ST stat.TH | We study sparse principal components analysis in the high-dimensional
setting, where $p$ (the number of variables) can be much larger than $n$ (the
number of observations). We prove optimal, non-asymptotic lower and upper
bounds on the minimax estimation error for the leading eigenvector when it
belongs to an $\ell_q$ ball for $q \in [0,1]$. Our bounds are sharp in $p$ and
$n$ for all $q \in [0, 1]$ over a wide class of distributions. The upper bound
is obtained by analyzing the performance of $\ell_q$-constrained PCA. In
particular, our results provide convergence rates for $\ell_1$-constrained PCA.
| Vincent Q. Vu and Jing Lei | null | 1202.0786 | null | null |
A Reconstruction Error Formulation for Semi-Supervised Multi-task and
Multi-view Learning | cs.LG stat.ML | A significant challenge to make learning techniques more suitable for general
purpose use is to move beyond i) complete supervision, ii) low dimensional
data, iii) a single task and single view per instance. Solving these challenges
allows working with "Big Data" problems that are typically high dimensional
with multiple (but possibly incomplete) labelings and views. While other work
has addressed each of these problems separately, in this paper we show how to
address them together, namely semi-supervised dimension reduction for
multi-task and multi-view learning (SSDR-MML), which performs optimization for
dimension reduction and label inference in semi-supervised setting. The
proposed framework is designed to handle both multi-task and multi-view
learning settings, and can be easily adapted to many useful applications.
Information obtained from all tasks and views is combined via reconstruction
errors in a linear fashion that can be efficiently solved using an alternating
optimization scheme. Our formulation has a number of advantages. We explicitly
model the information combining mechanism as a data structure (a
weight/nearest-neighbor matrix) which allows investigating fundamental
questions in multi-task and multi-view learning. We address one such question
by presenting a general measure to quantify the success of simultaneous
learning of multiple tasks or from multiple views. We show that our SSDR-MML
approach can outperform many state-of-the-art baseline methods and demonstrate
the effectiveness of connecting dimension reduction and learning.
| Buyue Qian, Xiang Wang and Ian Davidson | null | 1202.0855 | null | null |
Cramer Rao-Type Bounds for Sparse Bayesian Learning | cs.LG stat.ML | In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao
lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement
vector Sparse Bayesian Learning (SBL) problem of estimating compressible
vectors and their prior distribution parameters. We assume the unknown vector
to be drawn from a compressible Student-t prior distribution. We derive CRBs
that encompass the deterministic or random nature of the unknown parameters of
the prior distribution and the regression noise variance. We extend the MCRB to
the case where the compressible vector is distributed according to a general
compressible prior distribution, of which the generalized Pareto distribution
is a special case. We use the derived bounds to uncover the relationship
between the compressibility and Mean Square Error (MSE) in the estimates.
Further, we illustrate the tightness and utility of the bounds through
simulations, by comparing them with the MSE performance of two popular
SBL-based estimators. It is found that the MCRB is generally the tightest among
the bounds derived and that the MSE performance of the Expectation-Maximization
(EM) algorithm coincides with the MCRB for the compressible vector. Through
simulations, we demonstrate the dependence of the MSE performance of SBL based
estimators on the compressibility of the vector for several values of the
number of observations and at different signal powers.
| Ranjitha Prasad and Chandra R. Murthy | 10.1109/TSP.2012.2226165 | 1202.1119 | null | null |
rFerns: An Implementation of the Random Ferns Method for General-Purpose
Machine Learning | cs.LG stat.ML | In this paper I present an extended implementation of the Random ferns
algorithm contained in the R package rFerns. It differs from the original by
the ability of consuming categorical and numerical attributes instead of only
binary ones. Also, instead of using simple attribute subspace ensemble it
employs bagging and thus produce error approximation and variable importance
measure modelled after Random forest algorithm. I also present benchmarks'
results which show that although Random ferns' accuracy is mostly smaller than
achieved by Random forest, its speed and good quality of importance measure it
provides make rFerns a reasonable choice for a specific applications.
| Miron B. Kursa | null | 1202.1121 | null | null |
Contextual Bandit Learning with Predictable Rewards | cs.LG | Contextual bandit learning is a reinforcement learning problem where the
learner repeatedly receives a set of features (context), takes an action and
receives a reward based on the action and context. We consider this problem
under a realizability assumption: there exists a function in a (known) function
class, always capable of predicting the expected reward, given the action and
context. Under this assumption, we show three things. We present a new
algorithm---Regressor Elimination--- with a regret similar to the agnostic
setting (i.e. in the absence of realizability assumption). We prove a new lower
bound showing no algorithm can achieve superior performance in the worst case
even with the realizability assumption. However, we do show that for any set of
policies (mapping contexts to actions), there is a distribution over rewards
(given context) such that our new algorithm has constant regret unlike the
previous approaches.
| Alekh Agarwal and Miroslav Dud\'ik and Satyen Kale and John Langford
and Robert E. Schapire | null | 1202.1334 | null | null |
Information Forests | cs.LG stat.ML | We describe Information Forests, an approach to classification that
generalizes Random Forests by replacing the splitting criterion of non-leaf
nodes from a discriminative one -- based on the entropy of the label
distribution -- to a generative one -- based on maximizing the information
divergence between the class-conditional distributions in the resulting
partitions. The basic idea consists of deferring classification until a measure
of "classification confidence" is sufficiently high, and instead breaking down
the data so as to maximize this measure. In an alternative interpretation,
Information Forests attempt to partition the data into subsets that are "as
informative as possible" for the purpose of the task, which is to classify the
data. Classification confidence, or informative content of the subsets, is
quantified by the Information Divergence. Our approach relates to active
learning, semi-supervised learning, mixed generative/discriminative learning.
| Zhao Yi, Stefano Soatto, Maneesh Dewan, Yiqiang Zhan | null | 1202.1523 | null | null |
On the Performance of Maximum Likelihood Inverse Reinforcement Learning | cs.LG | Inverse reinforcement learning (IRL) addresses the problem of recovering a
task description given a demonstration of the optimal policy used to solve such
a task. The optimal policy is usually provided by an expert or teacher, making
IRL specially suitable for the problem of apprenticeship learning. The task
description is encoded in the form of a reward function of a Markov decision
process (MDP). Several algorithms have been proposed to find the reward
function corresponding to a set of demonstrations. One of the algorithms that
has provided best results in different applications is a gradient method to
optimize a policy squared error criterion. On a parallel line of research,
other authors have presented recently a gradient approximation of the maximum
likelihood estimate of the reward signal. In general, both approaches
approximate the gradient estimate and the criteria at different stages to make
the algorithm tractable and efficient. In this work, we provide a detailed
description of the different methods to highlight differences in terms of
reward estimation, policy similarity and computational costs. We also provide
experimental results to evaluate the differences in performance of the methods.
| H\'ector Ratia and Luis Montesano and Ruben Martinez-Cantin | null | 1202.1558 | null | null |
Predicting Contextual Sequences via Submodular Function Maximization | cs.AI cs.LG cs.RO | Sequence optimization, where the items in a list are ordered to maximize some
reward has many applications such as web advertisement placement, search, and
control libraries in robotics. Previous work in sequence optimization produces
a static ordering that does not take any features of the item or context of the
problem into account. In this work, we propose a general approach to order the
items within the sequence based on the context (e.g., perceptual information,
environment description, and goals). We take a simple, efficient,
reduction-based approach where the choice and order of the items is established
by repeatedly learning simple classifiers or regressors for each "slot" in the
sequence. Our approach leverages recent work on submodular function
maximization to provide a formal regret reduction from submodular sequence
optimization to simple cost-sensitive prediction. We apply our contextual
sequence prediction algorithm to optimize control libraries and demonstrate
results on two robotics problems: manipulator trajectory prediction and mobile
robot path planning.
| Debadeepta Dey, Tian Yu Liu, Martial Hebert, J. Andrew Bagnell | null | 1202.2112 | null | null |
Active Bayesian Optimization: Minimizing Minimizer Entropy | stat.ME cs.LG stat.ML | The ultimate goal of optimization is to find the minimizer of a target
function.However, typical criteria for active optimization often ignore the
uncertainty about the minimizer. We propose a novel criterion for global
optimization and an associated sequential active learning strategy using
Gaussian processes.Our criterion is the reduction of uncertainty in the
posterior distribution of the function minimizer. It can also flexibly
incorporate multiple global minimizers. We implement a tractable approximation
of the criterion and demonstrate that it obtains the global minimizer
accurately compared to conventional Bayesian optimization criteria.
| Il Memming Park, Marcel Nassar, Mijung Park | null | 1202.2143 | null | null |
Scene Parsing with Multiscale Feature Learning, Purity Trees, and
Optimal Covers | cs.CV cs.LG | Scene parsing, or semantic segmentation, consists in labeling each pixel in
an image with the category of the object it belongs to. It is a challenging
task that involves the simultaneous detection, segmentation and recognition of
all the objects in the image.
The scene parsing method proposed here starts by computing a tree of segments
from a graph of pixel dissimilarities. Simultaneously, a set of dense feature
vectors is computed which encodes regions of multiple sizes centered on each
pixel. The feature extractor is a multiscale convolutional network trained from
raw pixels. The feature vectors associated with the segments covered by each
node in the tree are aggregated and fed to a classifier which produces an
estimate of the distribution of object categories contained in the segment. A
subset of tree nodes that cover the image are then selected so as to maximize
the average "purity" of the class distributions, hence maximizing the overall
likelihood that each segment will contain a single object. The convolutional
network feature extractor is trained end-to-end from raw pixels, alleviating
the need for engineered features. After training, the system is parameter free.
The system yields record accuracies on the Stanford Background Dataset (8
classes), the Sift Flow Dataset (33 classes) and the Barcelona Dataset (170
classes) while being an order of magnitude faster than competing approaches,
producing a 320 \times 240 image labeling in less than 1 second.
| Cl\'ement Farabet and Camille Couprie and Laurent Najman and Yann
LeCun | null | 1202.2160 | null | null |
Craniofacial reconstruction as a prediction problem using a Latent Root
Regression model | cs.LG q-bio.TO | In this paper, we present a computer-assisted method for facial
reconstruction. This method provides an estimation of the facial shape
associated with unidentified skeletal remains. Current computer-assisted
methods using a statistical framework rely on a common set of extracted points
located on the bone and soft-tissue surfaces. Most of the facial reconstruction
methods then consist of predicting the position of the soft-tissue surface
points, when the positions of the bone surface points are known. We propose to
use Latent Root Regression for prediction. The results obtained are then
compared to those given by Principal Components Analysis linear models. In
conjunction, we have evaluated the influence of the number of skull landmarks
used. Anatomical skull landmarks are completed iteratively by points located
upon geodesics which link these anatomical landmarks, thus enabling us to
artificially increase the number of skull points. Facial points are obtained
using a mesh-matching algorithm between a common reference mesh and individual
soft-tissue surface meshes. The proposed method is validated in term of
accuracy, based on a leave-one-out cross-validation test applied to a
homogeneous database. Accuracy measures are obtained by computing the distance
between the original face surface and its reconstruction. Finally, these
results are discussed referring to current computer-assisted reconstruction
facial techniques.
| Maxime Berar (LITIS), Fran\c{c}oise Tilotta, Joan Alexis Glaun\`es
(MAP5), Yves Rozenholc (MAP5) | 10.1016/j.forsciint.2011.03.010 | 1202.2703 | null | null |
Towards minimax policies for online linear optimization with bandit
feedback | cs.LG stat.ML | We address the online linear optimization problem with bandit feedback. Our
contribution is twofold. First, we provide an algorithm (based on exponential
weights) with a regret of order $\sqrt{d n \log N}$ for any finite action set
with $N$ actions, under the assumption that the instantaneous loss is bounded
by 1. This shaves off an extraneous $\sqrt{d}$ factor compared to previous
works, and gives a regret bound of order $d \sqrt{n \log n}$ for any compact
set of actions. Without further assumptions on the action set, this last bound
is minimax optimal up to a logarithmic factor. Interestingly, our result also
shows that the minimax regret for bandit linear optimization with expert advice
in $d$ dimension is the same as for the basic $d$-armed bandit with expert
advice. Our second contribution is to show how to use the Mirror Descent
algorithm to obtain computationally efficient strategies with minimax optimal
regret bounds in specific examples. More precisely we study two canonical
action sets: the hypercube and the Euclidean ball. In the former case, we
obtain the first computationally efficient algorithm with a $d \sqrt{n}$
regret, thus improving by a factor $\sqrt{d \log n}$ over the best known result
for a computationally efficient algorithm. In the latter case, our approach
gives the first algorithm with a $\sqrt{d n \log n}$ regret, again shaving off
an extraneous $\sqrt{d}$ compared to previous works.
| S\'ebastien Bubeck, Nicol\`o Cesa-Bianchi, Sham M. Kakade | null | 1202.3079 | null | null |
Mirror Descent Meets Fixed Share (and feels no regret) | cs.LG stat.ML | Mirror descent with an entropic regularizer is known to achieve shifting
regret bounds that are logarithmic in the dimension. This is done using either
a carefully designed projection or by a weight sharing technique. Via a novel
unified analysis, we show that these two approaches deliver essentially
equivalent bounds on a notion of regret generalizing shifting, adaptive,
discounted, and other related regrets. Our analysis also captures and extends
the generalized weight sharing technique of Bousquet and Warmuth, and can be
refined in several ways, including improvements for small losses and adaptive
tuning of parameters.
| Nicol\`o Cesa-Bianchi, Pierre Gaillard (INRIA Paris - Rocquencourt,
DMA), Gabor Lugosi (ICREA), Gilles Stoltz (INRIA Paris - Rocquencourt, DMA,
GREGH) | null | 1202.3323 | null | null |
An efficient high-quality hierarchical clustering algorithm for
automatic inference of software architecture from the source code of a
software system | cs.AI cs.LG cs.SE | It is a high-quality algorithm for hierarchical clustering of large software
source code. This effectively allows to break the complexity of tens of
millions lines of source code, so that a human software engineer can comprehend
a software system at high level by means of looking at its architectural
diagram that is reconstructed automatically from the source code of the
software system. The architectural diagram shows a tree of subsystems having
OOP classes in its leaves (in the other words, a nested software
decomposition). The tool reconstructs the missing
(inconsistent/incomplete/inexistent) architectural documentation for a software
system from its source code. This facilitates software maintenance: change
requests can be performed substantially faster. Simply speaking, this unique
tool allows to lift the comprehensible grain of object-oriented software
systems from OOP class-level to subsystem-level. It is estimated that a
commercial tool, developed on the basis of this work, will reduce software
maintenance expenses 10 times on the current needs, and will allow to implement
next-generation software systems which are currently too complex to be within
the range of human comprehension, therefore can't yet be designed or
implemented. Implemented prototype in Open Source:
http://sourceforge.net/p/insoar/code-0/1/tree/
| Sarge Rogatch | null | 1202.3335 | null | null |
Near-optimal Coresets For Least-Squares Regression | cs.DS cs.LG | We study (constrained) least-squares regression as well as multiple response
least-squares regression and ask the question of whether a subset of the data,
a coreset, suffices to compute a good approximate solution to the regression.
We give deterministic, low order polynomial-time algorithms to construct such
coresets with approximation guarantees, together with lower bounds indicating
that there is not much room for improvement upon our results.
| Christos Boutsidis, Petros Drineas, Malik Magdon-Ismail | 10.1109/TIT.2013.2272457 | 1202.3505 | null | null |
Finding a most biased coin with fewest flips | cs.DS cs.LG | We study the problem of learning a most biased coin among a set of coins by
tossing the coins adaptively. The goal is to minimize the number of tosses
until we identify a coin i* whose posterior probability of being most biased is
at least 1-delta for a given delta. Under a particular probabilistic model, we
give an optimal algorithm, i.e., an algorithm that minimizes the expected
number of future tosses. The problem is closely related to finding the best arm
in the multi-armed bandit problem using adaptive strategies. Our algorithm
employs an optimal adaptive strategy -- a strategy that performs the best
possible action at each step after observing the outcomes of all previous coin
tosses. Consequently, our algorithm is also optimal for any starting history of
outcomes. To our knowledge, this is the first algorithm that employs an optimal
adaptive strategy under a Bayesian setting for this problem. Our proof of
optimality employs tools from the field of Markov games.
| Karthekeyan Chandrasekaran and Richard Karp | null | 1202.3639 | null | null |
Guaranteed clustering and biclustering via semidefinite programming | math.OC cs.LG | Identifying clusters of similar objects in data plays a significant role in a
wide range of applications. As a model problem for clustering, we consider the
densest k-disjoint-clique problem, whose goal is to identify the collection of
k disjoint cliques of a given weighted complete graph maximizing the sum of the
densities of the complete subgraphs induced by these cliques. In this paper, we
establish conditions ensuring exact recovery of the densest k cliques of a
given graph from the optimal solution of a particular semidefinite program. In
particular, the semidefinite relaxation is exact for input graphs corresponding
to data consisting of k large, distinct clusters and a smaller number of
outliers. This approach also yields a semidefinite relaxation for the
biclustering problem with similar recovery guarantees. Given a set of objects
and a set of features exhibited by these objects, biclustering seeks to
simultaneously group the objects and features according to their expression
levels. This problem may be posed as partitioning the nodes of a weighted
bipartite complete graph such that the sum of the densities of the resulting
bipartite complete subgraphs is maximized. As in our analysis of the densest
k-disjoint-clique problem, we show that the correct partition of the objects
and features can be recovered from the optimal solution of a semidefinite
program in the case that the given data consists of several disjoint sets of
objects exhibiting similar features. Empirical evidence from numerical
experiments supporting these theoretical guarantees is also provided.
| Brendan P. W. Ames | 10.1007/s10107-013-0729-x | 1202.3663 | null | null |
Active Diagnosis via AUC Maximization: An Efficient Approach for
Multiple Fault Identification in Large Scale, Noisy Networks | cs.LG cs.AI stat.ML | The problem of active diagnosis arises in several applications such as
disease diagnosis, and fault diagnosis in computer networks, where the goal is
to rapidly identify the binary states of a set of objects (e.g., faulty or
working) by sequentially selecting, and observing, (noisy) responses to binary
valued queries. Current algorithms in this area rely on loopy belief
propagation for active query selection. These algorithms have an exponential
time complexity, making them slow and even intractable in large networks. We
propose a rank-based greedy algorithm that sequentially chooses queries such
that the area under the ROC curve of the rank-based output is maximized. The
AUC criterion allows us to make a simplifying assumption that significantly
reduces the complexity of active query selection (from exponential to near
quadratic), with little or no compromise on the performance quality.
| Gowtham Bellala, Jason Stanley, Clayton Scott, Suresh K. Bhavnani | null | 1202.3701 | null | null |
Semi-supervised Learning with Density Based Distances | cs.LG stat.ML | We present a simple, yet effective, approach to Semi-Supervised Learning. Our
approach is based on estimating density-based distances (DBD) using a shortest
path calculation on a graph. These Graph-DBD estimates can then be used in any
distance-based supervised learning method, such as Nearest Neighbor methods and
SVMs with RBF kernels. In order to apply the method to very large data sets, we
also present a novel algorithm which integrates nearest neighbor computations
into the shortest path search and can find exact shortest paths even in
extremely large dense graphs. Significant runtime improvement over the commonly
used Laplacian regularization method is then shown on a large scale dataset.
| Avleen S. Bijral, Nathan Ratliff, Nathan Srebro | null | 1202.3702 | null | null |
Near-Optimal Target Learning With Stochastic Binary Signals | cs.LG stat.ML | We study learning in a noisy bisection model: specifically, Bayesian
algorithms to learn a target value V given access only to noisy realizations of
whether V is less than or greater than a threshold theta. At step t = 0, 1, 2,
..., the learner sets threshold theta t and observes a noisy realization of
sign(V - theta t). After T steps, the goal is to output an estimate V^ which is
within an eta-tolerance of V . This problem has been studied, predominantly in
environments with a fixed error probability q < 1/2 for the noisy realization
of sign(V - theta t). In practice, it is often the case that q can approach
1/2, especially as theta -> V, and there is little known when this happens. We
give a pseudo-Bayesian algorithm which provably converges to V. When the true
prior matches our algorithm's Gaussian prior, we show near-optimal expected
performance. Our methods extend to the general multiple-threshold setting where
the observation noisily indicates which of k >= 2 regions V belongs to.
| Mithun Chakraborty, Sanmay Das, Malik Magdon-Ismail | null | 1202.3704 | null | null |
Smoothing Proximal Gradient Method for General Structured Sparse
Learning | cs.LG stat.ML | We study the problem of learning high dimensional regression models
regularized by a structured-sparsity-inducing penalty that encodes prior
structural information on either input or output sides. We consider two widely
adopted types of such penalties as our motivating examples: 1) overlapping
group lasso penalty, based on the l1/l2 mixed-norm penalty, and 2) graph-guided
fusion penalty. For both types of penalties, due to their non-separability,
developing an efficient optimization method has remained a challenging problem.
In this paper, we propose a general optimization approach, called smoothing
proximal gradient method, which can solve the structured sparse regression
problems with a smooth convex loss and a wide spectrum of
structured-sparsity-inducing penalties. Our approach is based on a general
smoothing technique of Nesterov. It achieves a convergence rate faster than the
standard first-order method, subgradient method, and is much more scalable than
the most widely used interior-point method. Numerical results are reported to
demonstrate the efficiency and scalability of the proposed method.
| Xi Chen, Qihang Lin, Seyoung Kim, Jaime G. Carbonell, Eric P. Xing | null | 1202.3708 | null | null |
Ensembles of Kernel Predictors | cs.LG stat.ML | This paper examines the problem of learning with a finite and possibly large
set of p base kernels. It presents a theoretical and empirical analysis of an
approach addressing this problem based on ensembles of kernel predictors. This
includes novel theoretical guarantees based on the Rademacher complexity of the
corresponding hypothesis sets, the introduction and analysis of a learning
algorithm based on these hypothesis sets, and a series of experiments using
ensembles of kernel predictors with several data sets. Both convex combinations
of kernel-based hypotheses and more general Lq-regularized nonnegative
combinations are analyzed. These theoretical, algorithmic, and empirical
results are compared with those achieved by using learning kernel techniques,
which can be viewed as another approach for solving the same problem.
| Corinna Cortes, Mehryar Mohri, Afshin Rostamizadeh | null | 1202.3712 | null | null |
Active Learning for Developing Personalized Treatment | cs.LG stat.ML | The personalization of treatment via bio-markers and other risk categories
has drawn increasing interest among clinical scientists. Personalized treatment
strategies can be learned using data from clinical trials, but such trials are
very costly to run. This paper explores the use of active learning techniques
to design more efficient trials, addressing issues such as whom to recruit, at
what point in the trial, and which treatment to assign, throughout the duration
of the trial. We propose a minimax bandit model with two different optimization
criteria, and discuss the computational challenges and issues pertaining to
this approach. We evaluate our active learning policies using both simulated
data, and data modeled after a clinical trial for treating depressed
individuals, and contrast our methods with other plausible active learning
policies.
| Kun Deng, Joelle Pineau, Susan A. Murphy | null | 1202.3714 | null | null |
Boosting as a Product of Experts | cs.LG stat.ML | In this paper, we derive a novel probabilistic model of boosting as a Product
of Experts. We re-derive the boosting algorithm as a greedy incremental model
selection procedure which ensures that addition of new experts to the ensemble
does not decrease the likelihood of the data. These learning rules lead to a
generic boosting algorithm - POE- Boost which turns out to be similar to the
AdaBoost algorithm under certain assumptions on the expert probabilities. The
paper then extends the POEBoost algorithm to POEBoost.CS which handles
hypothesis that produce probabilistic predictions. This new algorithm is shown
to have better generalization performance compared to other state of the art
algorithms.
| Narayanan U. Edakunni, Gary Brown, Tim Kovacs | null | 1202.3716 | null | null |
PAC-Bayesian Policy Evaluation for Reinforcement Learning | cs.LG stat.ML | Bayesian priors offer a compact yet general means of incorporating domain
knowledge into many learning tasks. The correctness of the Bayesian analysis
and inference, however, largely depends on accuracy and correctness of these
priors. PAC-Bayesian methods overcome this problem by providing bounds that
hold regardless of the correctness of the prior distribution. This paper
introduces the first PAC-Bayesian bound for the batch reinforcement learning
problem with function approximation. We show how this bound can be used to
perform model-selection in a transfer learning scenario. Our empirical results
confirm that PAC-Bayesian policy evaluation is able to leverage prior
distributions when they are informative and, unlike standard Bayesian RL
approaches, ignore them when they are misleading.
| Mahdi MIlani Fard, Joelle Pineau, Csaba Szepesvari | null | 1202.3717 | null | null |
Hierarchical Affinity Propagation | cs.LG cs.AI stat.ML | Affinity propagation is an exemplar-based clustering algorithm that finds a
set of data-points that best exemplify the data, and associates each datapoint
with one exemplar. We extend affinity propagation in a principled way to solve
the hierarchical clustering problem, which arises in a variety of domains
including biology, sensor networks and decision making in operational research.
We derive an inference algorithm that operates by propagating information up
and down the hierarchy, and is efficient despite the high-order potentials
required for the graphical model formulation. We demonstrate that our method
outperforms greedy techniques that cluster one layer at a time. We show that on
an artificial dataset designed to mimic the HIV-strain mutation dynamics, our
method outperforms related methods. For real HIV sequences, where the ground
truth is not available, we show our method achieves better results, in terms of
the underlying objective function, and show the results correspond meaningfully
to geographical location and strain subtypes. Finally we report results on
using the method for the analysis of mass spectra, showing it performs
favorably compared to state-of-the-art methods.
| Inmar Givoni, Clement Chung, Brendan J. Frey | null | 1202.3722 | null | null |
Generalized Fisher Score for Feature Selection | cs.LG stat.ML | Fisher score is one of the most widely used supervised feature selection
methods. However, it selects each feature independently according to their
scores under the Fisher criterion, which leads to a suboptimal subset of
features. In this paper, we present a generalized Fisher score to jointly
select features. It aims at finding an subset of features, which maximize the
lower bound of traditional Fisher score. The resulting feature selection
problem is a mixed integer programming, which can be reformulated as a
quadratically constrained linear programming (QCLP). It is solved by cutting
plane algorithm, in each iteration of which a multiple kernel learning problem
is solved alternatively by multivariate ridge regression and projected gradient
descent. Experiments on benchmark data sets indicate that the proposed method
outperforms Fisher score as well as many other state-of-the-art feature
selection methods.
| Quanquan Gu, Zhenhui Li, Jiawei Han | null | 1202.3725 | null | null |
Active Semi-Supervised Learning using Submodular Functions | cs.LG stat.ML | We consider active, semi-supervised learning in an offline transductive
setting. We show that a previously proposed error bound for active learning on
undirected weighted graphs can be generalized by replacing graph cut with an
arbitrary symmetric submodular function. Arbitrary non-symmetric submodular
functions can be used via symmetrization. Different choices of submodular
functions give different versions of the error bound that are appropriate for
different kinds of problems. Moreover, the bound is deterministic and holds for
adversarially chosen labels. We show exactly minimizing this error bound is
NP-complete. However, we also introduce for any submodular function an
associated active semi-supervised learning method that approximately minimizes
the corresponding error bound. We show that the error bound is tight in the
sense that there is no other bound of the same form which is better. Our
theoretical results are supported by experiments on real data.
| Andrew Guillory, Jeff A. Bilmes | null | 1202.3726 | null | null |
Bregman divergence as general framework to estimate unnormalized
statistical models | cs.LG stat.ML | We show that the Bregman divergence provides a rich framework to estimate
unnormalized statistical models for continuous or discrete random variables,
that is, models which do not integrate or sum to one, respectively. We prove
that recent estimation methods such as noise-contrastive estimation, ratio
matching, and score matching belong to the proposed framework, and explain
their interconnection based on supervised learning. Further, we discuss the
role of boosting in unsupervised learning.
| Michael Gutmann, Jun-ichiro Hirayama | null | 1202.3727 | null | null |
Sequential Inference for Latent Force Models | cs.LG stat.ML | Latent force models (LFMs) are hybrid models combining mechanistic principles
with non-parametric components. In this article, we shall show how LFMs can be
equivalently formulated and solved using the state variable approach. We shall
also show how the Gaussian process prior used in LFMs can be equivalently
formulated as a linear statespace model driven by a white noise process and how
inference on the resulting model can be efficiently implemented using Kalman
filter and smoother. Then we shall show how the recently proposed switching LFM
can be reformulated using the state variable approach, and how we can construct
a probabilistic model for the switches by formulating a similar switching LFM
as a switching linear dynamic system (SLDS). We illustrate the performance of
the proposed methodology in simulated scenarios and apply it to inferring the
switching points in GPS data collected from car movement data in urban
environment.
| Jouni Hartikainen, Simo Sarkka | null | 1202.3730 | null | null |
What Cannot be Learned with Bethe Approximations | cs.LG stat.ML | We address the problem of learning the parameters in graphical models when
inference is intractable. A common strategy in this case is to replace the
partition function with its Bethe approximation. We show that there exists a
regime of empirical marginals where such Bethe learning will fail. By failure
we mean that the empirical marginals cannot be recovered from the approximated
maximum likelihood parameters (i.e., moment matching is not achieved). We
provide several conditions on empirical marginals that yield outer and inner
bounds on the set of Bethe learnable marginals. An interesting implication of
our results is that there exists a large class of marginals that cannot be
obtained as stable fixed points of belief propagation. Taken together our
results provide a novel approach to analyzing learning with Bethe
approximations and highlight when it can be expected to work or fail.
| Uri Heinemann, Amir Globerson | null | 1202.3731 | null | null |
Sum-Product Networks: A New Deep Architecture | cs.LG cs.AI stat.ML | The key limiting factor in graphical model inference and learning is the
complexity of the partition function. We thus ask the question: what are
general conditions under which the partition function is tractable? The answer
leads to a new kind of deep architecture, which we call sum-product networks
(SPNs). SPNs are directed acyclic graphs with variables as leaves, sums and
products as internal nodes, and weighted edges. We show that if an SPN is
complete and consistent it represents the partition function and all marginals
of some graphical model, and give semantics to its nodes. Essentially all
tractable graphical models can be cast as SPNs, but SPNs are also strictly more
general. We then propose learning algorithms for SPNs, based on backpropagation
and EM. Experiments show that inference and learning with SPNs can be both
faster and more accurate than with standard deep networks. For example, SPNs
perform image completion better than state-of-the-art deep networks for this
task. SPNs also have intriguing potential connections to the architecture of
the cortex.
| Hoifung Poon, Pedro Domingos | null | 1202.3732 | null | null |
Lipschitz Parametrization of Probabilistic Graphical Models | cs.LG stat.ML | We show that the log-likelihood of several probabilistic graphical models is
Lipschitz continuous with respect to the lp-norm of the parameters. We discuss
several implications of Lipschitz parametrization. We present an upper bound of
the Kullback-Leibler divergence that allows understanding methods that penalize
the lp-norm of differences of parameters as the minimization of that upper
bound. The expected log-likelihood is lower bounded by the negative lp-norm,
which allows understanding the generalization ability of probabilistic models.
The exponential of the negative lp-norm is involved in the lower bound of the
Bayes error rate, which shows that it is reasonable to use parameters as
features in algorithms that rely on metric spaces (e.g. classification,
dimensionality reduction, clustering). Our results do not rely on specific
algorithms for learning the structure or parameters. We show preliminary
results for activity recognition and temporal segmentation.
| Jean Honorio | null | 1202.3733 | null | null |
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