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Path Integral Policy Improvement with Covariance Matrix Adaptation | cs.LG | There has been a recent focus in reinforcement learning on addressing
continuous state and action problems by optimizing parameterized policies. PI2
is a recent example of this approach. It combines a derivation from first
principles of stochastic optimal control with tools from statistical estimation
theory. In this paper, we consider PI2 as a member of the wider family of
methods which share the concept of probability-weighted averaging to
iteratively update parameters to optimize a cost function. We compare PI2 to
other members of the same family - Cross-Entropy Methods and CMAES - at the
conceptual level and in terms of performance. The comparison suggests the
derivation of a novel algorithm which we call PI2-CMA for "Path Integral Policy
Improvement with Covariance Matrix Adaptation". PI2-CMA's main advantage is
that it determines the magnitude of the exploration noise automatically.
| Freek Stulp (Ecole Nationale Superieure de Techniques Avancees),
Olivier Sigaud (Universite Pierre et Marie Curie) | null | 1206.4621 | null | null |
A Graphical Model Formulation of Collaborative Filtering Neighbourhood
Methods with Fast Maximum Entropy Training | cs.LG cs.IR stat.ML | Item neighbourhood methods for collaborative filtering learn a weighted graph
over the set of items, where each item is connected to those it is most similar
to. The prediction of a user's rating on an item is then given by that rating
of neighbouring items, weighted by their similarity. This paper presents a new
neighbourhood approach which we call item fields, whereby an undirected
graphical model is formed over the item graph. The resulting prediction rule is
a simple generalization of the classical approaches, which takes into account
non-local information in the graph, allowing its best results to be obtained
when using drastically fewer edges than other neighbourhood approaches. A fast
approximate maximum entropy training method based on the Bethe approximation is
presented, which uses a simple gradient ascent procedure. When using
precomputed sufficient statistics on the Movielens datasets, our method is
faster than maximum likelihood approaches by two orders of magnitude.
| Aaron Defazio (ANU), Tiberio Caetano (NICTA and Australian National
University) | null | 1206.4622 | null | null |
On the Size of the Online Kernel Sparsification Dictionary | cs.LG stat.ML | We analyze the size of the dictionary constructed from online kernel
sparsification, using a novel formula that expresses the expected determinant
of the kernel Gram matrix in terms of the eigenvalues of the covariance
operator. Using this formula, we are able to connect the cardinality of the
dictionary with the eigen-decay of the covariance operator. In particular, we
show that under certain technical conditions, the size of the dictionary will
always grow sub-linearly in the number of data points, and, as a consequence,
the kernel linear regressor constructed from the resulting dictionary is
consistent.
| Yi Sun (IDSIA), Faustino Gomez (IDSIA), Juergen Schmidhuber (IDSIA) | null | 1206.4623 | null | null |
Robust Multiple Manifolds Structure Learning | cs.LG stat.ML | We present a robust multiple manifolds structure learning (RMMSL) scheme to
robustly estimate data structures under the multiple low intrinsic dimensional
manifolds assumption. In the local learning stage, RMMSL efficiently estimates
local tangent space by weighted low-rank matrix factorization. In the global
learning stage, we propose a robust manifold clustering method based on local
structure learning results. The proposed clustering method is designed to get
the flattest manifolds clusters by introducing a novel curved-level similarity
function. Our approach is evaluated and compared to state-of-the-art methods on
synthetic data, handwritten digit images, human motion capture data and
motorbike videos. We demonstrate the effectiveness of the proposed approach,
which yields higher clustering accuracy, and produces promising results for
challenging tasks of human motion segmentation and motion flow learning from
videos.
| Dian Gong (Univ. of Southern California), Xuemei Zhao (Univ of
Southern California), Gerard Medioni (University of Southern California) | null | 1206.4624 | null | null |
Optimizing F-measure: A Tale of Two Approaches | cs.LG | F-measures are popular performance metrics, particularly for tasks with
imbalanced data sets. Algorithms for learning to maximize F-measures follow two
approaches: the empirical utility maximization (EUM) approach learns a
classifier having optimal performance on training data, while the
decision-theoretic approach learns a probabilistic model and then predicts
labels with maximum expected F-measure. In this paper, we investigate the
theoretical justifications and connections for these two approaches, and we
study the conditions under which one approach is preferable to the other using
synthetic and real datasets. Given accurate models, our results suggest that
the two approaches are asymptotically equivalent given large training and test
sets. Nevertheless, empirically, the EUM approach appears to be more robust
against model misspecification, and given a good model, the decision-theoretic
approach appears to be better for handling rare classes and a common domain
adaptation scenario.
| Ye Nan (NUS), Kian Ming Chai (DSO National Laboratories), Wee Sun Lee
(NUS), Hai Leong Chieu (DSO National Laboratories) | null | 1206.4625 | null | null |
On-Line Portfolio Selection with Moving Average Reversion | cs.CE cs.LG q-fin.PM | On-line portfolio selection has attracted increasing interests in machine
learning and AI communities recently. Empirical evidences show that stock's
high and low prices are temporary and stock price relatives are likely to
follow the mean reversion phenomenon. While the existing mean reversion
strategies are shown to achieve good empirical performance on many real
datasets, they often make the single-period mean reversion assumption, which is
not always satisfied in some real datasets, leading to poor performance when
the assumption does not hold. To overcome the limitation, this article proposes
a multiple-period mean reversion, or so-called Moving Average Reversion (MAR),
and a new on-line portfolio selection strategy named "On-Line Moving Average
Reversion" (OLMAR), which exploits MAR by applying powerful online learning
techniques. From our empirical results, we found that OLMAR can overcome the
drawback of existing mean reversion algorithms and achieve significantly better
results, especially on the datasets where the existing mean reversion
algorithms failed. In addition to superior trading performance, OLMAR also runs
extremely fast, further supporting its practical applicability to a wide range
of applications.
| Bin Li (NTU), Steven C.H. Hoi (NTU) | null | 1206.4626 | null | null |
Convergence Rates of Biased Stochastic Optimization for Learning Sparse
Ising Models | cs.LG stat.ML | We study the convergence rate of stochastic optimization of exact (NP-hard)
objectives, for which only biased estimates of the gradient are available. We
motivate this problem in the context of learning the structure and parameters
of Ising models. We first provide a convergence-rate analysis of deterministic
errors for forward-backward splitting (FBS). We then extend our analysis to
biased stochastic errors, by first characterizing a family of samplers and
providing a high probability bound that allows understanding not only FBS, but
also proximal gradient (PG) methods. We derive some interesting conclusions:
FBS requires only a logarithmically increasing number of random samples in
order to converge (although at a very low rate); the required number of random
samples is the same for the deterministic and the biased stochastic setting for
FBS and basic PG; accelerated PG is not guaranteed to converge in the biased
stochastic setting.
| Jean Honorio (Stony Brook University) | null | 1206.4627 | null | null |
Robust PCA in High-dimension: A Deterministic Approach | cs.LG stat.ML | We consider principal component analysis for contaminated data-set in the
high dimensional regime, where the dimensionality of each observation is
comparable or even more than the number of observations. We propose a
deterministic high-dimensional robust PCA algorithm which inherits all
theoretical properties of its randomized counterpart, i.e., it is tractable,
robust to contaminated points, easily kernelizable, asymptotic consistent and
achieves maximal robustness -- a breakdown point of 50%. More importantly, the
proposed method exhibits significantly better computational efficiency, which
makes it suitable for large-scale real applications.
| Jiashi Feng (NUS), Huan Xu (NUS), Shuicheng Yan (NUS) | null | 1206.4628 | null | null |
Multiple Kernel Learning from Noisy Labels by Stochastic Programming | cs.LG | We study the problem of multiple kernel learning from noisy labels. This is
in contrast to most of the previous studies on multiple kernel learning that
mainly focus on developing efficient algorithms and assume perfectly labeled
training examples. Directly applying the existing multiple kernel learning
algorithms to noisily labeled examples often leads to suboptimal performance
due to the incorrect class assignments. We address this challenge by casting
multiple kernel learning from noisy labels into a stochastic programming
problem, and presenting a minimax formulation. We develop an efficient
algorithm for solving the related convex-concave optimization problem with a
fast convergence rate of $O(1/T)$ where $T$ is the number of iterations.
Empirical studies on UCI data sets verify both the effectiveness of the
proposed framework and the efficiency of the proposed optimization algorithm.
| Tianbao Yang (Michigan State University), Mehrdad Mahdavi (Michigan
State University), Rong Jin (Michigan State University), Lijun Zhang
(Michigan State University), Yang Zhou (Yahoo! Labs) | null | 1206.4629 | null | null |
Efficient Decomposed Learning for Structured Prediction | cs.LG | Structured prediction is the cornerstone of several machine learning
applications. Unfortunately, in structured prediction settings with expressive
inter-variable interactions, exact inference-based learning algorithms, e.g.
Structural SVM, are often intractable. We present a new way, Decomposed
Learning (DecL), which performs efficient learning by restricting the inference
step to a limited part of the structured spaces. We provide characterizations
based on the structure, target parameters, and gold labels, under which DecL is
equivalent to exact learning. We then show that in real world settings, where
our theoretical assumptions may not completely hold, DecL-based algorithms are
significantly more efficient and as accurate as exact learning.
| Rajhans Samdani (University of Illinois, U-C), Dan Roth (University of
Illinois, U-C) | null | 1206.4630 | null | null |
A Poisson convolution model for characterizing topical content with word
frequency and exclusivity | cs.LG cs.CL cs.IR stat.ME stat.ML | An ongoing challenge in the analysis of document collections is how to
summarize content in terms of a set of inferred themes that can be interpreted
substantively in terms of topics. The current practice of parametrizing the
themes in terms of most frequent words limits interpretability by ignoring the
differential use of words across topics. We argue that words that are both
common and exclusive to a theme are more effective at characterizing topical
content. We consider a setting where professional editors have annotated
documents to a collection of topic categories, organized into a tree, in which
leaf-nodes correspond to the most specific topics. Each document is annotated
to multiple categories, at different levels of the tree. We introduce a
hierarchical Poisson convolution model to analyze annotated documents in this
setting. The model leverages the structure among categories defined by
professional editors to infer a clear semantic description for each topic in
terms of words that are both frequent and exclusive. We carry out a large
randomized experiment on Amazon Turk to demonstrate that topic summaries based
on the FREX score are more interpretable than currently established frequency
based summaries, and that the proposed model produces more efficient estimates
of exclusivity than with currently models. We also develop a parallelized
Hamiltonian Monte Carlo sampler that allows the inference to scale to millions
of documents.
| Edoardo M Airoldi, Jonathan M Bischof | null | 1206.4631 | null | null |
Fast Bounded Online Gradient Descent Algorithms for Scalable
Kernel-Based Online Learning | cs.LG stat.ML | Kernel-based online learning has often shown state-of-the-art performance for
many online learning tasks. It, however, suffers from a major shortcoming, that
is, the unbounded number of support vectors, making it non-scalable and
unsuitable for applications with large-scale datasets. In this work, we study
the problem of bounded kernel-based online learning that aims to constrain the
number of support vectors by a predefined budget. Although several algorithms
have been proposed in literature, they are neither computationally efficient
due to their intensive budget maintenance strategy nor effective due to the use
of simple Perceptron algorithm. To overcome these limitations, we propose a
framework for bounded kernel-based online learning based on an online gradient
descent approach. We propose two efficient algorithms of bounded online
gradient descent (BOGD) for scalable kernel-based online learning: (i) BOGD by
maintaining support vectors using uniform sampling, and (ii) BOGD++ by
maintaining support vectors using non-uniform sampling. We present theoretical
analysis of regret bound for both algorithms, and found promising empirical
performance in terms of both efficacy and efficiency by comparing them to
several well-known algorithms for bounded kernel-based online learning on
large-scale datasets.
| Peilin Zhao (NTU), Jialei Wang (NTU), Pengcheng Wu (NTU), Rong Jin
(MSU), Steven C.H. Hoi (NTU) | null | 1206.4633 | null | null |
Artist Agent: A Reinforcement Learning Approach to Automatic Stroke
Generation in Oriental Ink Painting | cs.LG cs.GR stat.ML | Oriental ink painting, called Sumi-e, is one of the most appealing painting
styles that has attracted artists around the world. Major challenges in
computer-based Sumi-e simulation are to abstract complex scene information and
draw smooth and natural brush strokes. To automatically find such strokes, we
propose to model the brush as a reinforcement learning agent, and learn desired
brush-trajectories by maximizing the sum of rewards in the policy search
framework. We also provide elaborate design of actions, states, and rewards
tailored for a Sumi-e agent. The effectiveness of our proposed approach is
demonstrated through simulated Sumi-e experiments.
| Ning Xie (Tokyo Institute of Technology), Hirotaka Hachiya (Tokyo
Institute of Technology), Masashi Sugiyama (Tokyo Institute of Technology) | 10.1587/transinf.E96.D.1134 | 1206.4634 | null | null |
Deep Mixtures of Factor Analysers | cs.LG stat.ML | An efficient way to learn deep density models that have many layers of latent
variables is to learn one layer at a time using a model that has only one layer
of latent variables. After learning each layer, samples from the posterior
distributions for that layer are used as training data for learning the next
layer. This approach is commonly used with Restricted Boltzmann Machines, which
are undirected graphical models with a single hidden layer, but it can also be
used with Mixtures of Factor Analysers (MFAs) which are directed graphical
models. In this paper, we present a greedy layer-wise learning algorithm for
Deep Mixtures of Factor Analysers (DMFAs). Even though a DMFA can be converted
to an equivalent shallow MFA by multiplying together the factor loading
matrices at different levels, learning and inference are much more efficient in
a DMFA and the sharing of each lower-level factor loading matrix by many
different higher level MFAs prevents overfitting. We demonstrate empirically
that DMFAs learn better density models than both MFAs and two types of
Restricted Boltzmann Machine on a wide variety of datasets.
| Yichuan Tang (University of Toronto), Ruslan Salakhutdinov (University
of Toronto), Geoffrey Hinton (University of Toronto) | null | 1206.4635 | null | null |
Modeling Latent Variable Uncertainty for Loss-based Learning | cs.LG cs.AI cs.CV | We consider the problem of parameter estimation using weakly supervised
datasets, where a training sample consists of the input and a partially
specified annotation, which we refer to as the output. The missing information
in the annotation is modeled using latent variables. Previous methods
overburden a single distribution with two separate tasks: (i) modeling the
uncertainty in the latent variables during training; and (ii) making accurate
predictions for the output and the latent variables during testing. We propose
a novel framework that separates the demands of the two tasks using two
distributions: (i) a conditional distribution to model the uncertainty of the
latent variables for a given input-output pair; and (ii) a delta distribution
to predict the output and the latent variables for a given input. During
learning, we encourage agreement between the two distributions by minimizing a
loss-based dissimilarity coefficient. Our approach generalizes latent SVM in
two important ways: (i) it models the uncertainty over latent variables instead
of relying on a pointwise estimate; and (ii) it allows the use of loss
functions that depend on latent variables, which greatly increases its
applicability. We demonstrate the efficacy of our approach on two challenging
problems---object detection and action detection---using publicly available
datasets.
| M. Pawan Kumar (Ecole Centrale Paris), Ben Packer (Stanford
University), Daphne Koller (Stanford University) | null | 1206.4636 | null | null |
Learning to Identify Regular Expressions that Describe Email Campaigns | cs.LG cs.CL stat.ML | This paper addresses the problem of inferring a regular expression from a
given set of strings that resembles, as closely as possible, the regular
expression that a human expert would have written to identify the language.
This is motivated by our goal of automating the task of postmasters of an email
service who use regular expressions to describe and blacklist email spam
campaigns. Training data contains batches of messages and corresponding regular
expressions that an expert postmaster feels confident to blacklist. We model
this task as a learning problem with structured output spaces and an
appropriate loss function, derive a decoder and the resulting optimization
problem, and a report on a case study conducted with an email service.
| Paul Prasse (University of Potsdam), Christoph Sawade (University of
Potsdam), Niels Landwehr (University of Potsdam), Tobias Scheffer (University
of Potsdam) | null | 1206.4637 | null | null |
Adaptive Regularization for Weight Matrices | cs.LG cs.AI | Algorithms for learning distributions over weight-vectors, such as AROW were
recently shown empirically to achieve state-of-the-art performance at various
problems, with strong theoretical guaranties. Extending these algorithms to
matrix models pose challenges since the number of free parameters in the
covariance of the distribution scales as $n^4$ with the dimension $n$ of the
matrix, and $n$ tends to be large in real applications. We describe, analyze
and experiment with two new algorithms for learning distribution of matrix
models. Our first algorithm maintains a diagonal covariance over the parameters
and can handle large covariance matrices. The second algorithm factors the
covariance to capture inter-features correlation while keeping the number of
parameters linear in the size of the original matrix. We analyze both
algorithms in the mistake bound model and show a superior precision performance
of our approach over other algorithms in two tasks: retrieving similar images,
and ranking similar documents. The factored algorithm is shown to attain faster
convergence rate.
| Koby Crammer (The Technion), Gal Chechik (Bar Ilan University and
Google research) | null | 1206.4639 | null | null |
Stability of matrix factorization for collaborative filtering | cs.NA cs.LG stat.ML | We study the stability vis a vis adversarial noise of matrix factorization
algorithm for matrix completion. In particular, our results include: (I) we
bound the gap between the solution matrix of the factorization method and the
ground truth in terms of root mean square error; (II) we treat the matrix
factorization as a subspace fitting problem and analyze the difference between
the solution subspace and the ground truth; (III) we analyze the prediction
error of individual users based on the subspace stability. We apply these
results to the problem of collaborative filtering under manipulator attack,
which leads to useful insights and guidelines for collaborative filtering
system design.
| Yu-Xiang Wang (National University of Singapore), Huan Xu (National
University of Singapore) | null | 1206.4640 | null | null |
Total Variation and Euler's Elastica for Supervised Learning | cs.LG cs.CV stat.ML | In recent years, total variation (TV) and Euler's elastica (EE) have been
successfully applied to image processing tasks such as denoising and
inpainting. This paper investigates how to extend TV and EE to the supervised
learning settings on high dimensional data. The supervised learning problem can
be formulated as an energy functional minimization under Tikhonov
regularization scheme, where the energy is composed of a squared loss and a
total variation smoothing (or Euler's elastica smoothing). Its solution via
variational principles leads to an Euler-Lagrange PDE. However, the PDE is
always high-dimensional and cannot be directly solved by common methods.
Instead, radial basis functions are utilized to approximate the target
function, reducing the problem to finding the linear coefficients of basis
functions. We apply the proposed methods to supervised learning tasks
(including binary classification, multi-class classification, and regression)
on benchmark data sets. Extensive experiments have demonstrated promising
results of the proposed methods.
| Tong Lin (Peking University), Hanlin Xue (Peking University), Ling
Wang (LTCI, Telecom ParisTech, Paris), Hongbin Zha (Peking University) | null | 1206.4641 | null | null |
Fast Computation of Subpath Kernel for Trees | cs.DS cs.LG stat.ML | The kernel method is a potential approach to analyzing structured data such
as sequences, trees, and graphs; however, unordered trees have not been
investigated extensively. Kimura et al. (2011) proposed a kernel function for
unordered trees on the basis of their subpaths, which are vertical
substructures of trees responsible for hierarchical information in them. Their
kernel exhibits practically good performance in terms of accuracy and speed;
however, linear-time computation is not guaranteed theoretically, unlike the
case of the other unordered tree kernel proposed by Vishwanathan and Smola
(2003). In this paper, we propose a theoretically guaranteed linear-time kernel
computation algorithm that is practically fast, and we present an efficient
prediction algorithm whose running time depends only on the size of the input
tree. Experimental results show that the proposed algorithms are quite
efficient in practice.
| Daisuke Kimura (The University of Tokyo), Hisashi Kashima (The
University of Tokyo) | null | 1206.4642 | null | null |
Lightning Does Not Strike Twice: Robust MDPs with Coupled Uncertainty | cs.LG cs.GT cs.SY | We consider Markov decision processes under parameter uncertainty. Previous
studies all restrict to the case that uncertainties among different states are
uncoupled, which leads to conservative solutions. In contrast, we introduce an
intuitive concept, termed "Lightning Does not Strike Twice," to model coupled
uncertain parameters. Specifically, we require that the system can deviate from
its nominal parameters only a bounded number of times. We give probabilistic
guarantees indicating that this model represents real life situations and
devise tractable algorithms for computing optimal control policies using this
concept.
| Shie Mannor (Technion), Ofir Mebel (Technion), Huan Xu (National
University of Singapore) | null | 1206.4643 | null | null |
Groupwise Constrained Reconstruction for Subspace Clustering | cs.LG stat.ML | Reconstruction based subspace clustering methods compute a self
reconstruction matrix over the samples and use it for spectral clustering to
obtain the final clustering result. Their success largely relies on the
assumption that the underlying subspaces are independent, which, however, does
not always hold in the applications with increasing number of subspaces. In
this paper, we propose a novel reconstruction based subspace clustering model
without making the subspace independence assumption. In our model, certain
properties of the reconstruction matrix are explicitly characterized using the
latent cluster indicators, and the affinity matrix used for spectral clustering
can be directly built from the posterior of the latent cluster indicators
instead of the reconstruction matrix. Experimental results on both synthetic
and real-world datasets show that the proposed model can outperform the
state-of-the-art methods.
| Ruijiang Li (Fudan University), Bin Li (University of Technology,
Sydney), Ke Zhang (Fudan Univ.), Cheng Jin (Fudan University), Xiangyang Xue
(Fudan University) | null | 1206.4644 | null | null |
Ensemble Methods for Convex Regression with Applications to Geometric
Programming Based Circuit Design | cs.LG cs.NA stat.ME stat.ML | Convex regression is a promising area for bridging statistical estimation and
deterministic convex optimization. New piecewise linear convex regression
methods are fast and scalable, but can have instability when used to
approximate constraints or objective functions for optimization. Ensemble
methods, like bagging, smearing and random partitioning, can alleviate this
problem and maintain the theoretical properties of the underlying estimator. We
empirically examine the performance of ensemble methods for prediction and
optimization, and then apply them to device modeling and constraint
approximation for geometric programming based circuit design.
| Lauren Hannah (Duke University), David Dunson (Duke University) | null | 1206.4645 | null | null |
Partial-Hessian Strategies for Fast Learning of Nonlinear Embeddings | cs.LG stat.ML | Stochastic neighbor embedding (SNE) and related nonlinear manifold learning
algorithms achieve high-quality low-dimensional representations of similarity
data, but are notoriously slow to train. We propose a generic formulation of
embedding algorithms that includes SNE and other existing algorithms, and study
their relation with spectral methods and graph Laplacians. This allows us to
define several partial-Hessian optimization strategies, characterize their
global and local convergence, and evaluate them empirically. We achieve up to
two orders of magnitude speedup over existing training methods with a strategy
(which we call the spectral direction) that adds nearly no overhead to the
gradient and yet is simple, scalable and applicable to several existing and
future embedding algorithms.
| Max Vladymyrov (UC Merced), Miguel Carreira-Perpinan (UC Merced) | null | 1206.4646 | null | null |
Active Learning for Matching Problems | cs.LG cs.AI cs.IR | Effective learning of user preferences is critical to easing user burden in
various types of matching problems. Equally important is active query selection
to further reduce the amount of preference information users must provide. We
address the problem of active learning of user preferences for matching
problems, introducing a novel method for determining probabilistic matchings,
and developing several new active learning strategies that are sensitive to the
specific matching objective. Experiments with real-world data sets spanning
diverse domains demonstrate that matching-sensitive active learning
| Laurent Charlin (University of Toronto), Rich Zemel (University of
Toronto), Craig Boutilier (University of Toronto) | null | 1206.4647 | null | null |
Two-Manifold Problems with Applications to Nonlinear System
Identification | 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, 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. We propose a class of algorithms for two-manifold
problems, based on spectral decomposition of cross-covariance operators in
Hilbert space, and discuss when two-manifold problems are useful. Finally, we
demonstrate that solving a two-manifold problem can aid in learning a nonlinear
dynamical system from limited data.
| Byron Boots (Carnegie Mellon University), Geoff Gordon (Carnegie
Mellon University) | null | 1206.4648 | null | null |
Learning Efficient Structured Sparse Models | cs.LG cs.CV stat.ML | We present a comprehensive framework for structured sparse coding and
modeling extending the recent ideas of using learnable fast regressors to
approximate exact sparse codes. For this purpose, we develop a novel
block-coordinate proximal splitting method for the iterative solution of
hierarchical sparse coding problems, and show an efficient feed forward
architecture derived from its iteration. This architecture faithfully
approximates the exact structured sparse codes with a fraction of the
complexity of the standard optimization methods. We also show that by using
different training objective functions, learnable sparse encoders are no longer
restricted to be mere approximants of the exact sparse code for a pre-given
dictionary, as in earlier formulations, but can be rather used as full-featured
sparse encoders or even modelers. A simple implementation shows several orders
of magnitude speedup compared to the state-of-the-art at minimal performance
degradation, making the proposed framework suitable for real time and
large-scale applications.
| Alex Bronstein (Tel Aviv University), Pablo Sprechmann (University of
Minnesota), Guillermo Sapiro (University of Minnesota) | null | 1206.4649 | null | null |
Analysis of Kernel Mean Matching under Covariate Shift | cs.LG stat.ML | In real supervised learning scenarios, it is not uncommon that the training
and test sample follow different probability distributions, thus rendering the
necessity to correct the sampling bias. Focusing on a particular covariate
shift problem, we derive high probability confidence bounds for the kernel mean
matching (KMM) estimator, whose convergence rate turns out to depend on some
regularity measure of the regression function and also on some capacity measure
of the kernel. By comparing KMM with the natural plug-in estimator, we
establish the superiority of the former hence provide concrete
evidence/understanding to the effectiveness of KMM under covariate shift.
| Yaoliang Yu (University of Alberta), Csaba Szepesvari (University of
Alberta) | null | 1206.4650 | null | null |
Is margin preserved after random projection? | cs.LG cs.CV stat.ML | Random projections have been applied in many machine learning algorithms.
However, whether margin is preserved after random projection is non-trivial and
not well studied. In this paper we analyse margin distortion after random
projection, and give the conditions of margin preservation for binary
classification problems. We also extend our analysis to margin for multiclass
problems, and provide theoretical bounds on multiclass margin on the projected
data.
| Qinfeng Shi (The University of Adelaide), Chunhua Shen (The University
of Adelaide), Rhys Hill (The University of Adelaide), Anton van den Hengel
(the University of Adelaide) | null | 1206.4651 | null | null |
The Most Persistent Soft-Clique in a Set of Sampled Graphs | cs.LG cs.AI | When searching for characteristic subpatterns in potentially noisy graph
data, it appears self-evident that having multiple observations would be better
than having just one. However, it turns out that the inconsistencies introduced
when different graph instances have different edge sets pose a serious
challenge. In this work we address this challenge for the problem of finding
maximum weighted cliques.
We introduce the concept of most persistent soft-clique. This is subset of
vertices, that 1) is almost fully or at least densely connected, 2) occurs in
all or almost all graph instances, and 3) has the maximum weight. We present a
measure of clique-ness, that essentially counts the number of edge missing to
make a subset of vertices into a clique. With this measure, we show that the
problem of finding the most persistent soft-clique problem can be cast either
as: a) a max-min two person game optimization problem, or b) a min-min soft
margin optimization problem. Both formulations lead to the same solution when
using a partial Lagrangian method to solve the optimization problems. By
experiments on synthetic data and on real social network data, we show that the
proposed method is able to reliably find soft cliques in graph data, even if
that is distorted by random noise or unreliable observations.
| Novi Quadrianto (University of Cambridge), Chao Chen (IST Austria),
Christoph Lampert (IST Austria) | null | 1206.4652 | null | null |
Dimensionality Reduction by Local Discriminative Gaussians | cs.LG cs.CV stat.ML | We present local discriminative Gaussian (LDG) dimensionality reduction, a
supervised dimensionality reduction technique for classification. The LDG
objective function is an approximation to the leave-one-out training error of a
local quadratic discriminant analysis classifier, and thus acts locally to each
training point in order to find a mapping where similar data can be
discriminated from dissimilar data. While other state-of-the-art linear
dimensionality reduction methods require gradient descent or iterative solution
approaches, LDG is solved with a single eigen-decomposition. Thus, it scales
better for datasets with a large number of feature dimensions or training
examples. We also adapt LDG to the transfer learning setting, and show that it
achieves good performance when the test data distribution differs from that of
the training data.
| Nathan Parrish (University of Washington), Maya Gupta (University of
Washington) | null | 1206.4653 | null | null |
A Generalized Loop Correction Method for Approximate Inference in
Graphical Models | cs.AI cs.LG stat.ML | Belief Propagation (BP) is one of the most popular methods for inference in
probabilistic graphical models. BP is guaranteed to return the correct answer
for tree structures, but can be incorrect or non-convergent for loopy graphical
models. Recently, several new approximate inference algorithms based on cavity
distribution have been proposed. These methods can account for the effect of
loops by incorporating the dependency between BP messages. Alternatively,
region-based approximations (that lead to methods such as Generalized Belief
Propagation) improve upon BP by considering interactions within small clusters
of variables, thus taking small loops within these clusters into account. This
paper introduces an approach, Generalized Loop Correction (GLC), that benefits
from both of these types of loop correction. We show how GLC relates to these
two families of inference methods, then provide empirical evidence that GLC
works effectively in general, and can be significantly more accurate than both
correction schemes.
| Siamak Ravanbakhsh (University of Alberta), Chun-Nam Yu (University of
Alberta), Russell Greiner (University of Alberta) | null | 1206.4654 | null | null |
Modelling transition dynamics in MDPs with RKHS embeddings | cs.LG | We propose a new, nonparametric approach to learning and representing
transition dynamics in Markov decision processes (MDPs), which can be combined
easily with dynamic programming methods for policy optimisation and value
estimation. This approach makes use of a recently developed representation of
conditional distributions as \emph{embeddings} in a reproducing kernel Hilbert
space (RKHS). Such representations bypass the need for estimating transition
probabilities or densities, and apply to any domain on which kernels can be
defined. This avoids the need to calculate intractable integrals, since
expectations are represented as RKHS inner products whose computation has
linear complexity in the number of points used to represent the embedding. We
provide guarantees for the proposed applications in MDPs: in the context of a
value iteration algorithm, we prove convergence to either the optimal policy,
or to the closest projection of the optimal policy in our model class (an
RKHS), under reasonable assumptions. In experiments, we investigate a learning
task in a typical classical control setting (the under-actuated pendulum), and
on a navigation problem where only images from a sensor are observed. For
policy optimisation we compare with least-squares policy iteration where a
Gaussian process is used for value function estimation. For value estimation we
also compare to the NPDP method. Our approach achieves better performance in
all experiments.
| Steffen Grunewalder (University College London), Guy Lever (University
College London), Luca Baldassarre (University College London), Massi Pontil
(University College London), Arthur Gretton (MPI for Intelligent Systems) | null | 1206.4655 | null | null |
Machine Learning that Matters | cs.LG cs.AI stat.ML | Much of current machine learning (ML) research has lost its connection to
problems of import to the larger world of science and society. From this
perspective, there exist glaring limitations in the data sets we investigate,
the metrics we employ for evaluation, and the degree to which results are
communicated back to their originating domains. What changes are needed to how
we conduct research to increase the impact that ML has? We present six Impact
Challenges to explicitly focus the field?s energy and attention, and we discuss
existing obstacles that must be addressed. We aim to inspire ongoing discussion
and focus on ML that matters.
| Kiri Wagstaff (Jet Propulsion Laboratory) | null | 1206.4656 | null | null |
Projection-free Online Learning | cs.LG cs.DS | The computational bottleneck in applying online learning to massive data sets
is usually the projection step. We present efficient online learning algorithms
that eschew projections in favor of much more efficient linear optimization
steps using the Frank-Wolfe technique. We obtain a range of regret bounds for
online convex optimization, with better bounds for specific cases such as
stochastic online smooth convex optimization.
Besides the computational advantage, other desirable features of our
algorithms are that they are parameter-free in the stochastic case and produce
sparse decisions. We apply our algorithms to computationally intensive
applications of collaborative filtering, and show the theoretical improvements
to be clearly visible on standard datasets.
| Elad Hazan (Technion), Satyen Kale (IBM T.J. Watson Research Center) | null | 1206.4657 | null | null |
Dirichlet Process with Mixed Random Measures: A Nonparametric Topic
Model for Labeled Data | cs.LG stat.ML | We describe a nonparametric topic model for labeled data. The model uses a
mixture of random measures (MRM) as a base distribution of the Dirichlet
process (DP) of the HDP framework, so we call it the DP-MRM. To model labeled
data, we define a DP distributed random measure for each label, and the
resulting model generates an unbounded number of topics for each label. We
apply DP-MRM on single-labeled and multi-labeled corpora of documents and
compare the performance on label prediction with MedLDA, LDA-SVM, and
Labeled-LDA. We further enhance the model by incorporating ddCRP and modeling
multi-labeled images for image segmentation and object labeling, comparing the
performance with nCuts and rddCRP.
| Dongwoo Kim (KAIST), Suin Kim (KAIST), Alice Oh (KAIST) | null | 1206.4658 | null | null |
Max-Margin Nonparametric Latent Feature Models for Link Prediction | cs.LG stat.ML | We present a max-margin nonparametric latent feature model, which unites the
ideas of max-margin learning and Bayesian nonparametrics to discover
discriminative latent features for link prediction and automatically infer the
unknown latent social dimension. By minimizing a hinge-loss using the linear
expectation operator, we can perform posterior inference efficiently without
dealing with a highly nonlinear link likelihood function; by using a
fully-Bayesian formulation, we can avoid tuning regularization constants.
Experimental results on real datasets appear to demonstrate the benefits
inherited from max-margin learning and fully-Bayesian nonparametric inference.
| Jun Zhu (Tsinghua University) | null | 1206.4659 | null | null |
Learning with Augmented Features for Heterogeneous Domain Adaptation | cs.LG | We propose a new learning method for heterogeneous domain adaptation (HDA),
in which the data from the source domain and the target domain are represented
by heterogeneous features with different dimensions. Using two different
projection matrices, we first transform the data from two domains into a common
subspace in order to measure the similarity between the data from two domains.
We then propose two new feature mapping functions to augment the transformed
data with their original features and zeros. The existing learning methods
(e.g., SVM and SVR) can be readily incorporated with our newly proposed
augmented feature representations to effectively utilize the data from both
domains for HDA. Using the hinge loss function in SVM as an example, we
introduce the detailed objective function in our method called Heterogeneous
Feature Augmentation (HFA) for a linear case and also describe its
kernelization in order to efficiently cope with the data with very high
dimensions. Moreover, we also develop an alternating optimization algorithm to
effectively solve the nontrivial optimization problem in our HFA method.
Comprehensive experiments on two benchmark datasets clearly demonstrate that
HFA outperforms the existing HDA methods.
| Lixin Duan (Nanyang Technological University), Dong Xu (Nanyang
Technological University), Ivor Tsang (Nanyang Technological University) | null | 1206.4660 | null | null |
Predicting accurate probabilities with a ranking loss | cs.LG stat.ML | In many real-world applications of machine learning classifiers, it is
essential to predict the probability of an example belonging to a particular
class. This paper proposes a simple technique for predicting probabilities
based on optimizing a ranking loss, followed by isotonic regression. This
semi-parametric technique offers both good ranking and regression performance,
and models a richer set of probability distributions than statistical
workhorses such as logistic regression. We provide experimental results that
show the effectiveness of this technique on real-world applications of
probability prediction.
| Aditya Menon (UC San Diego), Xiaoqian Jiang (UC San Diego), Shankar
Vembu (University of Toronto), Charles Elkan (UC San Diego), Lucila
Ohno-Machado (UC San Diego) | null | 1206.4661 | null | null |
Bayesian Watermark Attacks | cs.CR cs.LG cs.MM | This paper presents an application of statistical machine learning to the
field of watermarking. We propose a new attack model on additive
spread-spectrum watermarking systems. The proposed attack is based on Bayesian
statistics. We consider the scenario in which a watermark signal is repeatedly
embedded in specific, possibly chosen based on a secret message bitstream,
segments (signals) of the host data. The host signal can represent a patch of
pixels from an image or a video frame. We propose a probabilistic model that
infers the embedded message bitstream and watermark signal, directly from the
watermarked data, without access to the decoder. We develop an efficient Markov
chain Monte Carlo sampler for updating the model parameters from their
conjugate full conditional posteriors. We also provide a variational Bayesian
solution, which further increases the convergence speed of the algorithm.
Experiments with synthetic and real image signals demonstrate that the attack
model is able to correctly infer a large part of the message bitstream and
obtain a very accurate estimate of the watermark signal.
| Ivo Shterev (Duke University), David Dunson (Duke University) | null | 1206.4662 | null | null |
The Convexity and Design of Composite Multiclass Losses | cs.LG stat.ML | We consider composite loss functions for multiclass prediction comprising a
proper (i.e., Fisher-consistent) loss over probability distributions and an
inverse link function. We establish conditions for their (strong) convexity and
explore the implications. We also show how the separation of concerns afforded
by using this composite representation allows for the design of families of
losses with the same Bayes risk.
| Mark Reid (The Australian National University and NICTA), Robert
Williamson (The Australian National University and NICTA), Peng Sun (Tsinghua
University) | null | 1206.4663 | null | null |
Tighter Variational Representations of f-Divergences via Restriction to
Probability Measures | cs.LG stat.ML | We show that the variational representations for f-divergences currently used
in the literature can be tightened. This has implications to a number of
methods recently proposed based on this representation. As an example
application we use our tighter representation to derive a general f-divergence
estimator based on two i.i.d. samples and derive the dual program for this
estimator that performs well empirically. We also point out a connection
between our estimator and MMD.
| Avraham Ruderman (Australian National University and NICTA), Mark Reid
(Australian National University and NICTA), Dario Garcia-Garcia (Australian
National University and NICTA), James Petterson (NICTA) | null | 1206.4664 | null | null |
Nonparametric variational inference | cs.LG stat.ML | Variational methods are widely used for approximate posterior inference.
However, their use is typically limited to families of distributions that enjoy
particular conjugacy properties. To circumvent this limitation, we propose a
family of variational approximations inspired by nonparametric kernel density
estimation. The locations of these kernels and their bandwidth are treated as
variational parameters and optimized to improve an approximate lower bound on
the marginal likelihood of the data. Using multiple kernels allows the
approximation to capture multiple modes of the posterior, unlike most other
variational approximations. We demonstrate the efficacy of the nonparametric
approximation with a hierarchical logistic regression model and a nonlinear
matrix factorization model. We obtain predictive performance as good as or
better than more specialized variational methods and sample-based
approximations. The method is easy to apply to more general graphical models
for which standard variational methods are difficult to derive.
| Samuel Gershman (Princeton University), Matt Hoffman (Princeton
University), David Blei (Princeton University) | null | 1206.4665 | null | null |
A Bayesian Approach to Approximate Joint Diagonalization of Square
Matrices | stat.CO cs.LG stat.ME | We present a Bayesian scheme for the approximate diagonalisation of several
square matrices which are not necessarily symmetric. A Gibbs sampler is derived
to simulate samples of the common eigenvectors and the eigenvalues for these
matrices. Several synthetic examples are used to illustrate the performance of
the proposed Gibbs sampler and we then provide comparisons to several other
joint diagonalization algorithms, which shows that the Gibbs sampler achieves
the state-of-the-art performance on the examples considered. As a byproduct,
the output of the Gibbs sampler could be used to estimate the log marginal
likelihood, however we employ the approximation based on the Bayesian
information criterion (BIC) which in the synthetic examples considered
correctly located the number of common eigenvectors. We then succesfully
applied the sampler to the source separation problem as well as the common
principal component analysis and the common spatial pattern analysis problems.
| Mingjun Zhong (Dalian University of Tech.), Mark Girolami (University
College London) | null | 1206.4666 | null | null |
Unachievable Region in Precision-Recall Space and Its Effect on
Empirical Evaluation | cs.LG cs.AI cs.IR | Precision-recall (PR) curves and the areas under them are widely used to
summarize machine learning results, especially for data sets exhibiting class
skew. They are often used analogously to ROC curves and the area under ROC
curves. It is known that PR curves vary as class skew changes. What was not
recognized before this paper is that there is a region of PR space that is
completely unachievable, and the size of this region depends only on the skew.
This paper precisely characterizes the size of that region and discusses its
implications for empirical evaluation methodology in machine learning.
| Kendrick Boyd (University of Wisconsin Madison), Vitor Santos Costa
(University of Porto), Jesse Davis (KU Leuven), David Page (University of
Wisconsin Madison) | null | 1206.4667 | null | null |
Approximate Principal Direction Trees | cs.LG cs.DS stat.ML | We introduce a new spatial data structure for high dimensional data called
the \emph{approximate principal direction tree} (APD tree) that adapts to the
intrinsic dimension of the data. Our algorithm ensures vector-quantization
accuracy similar to that of computationally-expensive PCA trees with similar
time-complexity to that of lower-accuracy RP trees.
APD trees use a small number of power-method iterations to find splitting
planes for recursively partitioning the data. As such they provide a natural
trade-off between the running-time and accuracy achieved by RP and PCA trees.
Our theoretical results establish a) strong performance guarantees regardless
of the convergence rate of the power-method and b) that $O(\log d)$ iterations
suffice to establish the guarantee of PCA trees when the intrinsic dimension is
$d$. We demonstrate this trade-off and the efficacy of our data structure on
both the CPU and GPU.
| Mark McCartin-Lim (University of Massachusetts), Andrew McGregor
(University of Massachusetts), Rui Wang (University of Massachusetts) | null | 1206.4668 | null | null |
Sparse Additive Functional and Kernel CCA | cs.LG stat.ML | Canonical Correlation Analysis (CCA) is a classical tool for finding
correlations among the components of two random vectors. In recent years, CCA
has been widely applied to the analysis of genomic data, where it is common for
researchers to perform multiple assays on a single set of patient samples.
Recent work has proposed sparse variants of CCA to address the high
dimensionality of such data. However, classical and sparse CCA are based on
linear models, and are thus limited in their ability to find general
correlations. In this paper, we present two approaches to high-dimensional
nonparametric CCA, building on recent developments in high-dimensional
nonparametric regression. We present estimation procedures for both approaches,
and analyze their theoretical properties in the high-dimensional setting. We
demonstrate the effectiveness of these procedures in discovering nonlinear
correlations via extensive simulations, as well as through experiments with
genomic data.
| Sivaraman Balakrishnan (Carnegie Mellon University), Kriti Puniyani
(Carnegie Mellon University), John Lafferty (Carnegie Mellon University) | null | 1206.4669 | null | null |
State-Space Inference for Non-Linear Latent Force Models with
Application to Satellite Orbit Prediction | cs.IT astro-ph.EP cs.LG math.IT physics.data-an | Latent force models (LFMs) are flexible models that combine mechanistic
modelling principles (i.e., physical models) with non-parametric data-driven
components. Several key applications of LFMs need non-linearities, which
results in analytically intractable inference. In this work we show how
non-linear LFMs can be represented as non-linear white noise driven state-space
models and present an efficient non-linear Kalman filtering and smoothing based
method for approximate state and parameter inference. We illustrate the
performance of the proposed methodology via two simulated examples, and apply
it to a real-world problem of long-term prediction of GPS satellite orbits.
| Jouni Hartikainen (Aalto University), Mari Seppanen (Tampere
University of Technology), Simo Sarkka (Aalto University) | null | 1206.4670 | null | null |
Dependent Hierarchical Normalized Random Measures for Dynamic Topic
Modeling | cs.LG stat.ML | We develop dependent hierarchical normalized random measures and apply them
to dynamic topic modeling. The dependency arises via superposition, subsampling
and point transition on the underlying Poisson processes of these measures. The
measures used include normalised generalised Gamma processes that demonstrate
power law properties, unlike Dirichlet processes used previously in dynamic
topic modeling. Inference for the model includes adapting a recently developed
slice sampler to directly manipulate the underlying Poisson process.
Experiments performed on news, blogs, academic and Twitter collections
demonstrate the technique gives superior perplexity over a number of previous
models.
| Changyou Chen (ANU & NICTA), Nan Ding (Purdue University), Wray
Buntine (NICTA) | null | 1206.4671 | null | null |
Efficient Active Algorithms for Hierarchical Clustering | cs.LG stat.ML | Advances in sensing technologies and the growth of the internet have resulted
in an explosion in the size of modern datasets, while storage and processing
power continue to lag behind. This motivates the need for algorithms that are
efficient, both in terms of the number of measurements needed and running time.
To combat the challenges associated with large datasets, we propose a general
framework for active hierarchical clustering that repeatedly runs an
off-the-shelf clustering algorithm on small subsets of the data and comes with
guarantees on performance, measurement complexity and runtime complexity. We
instantiate this framework with a simple spectral clustering algorithm and
provide concrete results on its performance, showing that, under some
assumptions, this algorithm recovers all clusters of size ?(log n) using O(n
log^2 n) similarities and runs in O(n log^3 n) time for a dataset of n objects.
Through extensive experimentation we also demonstrate that this framework is
practically alluring.
| Akshay Krishnamurthy (Carnegie Mellon University), Sivaraman
Balakrishnan (Carnegie Mellon University), Min Xu (Carnegie Mellon
University), Aarti Singh (Carnegie Mellon University) | null | 1206.4672 | null | null |
Group Sparse Additive Models | cs.LG stat.ML | We consider the problem of sparse variable selection in nonparametric
additive models, with the prior knowledge of the structure among the covariates
to encourage those variables within a group to be selected jointly. Previous
works either study the group sparsity in the parametric setting (e.g., group
lasso), or address the problem in the non-parametric setting without exploiting
the structural information (e.g., sparse additive models). In this paper, we
present a new method, called group sparse additive models (GroupSpAM), which
can handle group sparsity in additive models. We generalize the l1/l2 norm to
Hilbert spaces as the sparsity-inducing penalty in GroupSpAM. Moreover, we
derive a novel thresholding condition for identifying the functional sparsity
at the group level, and propose an efficient block coordinate descent algorithm
for constructing the estimate. We demonstrate by simulation that GroupSpAM
substantially outperforms the competing methods in terms of support recovery
and prediction accuracy in additive models, and also conduct a comparative
experiment on a real breast cancer dataset.
| Junming Yin (Carnegie Mellon University), Xi Chen (Carnegie Mellon
University), Eric Xing (Carnegie Mellon University) | null | 1206.4673 | null | null |
Comparison-Based Learning with Rank Nets | cs.LG cs.DS stat.ML | We consider the problem of search through comparisons, where a user is
presented with two candidate objects and reveals which is closer to her
intended target. We study adaptive strategies for finding the target, that
require knowledge of rank relationships but not actual distances between
objects. We propose a new strategy based on rank nets, and show that for target
distributions with a bounded doubling constant, it finds the target in a number
of comparisons close to the entropy of the target distribution and, hence, of
the optimum. We extend these results to the case of noisy oracles, and compare
this strategy to prior art over multiple datasets.
| Amin Karbasi (EPFL), Stratis Ioannidis (Technicolor), laurent
Massoulie (Technicolor) | null | 1206.4674 | null | null |
Finding Botnets Using Minimal Graph Clusterings | cs.CR cs.DC cs.LG | We study the problem of identifying botnets and the IP addresses which they
comprise, based on the observation of a fraction of the global email spam
traffic. Observed mailing campaigns constitute evidence for joint botnet
membership, they are represented by cliques in the graph of all messages. No
evidence against an association of nodes is ever available. We reduce the
problem of identifying botnets to a problem of finding a minimal clustering of
the graph of messages. We directly model the distribution of clusterings given
the input graph; this avoids potential errors caused by distributional
assumptions of a generative model. We report on a case study in which we
evaluate the model by its ability to predict the spam campaign that a given IP
address is going to participate in.
| Peter Haider (University of Potsdam), Tobias Scheffer (University of
Potsdam) | null | 1206.4675 | null | null |
Clustering by Low-Rank Doubly Stochastic Matrix Decomposition | cs.LG cs.CV cs.NA stat.ML | Clustering analysis by nonnegative low-rank approximations has achieved
remarkable progress in the past decade. However, most approximation approaches
in this direction are still restricted to matrix factorization. We propose a
new low-rank learning method to improve the clustering performance, which is
beyond matrix factorization. The approximation is based on a two-step bipartite
random walk through virtual cluster nodes, where the approximation is formed by
only cluster assigning probabilities. Minimizing the approximation error
measured by Kullback-Leibler divergence is equivalent to maximizing the
likelihood of a discriminative model, which endows our method with a solid
probabilistic interpretation. The optimization is implemented by a relaxed
Majorization-Minimization algorithm that is advantageous in finding good local
minima. Furthermore, we point out that the regularized algorithm with Dirichlet
prior only serves as initialization. Experimental results show that the new
method has strong performance in clustering purity for various datasets,
especially for large-scale manifold data.
| Zhirong Yang (Aalto University), Erkki Oja (Aalto University) | null | 1206.4676 | null | null |
Semi-Supervised Learning of Class Balance under Class-Prior Change by
Distribution Matching | cs.LG stat.ML | In real-world classification problems, the class balance in the training
dataset does not necessarily reflect that of the test dataset, which can cause
significant estimation bias. If the class ratio of the test dataset is known,
instance re-weighting or resampling allows systematical bias correction.
However, learning the class ratio of the test dataset is challenging when no
labeled data is available from the test domain. In this paper, we propose to
estimate the class ratio in the test dataset by matching probability
distributions of training and test input data. We demonstrate the utility of
the proposed approach through experiments.
| Marthinus Du Plessis (Tokyo Institute of Technology), Masashi Sugiyama
(Tokyo Institute of Technology) | null | 1206.4677 | null | null |
Linear Regression with Limited Observation | cs.LG stat.ML | We consider the most common variants of linear regression, including Ridge,
Lasso and Support-vector regression, in a setting where the learner is allowed
to observe only a fixed number of attributes of each example at training time.
We present simple and efficient algorithms for these problems: for Lasso and
Ridge regression they need the same total number of attributes (up to
constants) as do full-information algorithms, for reaching a certain accuracy.
For Support-vector regression, we require exponentially less attributes
compared to the state of the art. By that, we resolve an open problem recently
posed by Cesa-Bianchi et al. (2010). Experiments show the theoretical bounds to
be justified by superior performance compared to the state of the art.
| Elad Hazan (Technion), Tomer Koren (Technion) | null | 1206.4678 | null | null |
Factorized Asymptotic Bayesian Hidden Markov Models | cs.LG stat.ML | This paper addresses the issue of model selection for hidden Markov models
(HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has
been recently developed for model selection on independent hidden variables
(i.e., mixture models), for time-dependent hidden variables. As with FAB in
mixture models, FAB for HMMs is derived as an iterative lower bound
maximization algorithm of a factorized information criterion (FIC). It
inherits, from FAB for mixture models, several desirable properties for
learning HMMs, such as asymptotic consistency of FIC with marginal
log-likelihood, a shrinkage effect for hidden state selection, monotonic
increase of the lower FIC bound through the iterative optimization. Further, it
does not have a tunable hyper-parameter, and thus its model selection process
can be fully automated. Experimental results shows that FAB outperforms
states-of-the-art variational Bayesian HMM and non-parametric Bayesian HMM in
terms of model selection accuracy and computational efficiency.
| Ryohei Fujimaki (NEC Laboratories America), Kohei Hayashi (Nara
Institute of Science and Technology) | null | 1206.4679 | null | null |
Fast Prediction of New Feature Utility | cs.LG math.ST stat.TH | We study the new feature utility prediction problem: statistically testing
whether adding a new feature to the data representation can improve predictive
accuracy on a supervised learning task. In many applications, identifying new
informative features is the primary pathway for improving performance. However,
evaluating every potential feature by re-training the predictor with it can be
costly. The paper describes an efficient, learner-independent technique for
estimating new feature utility without re-training based on the current
predictor's outputs. The method is obtained by deriving a connection between
loss reduction potential and the new feature's correlation with the loss
gradient of the current predictor. This leads to a simple yet powerful
hypothesis testing procedure, for which we prove consistency. Our theoretical
analysis is accompanied by empirical evaluation on standard benchmarks and a
large-scale industrial dataset.
| Hoyt Koepke (University of Washington), Mikhail Bilenko (Microsoft
Research) | null | 1206.4680 | null | null |
LPQP for MAP: Putting LP Solvers to Better Use | cs.LG stat.ML | MAP inference for general energy functions remains a challenging problem.
While most efforts are channeled towards improving the linear programming (LP)
based relaxation, this work is motivated by the quadratic programming (QP)
relaxation. We propose a novel MAP relaxation that penalizes the
Kullback-Leibler divergence between the LP pairwise auxiliary variables, and QP
equivalent terms given by the product of the unaries. We develop two efficient
algorithms based on variants of this relaxation. The algorithms minimize the
non-convex objective using belief propagation and dual decomposition as
building blocks. Experiments on synthetic and real-world data show that the
solutions returned by our algorithms substantially improve over the LP
relaxation.
| Patrick Pletscher (ETH Zurich), Sharon Wulff (ETH Zurich) | null | 1206.4681 | null | null |
Copula-based Kernel Dependency Measures | cs.LG math.ST stat.ML stat.TH | The paper presents a new copula based method for measuring dependence between
random variables. Our approach extends the Maximum Mean Discrepancy to the
copula of the joint distribution. We prove that this approach has several
advantageous properties. Similarly to Shannon mutual information, the proposed
dependence measure is invariant to any strictly increasing transformation of
the marginal variables. This is important in many applications, for example in
feature selection. The estimator is consistent, robust to outliers, and uses
rank statistics only. We derive upper bounds on the convergence rate and
propose independence tests too. We illustrate the theoretical contributions
through a series of experiments in feature selection and low-dimensional
embedding of distributions.
| Barnabas Poczos (Carnegie Mellon University), Zoubin Ghahramani
(University of Cambridge), Jeff Schneider (Carnegie Mellon University) | null | 1206.4682 | null | null |
Marginalized Denoising Autoencoders for Domain Adaptation | cs.LG | Stacked denoising autoencoders (SDAs) have been successfully used to learn
new representations for domain adaptation. Recently, they have attained record
accuracy on standard benchmark tasks of sentiment analysis across different
text domains. SDAs learn robust data representations by reconstruction,
recovering original features from data that are artificially corrupted with
noise. In this paper, we propose marginalized SDA (mSDA) that addresses two
crucial limitations of SDAs: high computational cost and lack of scalability to
high-dimensional features. In contrast to SDAs, our approach of mSDA
marginalizes noise and thus does not require stochastic gradient descent or
other optimization algorithms to learn parameters ? in fact, they are computed
in closed-form. Consequently, mSDA, which can be implemented in only 20 lines
of MATLAB^{TM}, significantly speeds up SDAs by two orders of magnitude.
Furthermore, the representations learnt by mSDA are as effective as the
traditional SDAs, attaining almost identical accuracies in benchmark tasks.
| Minmin Chen (Washington University), Zhixiang Xu (Washington
University), Kilian Weinberger (Washington University), Fei Sha (University
of Southern California) | null | 1206.4683 | null | null |
Sparse-GEV: Sparse Latent Space Model for Multivariate Extreme Value
Time Serie Modeling | stat.ME cs.LG stat.AP | In many applications of time series models, such as climate analysis and
social media analysis, we are often interested in extreme events, such as
heatwave, wind gust, and burst of topics. These time series data usually
exhibit a heavy-tailed distribution rather than a Gaussian distribution. This
poses great challenges to existing approaches due to the significantly
different assumptions on the data distributions and the lack of sufficient past
data on extreme events. In this paper, we propose the Sparse-GEV model, a
latent state model based on the theory of extreme value modeling to
automatically learn sparse temporal dependence and make predictions. Our model
is theoretically significant because it is among the first models to learn
sparse temporal dependencies among multivariate extreme value time series. We
demonstrate the superior performance of our algorithm to the state-of-art
methods, including Granger causality, copula approach, and transfer entropy, on
one synthetic dataset, one climate dataset and two Twitter datasets.
| Yan Liu (USC), Taha Bahadori (USC), Hongfei Li (IBM T.J. Watson
Research Center) | null | 1206.4685 | null | null |
Discriminative Probabilistic Prototype Learning | cs.LG stat.ML | In this paper we propose a simple yet powerful method for learning
representations in supervised learning scenarios where each original input
datapoint is described by a set of vectors and their associated outputs may be
given by soft labels indicating, for example, class probabilities. We represent
an input datapoint as a mixture of probabilities over the corresponding set of
feature vectors where each probability indicates how likely each vector is to
belong to an unknown prototype pattern. We propose a probabilistic model that
parameterizes these prototype patterns in terms of hidden variables and
therefore it can be trained with conventional approaches based on likelihood
maximization. More importantly, both the model parameters and the prototype
patterns can be learned from data in a discriminative way. We show that our
model can be seen as a probabilistic generalization of learning vector
quantization (LVQ). We apply our method to the problems of shape
classification, hyperspectral imaging classification and people's work class
categorization, showing the superior performance of our method compared to the
standard prototype-based classification approach and other competitive
benchmark methods.
| Edwin Bonilla (NICTA), Antonio Robles-Kelly (NICTA) | null | 1206.4686 | null | null |
Feature extraction in protein sequences classification : a new stability
measure | cs.LG cs.CE q-bio.QM | Feature extraction is an unavoidable task, especially in the critical step of
preprocessing biological sequences. This step consists for example in
transforming the biological sequences into vectors of motifs where each motif
is a subsequence that can be seen as a property (or attribute) characterizing
the sequence. Hence, we obtain an object-property table where objects are
sequences and properties are motifs extracted from sequences. This output can
be used to apply standard machine learning tools to perform data mining tasks
such as classification. Several previous works have described feature
extraction methods for bio-sequence classification, but none of them discussed
the robustness of these methods when perturbing the input data. In this work,
we introduce the notion of stability of the generated motifs in order to study
the robustness of motif extraction methods. We express this robustness in terms
of the ability of the method to reveal any change occurring in the input data
and also its ability to target the interesting motifs. We use these criteria to
evaluate and experimentally compare four existing extraction methods for
biological sequences.
| Rabie Saidi, Sabeur Aridhi, Mondher Maddouri and Engelbert Mephu
Nguifo | 10.1145/2382936.2383060 | 1206.4822 | null | null |
Smoothed Functional Algorithms for Stochastic Optimization using
q-Gaussian Distributions | cs.IT cs.LG math.IT stat.ME | Smoothed functional (SF) schemes for gradient estimation are known to be
efficient in stochastic optimization algorithms, specially when the objective
is to improve the performance of a stochastic system. However, the performance
of these methods depends on several parameters, such as the choice of a
suitable smoothing kernel. Different kernels have been studied in literature,
which include Gaussian, Cauchy and uniform distributions among others. This
paper studies a new class of kernels based on the q-Gaussian distribution, that
has gained popularity in statistical physics over the last decade. Though the
importance of this family of distributions is attributed to its ability to
generalize the Gaussian distribution, we observe that this class encompasses
almost all existing smoothing kernels. This motivates us to study SF schemes
for gradient estimation using the q-Gaussian distribution. Using the derived
gradient estimates, we propose two-timescale algorithms for optimization of a
stochastic objective function in a constrained setting with projected gradient
search approach. We prove the convergence of our algorithms to the set of
stationary points of an associated ODE. We also demonstrate their performance
numerically through simulations on a queuing model.
| Debarghya Ghoshdastidar, Ambedkar Dukkipati, Shalabh Bhatnagar | 10.1145/2628434 | 1206.4832 | null | null |
Estimating Densities with Non-Parametric Exponential Families | stat.ML cs.LG | We propose a novel approach for density estimation with exponential families
for the case when the true density may not fall within the chosen family. Our
approach augments the sufficient statistics with features designed to
accumulate probability mass in the neighborhood of the observed points,
resulting in a non-parametric model similar to kernel density estimators. We
show that under mild conditions, the resulting model uses only the sufficient
statistics if the density is within the chosen exponential family, and
asymptotically, it approximates densities outside of the chosen exponential
family. Using the proposed approach, we modify the exponential random graph
model, commonly used for modeling small-size graph distributions, to address
the well-known issue of model degeneracy.
| Lin Yuan, Sergey Kirshner and Robert Givan | null | 1206.5036 | null | null |
The Robustness and Super-Robustness of L^p Estimation, when p < 1 | cs.LG math.ST stat.TH | In robust statistics, the breakdown point of an estimator is the percentage
of outliers with which an estimator still generates reliable estimation. The
upper bound of breakdown point is 50%, which means it is not possible to
generate reliable estimation with more than half outliers.
In this paper, it is shown that for majority of experiences, when the
outliers exceed 50%, but if they are distributed randomly enough, it is still
possible to generate a reliable estimation from minority good observations. The
phenomenal of that the breakdown point is larger than 50% is named as super
robustness. And, in this paper, a robust estimator is called strict robust if
it generates a perfect estimation when all the good observations are perfect.
More specifically, the super robustness of the maximum likelihood estimator
of the exponential power distribution, or L^p estimation, where p<1, is
investigated. This paper starts with proving that L^p (p<1) is a strict robust
location estimator. Further, it is proved that L^p (p < 1)has the property of
strict super-robustness on translation, rotation, scaling transformation and
robustness on Euclidean transform.
| Qinghuai Gao | null | 1206.5057 | null | null |
Hidden Markov Models with mixtures as emission distributions | stat.ML cs.LG stat.CO | In unsupervised classification, Hidden Markov Models (HMM) are used to
account for a neighborhood structure between observations. The emission
distributions are often supposed to belong to some parametric family. In this
paper, a semiparametric modeling where the emission distributions are a mixture
of parametric distributions is proposed to get a higher flexibility. We show
that the classical EM algorithm can be adapted to infer the model parameters.
For the initialisation step, starting from a large number of components, a
hierarchical method to combine them into the hidden states is proposed. Three
likelihood-based criteria to select the components to be combined are
discussed. To estimate the number of hidden states, BIC-like criteria are
derived. A simulation study is carried out both to determine the best
combination between the merging criteria and the model selection criteria and
to evaluate the accuracy of classification. The proposed method is also
illustrated using a biological dataset from the model plant Arabidopsis
thaliana. A R package HMMmix is freely available on the CRAN.
| Stevenn Volant, Caroline B\'erard, Marie-Laure Martin-Magniette and
St\'ephane Robin | null | 1206.5102 | null | null |
Fast Variational Inference in the Conjugate Exponential Family | cs.LG stat.ML | We present a general method for deriving collapsed variational inference
algo- rithms for probabilistic models in the conjugate exponential family. Our
method unifies many existing approaches to collapsed variational inference. Our
collapsed variational inference leads to a new lower bound on the marginal
likelihood. We exploit the information geometry of the bound to derive much
faster optimization methods based on conjugate gradients for these models. Our
approach is very general and is easily applied to any model where the mean
field update equations have been derived. Empirically we show significant
speed-ups for probabilistic models optimized using our bound.
| James Hensman, Magnus Rattray and Neil D. Lawrence | null | 1206.5162 | null | null |
Stock prices assessment: proposal of a new index based on volume
weighted historical prices through the use of computer modeling | q-fin.ST cs.LG | The importance of considering the volumes to analyze stock prices movements
can be considered as a well-accepted practice in the financial area. However,
when we look at the scientific production in this field, we still cannot find a
unified model that includes volume and price variations for stock assessment
purposes. In this paper we present a computer model that could fulfill this
gap, proposing a new index to evaluate stock prices based on their historical
prices and volumes traded. Besides the model can be considered mathematically
very simple, it was able to improve significantly the performance of agents
operating with real financial data. Based on the results obtained, and also on
the very intuitive logic of our model, we believe that the index proposed here
can be very useful to help investors on the activity of determining ideal price
ranges for buying and selling stocks in the financial market.
| Tiago Colliri, Fernando F. Ferreira | 10.1109/BWSS.2012.23 | 1206.5224 | null | null |
Analysis of Semi-Supervised Learning with the Yarowsky Algorithm | cs.LG stat.ML | The Yarowsky algorithm is a rule-based semi-supervised learning algorithm
that has been successfully applied to some problems in computational
linguistics. The algorithm was not mathematically well understood until (Abney
2004) which analyzed some specific variants of the algorithm, and also proposed
some new algorithms for bootstrapping. In this paper, we extend Abney's work
and show that some of his proposed algorithms actually optimize (an upper-bound
on) an objective function based on a new definition of cross-entropy which is
based on a particular instantiation of the Bregman distance between probability
distributions. Moreover, we suggest some new algorithms for rule-based
semi-supervised learning and show connections with harmonic functions and
minimum multi-way cuts in graph-based semi-supervised learning.
| Gholam Reza Haffari, Anoop Sarkar | null | 1206.5240 | null | null |
Shift-Invariance Sparse Coding for Audio Classification | cs.LG stat.ML | Sparse coding is an unsupervised learning algorithm that learns a succinct
high-level representation of the inputs given only unlabeled data; it
represents each input as a sparse linear combination of a set of basis
functions. Originally applied to modeling the human visual cortex, sparse
coding has also been shown to be useful for self-taught learning, in which the
goal is to solve a supervised classification task given access to additional
unlabeled data drawn from different classes than that in the supervised
learning problem. Shift-invariant sparse coding (SISC) is an extension of
sparse coding which reconstructs a (usually time-series) input using all of the
basis functions in all possible shifts. In this paper, we present an efficient
algorithm for learning SISC bases. Our method is based on iteratively solving
two large convex optimization problems: The first, which computes the linear
coefficients, is an L1-regularized linear least squares problem with
potentially hundreds of thousands of variables. Existing methods typically use
a heuristic to select a small subset of the variables to optimize, but we
present a way to efficiently compute the exact solution. The second, which
solves for bases, is a constrained linear least squares problem. By optimizing
over complex-valued variables in the Fourier domain, we reduce the coupling
between the different variables, allowing the problem to be solved efficiently.
We show that SISC's learned high-level representations of speech and music
provide useful features for classification tasks within those domains. When
applied to classification, under certain conditions the learned features
outperform state of the art spectral and cepstral features.
| Roger Grosse, Rajat Raina, Helen Kwong, Andrew Y. Ng | null | 1206.5241 | null | null |
Convergent Propagation Algorithms via Oriented Trees | cs.LG stat.ML | Inference problems in graphical models are often approximated by casting them
as constrained optimization problems. Message passing algorithms, such as
belief propagation, have previously been suggested as methods for solving these
optimization problems. However, there are few convergence guarantees for such
algorithms, and the algorithms are therefore not guaranteed to solve the
corresponding optimization problem. Here we present an oriented tree
decomposition algorithm that is guaranteed to converge to the global optimum of
the Tree-Reweighted (TRW) variational problem. Our algorithm performs local
updates in the convex dual of the TRW problem - an unconstrained generalized
geometric program. Primal updates, also local, correspond to oriented
reparametrization operations that leave the distribution intact.
| Amir Globerson, Tommi S. Jaakkola | null | 1206.5243 | null | null |
A new parameter Learning Method for Bayesian Networks with Qualitative
Influences | cs.AI cs.LG stat.ME | We propose a new method for parameter learning in Bayesian networks with
qualitative influences. This method extends our previous work from networks of
binary variables to networks of discrete variables with ordered values. The
specified qualitative influences correspond to certain order restrictions on
the parameters in the network. These parameters may therefore be estimated
using constrained maximum likelihood estimation. We propose an alternative
method, based on the isotonic regression. The constrained maximum likelihood
estimates are fairly complicated to compute, whereas computation of the
isotonic regression estimates only requires the repeated application of the
Pool Adjacent Violators algorithm for linear orders. Therefore, the isotonic
regression estimator is to be preferred from the viewpoint of computational
complexity. Through experiments on simulated and real data, we show that the
new learning method is competitive in performance to the constrained maximum
likelihood estimator, and that both estimators improve on the standard
estimator.
| Ad Feelders | null | 1206.5245 | null | null |
Bayesian structure learning using dynamic programming and MCMC | cs.LG stat.ML | MCMC methods for sampling from the space of DAGs can mix poorly due to the
local nature of the proposals that are commonly used. It has been shown that
sampling from the space of node orders yields better results [FK03, EW06].
Recently, Koivisto and Sood showed how one can analytically marginalize over
orders using dynamic programming (DP) [KS04, Koi06]. Their method computes the
exact marginal posterior edge probabilities, thus avoiding the need for MCMC.
Unfortunately, there are four drawbacks to the DP technique: it can only use
modular priors, it can only compute posteriors over modular features, it is
difficult to compute a predictive density, and it takes exponential time and
space. We show how to overcome the first three of these problems by using the
DP algorithm as a proposal distribution for MCMC in DAG space. We show that
this hybrid technique converges to the posterior faster than other methods,
resulting in more accurate structure learning and higher predictive likelihoods
on test data.
| Daniel Eaton, Kevin Murphy | null | 1206.5247 | null | null |
Statistical Translation, Heat Kernels and Expected Distances | cs.LG cs.CV cs.IR stat.ML | High dimensional structured data such as text and images is often poorly
understood and misrepresented in statistical modeling. The standard histogram
representation suffers from high variance and performs poorly in general. We
explore novel connections between statistical translation, heat kernels on
manifolds and graphs, and expected distances. These connections provide a new
framework for unsupervised metric learning for text documents. Experiments
indicate that the resulting distances are generally superior to their more
standard counterparts.
| Joshua Dillon, Yi Mao, Guy Lebanon, Jian Zhang | null | 1206.5248 | null | null |
Discovering Patterns in Biological Sequences by Optimal Segmentation | cs.CE cs.LG q-bio.QM stat.AP | Computational methods for discovering patterns of local correlations in
sequences are important in computational biology. Here we show how to determine
the optimal partitioning of aligned sequences into non-overlapping segments
such that positions in the same segment are strongly correlated while positions
in different segments are not. Our approach involves discovering the hidden
variables of a Bayesian network that interact with observed sequences so as to
form a set of independent mixture models. We introduce a dynamic program to
efficiently discover the optimal segmentation, or equivalently the optimal set
of hidden variables. We evaluate our approach on two computational biology
tasks. One task is related to the design of vaccines against polymorphic
pathogens and the other task involves analysis of single nucleotide
polymorphisms (SNPs) in human DNA. We show how common tasks in these problems
naturally correspond to inference procedures in the learned models. Error rates
of our learned models for the prediction of missing SNPs are up to 1/3 less
than the error rates of a state-of-the-art SNP prediction method. Source code
is available at www.uwm.edu/~joebock/segmentation.
| Joseph Bockhorst, Nebojsa Jojic | null | 1206.5256 | null | null |
Mixture-of-Parents Maximum Entropy Markov Models | cs.LG cs.AI stat.ML | We present the mixture-of-parents maximum entropy Markov model (MoP-MEMM), a
class of directed graphical models extending MEMMs. The MoP-MEMM allows
tractable incorporation of long-range dependencies between nodes by restricting
the conditional distribution of each node to be a mixture of distributions
given the parents. We show how to efficiently compute the exact marginal
posterior node distributions, regardless of the range of the dependencies. This
enables us to model non-sequential correlations present within text documents,
as well as between interconnected documents, such as hyperlinked web pages. We
apply the MoP-MEMM to a named entity recognition task and a web page
classification task. In each, our model shows significant improvement over the
basic MEMM, and is competitive with other long-range sequence models that use
approximate inference.
| David S. Rosenberg, Dan Klein, Ben Taskar | null | 1206.5261 | null | null |
Reading Dependencies from Polytree-Like Bayesian Networks | cs.AI cs.LG stat.ML | We present a graphical criterion for reading dependencies from the minimal
directed independence map G of a graphoid p when G is a polytree and p
satisfies composition and weak transitivity. We prove that the criterion is
sound and complete. We argue that assuming composition and weak transitivity is
not too restrictive.
| Jose M. Pena | null | 1206.5263 | null | null |
Apprenticeship Learning using Inverse Reinforcement Learning and
Gradient Methods | cs.LG stat.ML | In this paper we propose a novel gradient algorithm to learn a policy from an
expert's observed behavior assuming that the expert behaves optimally with
respect to some unknown reward function of a Markovian Decision Problem. The
algorithm's aim is to find a reward function such that the resulting optimal
policy matches well the expert's observed behavior. The main difficulty is that
the mapping from the parameters to policies is both nonsmooth and highly
redundant. Resorting to subdifferentials solves the first difficulty, while the
second one is over- come by computing natural gradients. We tested the proposed
method in two artificial domains and found it to be more reliable and efficient
than some previous methods.
| Gergely Neu, Csaba Szepesvari | null | 1206.5264 | null | null |
Consensus ranking under the exponential model | cs.LG cs.AI stat.ML | We analyze the generalized Mallows model, a popular exponential model over
rankings. Estimating the central (or consensus) ranking from data is NP-hard.
We obtain the following new results: (1) We show that search methods can
estimate both the central ranking pi0 and the model parameters theta exactly.
The search is n! in the worst case, but is tractable when the true distribution
is concentrated around its mode; (2) We show that the generalized Mallows model
is jointly exponential in (pi0; theta), and introduce the conjugate prior for
this model class; (3) The sufficient statistics are the pairwise marginal
probabilities that item i is preferred to item j. Preliminary experiments
confirm the theoretical predictions and compare the new algorithm and existing
heuristics.
| Marina Meila, Kapil Phadnis, Arthur Patterson, Jeff A. Bilmes | null | 1206.5265 | null | null |
Collaborative Filtering and the Missing at Random Assumption | cs.LG cs.IR stat.ML | Rating prediction is an important application, and a popular research topic
in collaborative filtering. However, both the validity of learning algorithms,
and the validity of standard testing procedures rest on the assumption that
missing ratings are missing at random (MAR). In this paper we present the
results of a user study in which we collect a random sample of ratings from
current users of an online radio service. An analysis of the rating data
collected in the study shows that the sample of random ratings has markedly
different properties than ratings of user-selected songs. When asked to report
on their own rating behaviour, a large number of users indicate they believe
their opinion of a song does affect whether they choose to rate that song, a
violation of the MAR condition. Finally, we present experimental results
showing that incorporating an explicit model of the missing data mechanism can
lead to significant improvements in prediction performance on the random sample
of ratings.
| Benjamin Marlin, Richard S. Zemel, Sam Roweis, Malcolm Slaney | null | 1206.5267 | null | null |
Nonparametric Bayes Pachinko Allocation | cs.IR cs.LG stat.ML | Recent advances in topic models have explored complicated structured
distributions to represent topic correlation. For example, the pachinko
allocation model (PAM) captures arbitrary, nested, and possibly sparse
correlations between topics using a directed acyclic graph (DAG). While PAM
provides more flexibility and greater expressive power than previous models
like latent Dirichlet allocation (LDA), it is also more difficult to determine
the appropriate topic structure for a specific dataset. In this paper, we
propose a nonparametric Bayesian prior for PAM based on a variant of the
hierarchical Dirichlet process (HDP). Although the HDP can capture topic
correlations defined by nested data structure, it does not automatically
discover such correlations from unstructured data. By assuming an HDP-based
prior for PAM, we are able to learn both the number of topics and how the
topics are correlated. We evaluate our model on synthetic and real-world text
datasets, and show that nonparametric PAM achieves performance matching the
best of PAM without manually tuning the number of topics.
| Wei Li, David Blei, Andrew McCallum | null | 1206.5270 | null | null |
On Discarding, Caching, and Recalling Samples in Active Learning | cs.LG stat.ML | We address challenges of active learning under scarce informational resources
in non-stationary environments. In real-world settings, data labeled and
integrated into a predictive model may become invalid over time. However, the
data can become informative again with switches in context and such changes may
indicate unmodeled cyclic or other temporal dynamics. We explore principles for
discarding, caching, and recalling labeled data points in active learning based
on computations of value of information. We review key concepts and study the
value of the methods via investigations of predictive performance and costs of
acquiring data for simulated and real-world data sets.
| Ashish Kapoor, Eric J. Horvitz | null | 1206.5274 | null | null |
Accuracy Bounds for Belief Propagation | cs.AI cs.LG stat.ML | The belief propagation (BP) algorithm is widely applied to perform
approximate inference on arbitrary graphical models, in part due to its
excellent empirical properties and performance. However, little is known
theoretically about when this algorithm will perform well. Using recent
analysis of convergence and stability properties in BP and new results on
approximations in binary systems, we derive a bound on the error in BP's
estimates for pairwise Markov random fields over discrete valued random
variables. Our bound is relatively simple to compute, and compares favorably
with a previous method of bounding the accuracy of BP.
| Alexander T. Ihler | null | 1206.5277 | null | null |
Fast Nonparametric Conditional Density Estimation | stat.ME cs.LG stat.ML | Conditional density estimation generalizes regression by modeling a full
density f(yjx) rather than only the expected value E(yjx). This is important
for many tasks, including handling multi-modality and generating prediction
intervals. Though fundamental and widely applicable, nonparametric conditional
density estimators have received relatively little attention from statisticians
and little or none from the machine learning community. None of that work has
been applied to greater than bivariate data, presumably due to the
computational difficulty of data-driven bandwidth selection. We describe the
double kernel conditional density estimator and derive fast dual-tree-based
algorithms for bandwidth selection using a maximum likelihood criterion. These
techniques give speedups of up to 3.8 million in our experiments, and enable
the first applications to previously intractable large multivariate datasets,
including a redshift prediction problem from the Sloan Digital Sky Survey.
| Michael P. Holmes, Alexander G. Gray, Charles Lee Isbell | null | 1206.5278 | null | null |
Learning Selectively Conditioned Forest Structures with Applications to
DBNs and Classification | cs.LG stat.ML | Dealing with uncertainty in Bayesian Network structures using maximum a
posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often
intractable due to the superexponential number of possible directed, acyclic
graphs. When the prior is decomposable, two classes of graphs where efficient
learning can take place are tree structures, and fixed-orderings with limited
in-degree. We show how MAP estimates and BMA for selectively conditioned
forests (SCF), a combination of these two classes, can be computed efficiently
for ordered sets of variables. We apply SCFs to temporal data to learn Dynamic
Bayesian Networks having an intra-timestep forest and inter-timestep limited
in-degree structure, improving model accuracy over DBNs without the combination
of structures. We also apply SCFs to Bayes Net classification to learn
selective forest augmented Naive Bayes classifiers. We argue that the built-in
feature selection of selective augmented Bayes classifiers makes them
preferable to similar non-selective classifiers based on empirical evidence.
| Brian D. Ziebart, Anind K. Dey, J Andrew Bagnell | null | 1206.5281 | null | null |
A Characterization of Markov Equivalence Classes for Directed Acyclic
Graphs with Latent Variables | stat.ME cs.LG stat.ML | Different directed acyclic graphs (DAGs) may be Markov equivalent in the
sense that they entail the same conditional independence relations among the
observed variables. Meek (1995) characterizes Markov equivalence classes for
DAGs (with no latent variables) by presenting a set of orientation rules that
can correctly identify all arrow orientations shared by all DAGs in a Markov
equivalence class, given a member of that class. For DAG models with latent
variables, maximal ancestral graphs (MAGs) provide a neat representation that
facilitates model search. Earlier work (Ali et al. 2005) has identified a set
of orientation rules sufficient to construct all arrowheads common to a Markov
equivalence class of MAGs. In this paper, we provide extra rules sufficient to
construct all common tails as well. We end up with a set of orientation rules
sound and complete for identifying commonalities across a Markov equivalence
class of MAGs, which is particularly useful for causal inference.
| Jiji Zhang | null | 1206.5282 | null | null |
Bayesian Active Distance Metric Learning | cs.LG stat.ML | Distance metric learning is an important component for many tasks, such as
statistical classification and content-based image retrieval. Existing
approaches for learning distance metrics from pairwise constraints typically
suffer from two major problems. First, most algorithms only offer point
estimation of the distance metric and can therefore be unreliable when the
number of training examples is small. Second, since these algorithms generally
select their training examples at random, they can be inefficient if labeling
effort is limited. This paper presents a Bayesian framework for distance metric
learning that estimates a posterior distribution for the distance metric from
labeled pairwise constraints. We describe an efficient algorithm based on the
variational method for the proposed Bayesian approach. Furthermore, we apply
the proposed Bayesian framework to active distance metric learning by selecting
those unlabeled example pairs with the greatest uncertainty in relative
distance. Experiments in classification demonstrate that the proposed framework
achieves higher classification accuracy and identifies more informative
training examples than the non-Bayesian approach and state-of-the-art distance
metric learning algorithms.
| Liu Yang, Rong Jin, Rahul Sukthankar | null | 1206.5283 | null | null |
MAP Estimation, Linear Programming and Belief Propagation with Convex
Free Energies | cs.AI cs.LG stat.ML | Finding the most probable assignment (MAP) in a general graphical model is
known to be NP hard but good approximations have been attained with max-product
belief propagation (BP) and its variants. In particular, it is known that using
BP on a single-cycle graph or tree reweighted BP on an arbitrary graph will
give the MAP solution if the beliefs have no ties. In this paper we extend the
setting under which BP can be used to provably extract the MAP. We define
Convex BP as BP algorithms based on a convex free energy approximation and show
that this class includes ordinary BP with single-cycle, tree reweighted BP and
many other BP variants. We show that when there are no ties, fixed-points of
convex max-product BP will provably give the MAP solution. We also show that
convex sum-product BP at sufficiently small temperatures can be used to solve
linear programs that arise from relaxing the MAP problem. Finally, we derive a
novel condition that allows us to derive the MAP solution even if some of the
convex BP beliefs have ties. In experiments, we show that our theorems allow us
to find the MAP in many real-world instances of graphical models where exact
inference using junction-tree is impossible.
| Yair Weiss, Chen Yanover, Talya Meltzer | null | 1206.5286 | null | null |
Imitation Learning with a Value-Based Prior | cs.LG cs.AI stat.ML | The goal of imitation learning is for an apprentice to learn how to behave in
a stochastic environment by observing a mentor demonstrating the correct
behavior. Accurate prior knowledge about the correct behavior can reduce the
need for demonstrations from the mentor. We present a novel approach to
encoding prior knowledge about the correct behavior, where we assume that this
prior knowledge takes the form of a Markov Decision Process (MDP) that is used
by the apprentice as a rough and imperfect model of the mentor's behavior.
Specifically, taking a Bayesian approach, we treat the value of a policy in
this modeling MDP as the log prior probability of the policy. In other words,
we assume a priori that the mentor's behavior is likely to be a high value
policy in the modeling MDP, though quite possibly different from the optimal
policy. We describe an efficient algorithm that, given a modeling MDP and a set
of demonstrations by a mentor, provably converges to a stationary point of the
log posterior of the mentor's policy, where the posterior is computed with
respect to the "value based" prior. We also present empirical evidence that
this prior does in fact speed learning of the mentor's policy, and is an
improvement in our experiments over similar previous methods.
| Umar Syed, Robert E. Schapire | null | 1206.5290 | null | null |
Improved Dynamic Schedules for Belief Propagation | cs.LG cs.AI stat.ML | Belief propagation and its variants are popular methods for approximate
inference, but their running time and even their convergence depend greatly on
the schedule used to send the messages. Recently, dynamic update schedules have
been shown to converge much faster on hard networks than static schedules,
namely the residual BP schedule of Elidan et al. [2006]. But that RBP algorithm
wastes message updates: many messages are computed solely to determine their
priority, and are never actually performed. In this paper, we show that
estimating the residual, rather than calculating it directly, leads to
significant decreases in the number of messages required for convergence, and
in the total running time. The residual is estimated using an upper bound based
on recent work on message errors in BP. On both synthetic and real-world
networks, this dramatically decreases the running time of BP, in some cases by
a factor of five, without affecting the quality of the solution.
| Charles Sutton, Andrew McCallum | null | 1206.5291 | null | null |
On Sensitivity of the MAP Bayesian Network Structure to the Equivalent
Sample Size Parameter | cs.LG stat.ML | BDeu marginal likelihood score is a popular model selection criterion for
selecting a Bayesian network structure based on sample data. This
non-informative scoring criterion assigns same score for network structures
that encode same independence statements. However, before applying the BDeu
score, one must determine a single parameter, the equivalent sample size alpha.
Unfortunately no generally accepted rule for determining the alpha parameter
has been suggested. This is disturbing, since in this paper we show through a
series of concrete experiments that the solution of the network structure
optimization problem is highly sensitive to the chosen alpha parameter value.
Based on these results, we are able to give explanations for how and why this
phenomenon happens, and discuss ideas for solving this problem.
| Tomi Silander, Petri Kontkanen, Petri Myllymaki | null | 1206.5293 | null | null |
Dynamic Pricing under Finite Space Demand Uncertainty: A Multi-Armed
Bandit with Dependent Arms | cs.LG | We consider a dynamic pricing problem under unknown demand models. In this
problem a seller offers prices to a stream of customers and observes either
success or failure in each sale attempt. The underlying demand model is unknown
to the seller and can take one of N possible forms. In this paper, we show that
this problem can be formulated as a multi-armed bandit with dependent arms. We
propose a dynamic pricing policy based on the likelihood ratio test. We show
that the proposed policy achieves complete learning, i.e., it offers a bounded
regret where regret is defined as the revenue loss with respect to the case
with a known demand model. This is in sharp contrast with the logarithmic
growing regret in multi-armed bandit with independent arms.
| Pouya Tehrani, Yixuan Zhai, Qing Zhao | null | 1206.5345 | null | null |
Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian
Mixtures and Autoencoders | cs.LG cs.DS | We present a new algorithm for Independent Component Analysis (ICA) which has
provable performance guarantees. In particular, suppose we are given samples of
the form $y = Ax + \eta$ where $A$ is an unknown $n \times n$ matrix and $x$ is
a random variable whose components are independent and have a fourth moment
strictly less than that of a standard Gaussian random variable and $\eta$ is an
$n$-dimensional Gaussian random variable with unknown covariance $\Sigma$: We
give an algorithm that provable recovers $A$ and $\Sigma$ up to an additive
$\epsilon$ and whose running time and sample complexity are polynomial in $n$
and $1 / \epsilon$. To accomplish this, we introduce a novel "quasi-whitening"
step that may be useful in other contexts in which the covariance of Gaussian
noise is not known in advance. We also give a general framework for finding all
local optima of a function (given an oracle for approximately finding just one)
and this is a crucial step in our algorithm, one that has been overlooked in
previous attempts, and allows us to control the accumulation of error when we
find the columns of $A$ one by one via local search.
| Sanjeev Arora, Rong Ge, Ankur Moitra, Sushant Sachdeva | null | 1206.5349 | null | null |
Practical recommendations for gradient-based training of deep
architectures | cs.LG | Learning algorithms related to artificial neural networks and in particular
for Deep Learning may seem to involve many bells and whistles, called
hyper-parameters. This chapter is meant as a practical guide with
recommendations for some of the most commonly used hyper-parameters, in
particular in the context of learning algorithms based on back-propagated
gradient and gradient-based optimization. It also discusses how to deal with
the fact that more interesting results can be obtained when allowing one to
adjust many hyper-parameters. Overall, it describes elements of the practice
used to successfully and efficiently train and debug large-scale and often deep
multi-layer neural networks. It closes with open questions about the training
difficulties observed with deeper architectures.
| Yoshua Bengio | null | 1206.5533 | null | null |
Representation Learning: A Review and New Perspectives | cs.LG | The success of machine learning algorithms generally depends on data
representation, and we hypothesize that this is because different
representations can entangle and hide more or less the different explanatory
factors of variation behind the data. Although specific domain knowledge can be
used to help design representations, learning with generic priors can also be
used, and the quest for AI is motivating the design of more powerful
representation-learning algorithms implementing such priors. This paper reviews
recent work in the area of unsupervised feature learning and deep learning,
covering advances in probabilistic models, auto-encoders, manifold learning,
and deep networks. This motivates longer-term unanswered questions about the
appropriate objectives for learning good representations, for computing
representations (i.e., inference), and the geometrical connections between
representation learning, density estimation and manifold learning.
| Yoshua Bengio and Aaron Courville and Pascal Vincent | null | 1206.5538 | null | null |
A Geometric Algorithm for Scalable Multiple Kernel Learning | cs.LG stat.ML | We present a geometric formulation of the Multiple Kernel Learning (MKL)
problem. To do so, we reinterpret the problem of learning kernel weights as
searching for a kernel that maximizes the minimum (kernel) distance between two
convex polytopes. This interpretation combined with novel structural insights
from our geometric formulation allows us to reduce the MKL problem to a simple
optimization routine that yields provable convergence as well as quality
guarantees. As a result our method scales efficiently to much larger data sets
than most prior methods can handle. Empirical evaluation on eleven datasets
shows that we are significantly faster and even compare favorably with a
uniform unweighted combination of kernels.
| John Moeller, Parasaran Raman, Avishek Saha, Suresh Venkatasubramanian | null | 1206.5580 | null | null |
Learning mixtures of spherical Gaussians: moment methods and spectral
decompositions | cs.LG stat.ML | This work provides a computationally efficient and statistically consistent
moment-based estimator for mixtures of spherical Gaussians. Under the condition
that component means are in general position, a simple spectral decomposition
technique yields consistent parameter estimates from low-order observable
moments, without additional minimum separation assumptions needed by previous
computationally efficient estimation procedures. Thus computational and
information-theoretic barriers to efficient estimation in mixture models are
precluded when the mixture components have means in general position and
spherical covariances. Some connections are made to estimation problems related
to independent component analysis.
| Daniel Hsu, Sham M. Kakade | null | 1206.5766 | null | null |
Exact Recovery of Sparsely-Used Dictionaries | cs.LG cs.IT math.IT | We consider the problem of learning sparsely used dictionaries with an
arbitrary square dictionary and a random, sparse coefficient matrix. We prove
that $O (n \log n)$ samples are sufficient to uniquely determine the
coefficient matrix. Based on this proof, we design a polynomial-time algorithm,
called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that
it probably recovers the dictionary and coefficient matrix when the coefficient
matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the
true dictionary as well as the coefficients with probability higher than many
state-of-the-art algorithms.
| Daniel A. Spielman, Huan Wang, John Wright | null | 1206.5882 | null | null |
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