We examine the problem of generating state-space compressions of POMDPs in a way that minimally impacts decision quality. We analyze the impact of compressions ondecision quality, observing that compressions that allow accurate policy evaluation (prediction of expected future reward) will not affect decision quality. Wederive a set of sufficient conditions that ensure accurate prediction in this respect, illustrate interesting mathematical properties these confer on lossless linear compressions,and use these to derive an iterative procedure for finding good linear lossy compressions. We also elaborate on how structured representations of a POMDP can be used to find such compressions.

We present an algorithm that uses multiple cues to recover shading and reflectance intrinsic images from a single image. Using both color information and a classifier trained to recognize gray-scale patterns, each image derivative is classified as being caused by shading or a change in the surface's reflectance. Generalized Belief Propagation is then used to propagate information from areas where the correct classification is clear to areas where it is ambiguous. We also show results on real images.

We consider loopy belief propagation for approximate inference in probabilistic graphical models. A limitation of the standard algorithm is that clique marginals are computed as if there were no loops in the graph. To overcome this limitation, we introduce fractional belief propagation. Fractional belief propagation is formulated in terms of a family of approximate free energies, which includes the Bethe free energy and the naive mean-field free as special cases. Using the linear response correction of the clique marginals, the scale parameters can be tuned. Simulation results illustrate the potential merits of the approach.

We introduce a family of classifiers based on a physical analogy to an electrostatic system of charged conductors. The family, called Coulomb classifiers, includes the two best-known support-vector machines (SVMs), the ν-SVM and the C-SVM. In the electrostatics analogy,a training example corresponds to a charged conductor at a given location in space, the classification function corresponds to the electrostatic potential function, and the training objective function corresponds to the Coulomb energy. The electrostatic framework provides not only a novel interpretation of existing algorithms andtheir interrelationships, but it suggests a variety of new methods for SVMs including kernels that bridge the gap between polynomial and radial-basis functions, objective functions that do not require positive-definite kernels, regularization techniques that allow for the construction of an optimal classifier in Minkowski space. Based on the framework, we propose novel SVMs and perform simulationstudies to show that they are comparable or superior tostandard SVMs. The experiments include classification tasks on data which are represented in terms of their pairwise proximities, wherea Coulomb Classifier outperformed standard SVMs.

Identity uncertainty is a pervasive problem in real-world data analysis. It arises whenever objects are not labeled with unique identifiers or when those identifiers may not be perceived perfectly. In such cases, two observations mayor may not correspond to the same object. In this paper, we consider the problem in the context of citation matching--the problem ofdeciding which citations correspond to the same publication. Our approach is based on the use of a relational probability model to define a generative model for the domain, including models of author and title corruption and a probabilistic citation grammar. Identity uncertainty is handled by extending standard models to incorporate probabilities over the possible mappings between terms in the language and objects in the domain. Inference is based on Markov chain Monte Carlo, augmented with specific methods for generating efficient proposals when the domain contains many objects. Results on several citation data sets show that the method outperforms current algorithms for citation matching. The declarative, relational nature of the model also means that our algorithm can determine object characteristics such as author names by combining multiple citations of multiple papers.

A framework is introduced for assessing the encoding accuracy and the discriminational ability of a population of neurons upon simultaneous presentation of multiple stimuli. Minimal square estimation errors are obtained from a Fisher information analysis in an abstract compound space comprising the features of all stimuli. Even for the simplest case of linear superposition of responses and Gaussian tuning, the symmetries in the compound space are very different from those in the case of a single stimulus. The analysis allows for a quantitative description of attentional effects and can be extended to include neural nonlinearities such as nonclassical receptive fields.

We propose a dynamic Bayesian model for motifs in biopolymer sequences which captures rich biological prior knowledge and positional dependencies in motif structure in a principled way. Our model posits that the position-specific multinomial parameters for monomer distribution are distributed as a latent Dirichlet-mixture random variable, and the position-specific Dirichlet component is determined by a hidden Markov process. Model parameters can be fit on training motifs using a variational EM algorithm within an empirical Bayesian framework. Variational inference is also used for detecting hidden motifs. Our model improves over previous models that ignore biological priors and positional dependence. It has much higher sensitivity to motifs during detection and a notable ability to distinguish genuine motifs from false recurring patterns.

Most text categorization systems use simple models of documents and document collections. In this paper we describe a technique that improves a simple web page classifier's performance on pages from a new, unseen web site, by exploiting link structure within a site as well as page structure within hub pages. On real-world test cases, this technique significantly and substantially improves the accuracy of a bag-of-words classifier, reducing error rate by about half, on average. The system uses a variant of co-training to exploit unlabeled data from a new site. Pages are labeled using the base classifier; the results are used by a restricted wrapper-learner to propose potential "main-category anchor wrappers"; and finally, these wrappers are used as features by a third learner to find a categorization of the site that implies a simple hub structure, but which also largely agrees with the original bag-of-words classifier.

The problem of learning a semantic representation of a text document from data is addressed, in the situation where a corpus of unlabeled paired documents is available, each pair being formed by a short English document and its French translation. This representation can then be used for any retrieval, categorization or clustering task, both in a standard and in a cross-lingual setting. By using kernel functions, in this case simple bag-of-words inner products, each part of the corpus is mapped to a high-dimensional space. The correlations between the two spaces are then learnt by using kernel Canonical Correlation Analysis. A set of directions is found in the first and in the second space that are maximally correlated. Since we assume the two representations are completely independent apart from the semantic content, any correlation between them should reflect some semantic similarity. Certain patterns of English words that relate to a specific meaning should correlate with certain patterns of French words corresponding to the same meaning, across the corpus. Using the semantic representation obtained in this way we first demonstrate that the correlations detected between the two versions of the corpus are significantly higher than random, and hence that a representation based on such features does capture statistical patterns that should reflect semantic information. Then we use such representation both in cross-language and in single-language retrieval tasks, observing performance that is consistently and significantly superior to LSI on the same data.

We address the question of feature selection in the context of visual recognition. It is shown that, besides efficient from a computational standpoint, the infomax principle is nearly optimal in the minimum Bayes error sense. The concept of marginal diversity is introduced, leading to a generic principle for feature selection (the principle of maximum marginal diversity) of extreme computational simplicity. The relationships between infomax and the maximization of marginal diversity are identified, uncovering the existence of a family of classification procedures for which near optimal (in the Bayes error sense) feature selection does not require combinatorial search. Examination of this family in light of recent studies on the statistics of natural images suggests that visual recognition problems are a subset of it.