Probabilistic topic models (and their extensions) have become popular as models of latent structures in collections of text documents or images. These models are usually treated as generative models and trained using maximum likelihood estimation, an approach which may be suboptimal in the context of an overall classification problem. In this paper, we describe DiscLDA, a discriminative learning framework for such models as Latent Dirichlet Allocation (LDA) in the setting of dimensionality reduction with supervised side information. In DiscLDA, a class-dependent linear transformation is introduced on the topic mixture proportions. This parameter is estimated by maximizing the conditional likelihood using Monte Carlo EM.

Situations in which people with opposing prior beliefs observe the same evidence and then strengthen those existing beliefs are frequently offered as evidence of human irrationality. This phenomenon, termed belief polarization, is typically assumed to be non-normative. We demonstrate, however, that a variety of cases of belief polarization are consistent with a Bayesian approach to belief revision. Simulation results indicate that belief polarization is not only possible but relatively common within the class of Bayesian models that we consider. Papers published at the Neural Information Processing Systems Conference.

Adaptation of visually guided reaching movements in novel visuomotor environments (e.g. Previous computational models of the sensory component of visuomotor adaptation have assumed that it is driven purely by the discrepancy introduced between visual and proprioceptive estimates of hand position and is independent of any motor component of adaptation. We instead propose a unified model in which sensory and motor adaptation are jointly driven by optimal Bayesian estimation of the sensory and motor contributions to perceived errors. Our model is able to account for patterns of performance errors during visuomotor adaptation as well as the subsequent perceptual aftereffects. This unified model also makes the surprising prediction that force field adaptation will elicit similar perceptual shifts, even though there is never any discrepancy between visual and proprioceptive observations.

Computing a {\em maximum a posteriori} (MAP) assignment in graphical models is a crucial inference problem for many practical applications. Several provably convergent approaches have been successfully developed using linear programming (LP) relaxation of the MAP problem. We present an alternative approach, which transforms the MAP problem into that of inference in a finite mixture of simple Bayes nets. We then derive the Expectation Maximization (EM) algorithm for this mixture that also monotonically increases a lower bound on the MAP assignment until convergence. The update equations for the EM algorithm are remarkably simple, both conceptually and computationally, and can be implemented using a graph-based message passing paradigm similar to max-product computation.

We consider the problem of binary classification where the classifier may abstain instead of classifying each observation. The Bayes decision rule for this setup, known as Chow's rule, is defined by two thresholds on posterior probabilities. From simple desiderata, namely the consistency and the sparsity of the classifier, we derive the double hinge loss function that focuses on estimating conditional probabilities only in the vicinity of the threshold points of the optimal decision rule. We show that, for suitable kernel machines, our approach is universally consistent. We cast the problem of minimizing the double hinge loss as a quadratic program akin to the standard SVM optimization problem and propose an active set method to solve it efficiently.

Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. In this paper, we present a nonparametric approach to the learning of an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with an efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, and the IBOVESPA stock index.

With the increased availability of data for complex domains, it is desirable to learn Bayesian network structures that are sufficiently expressive for generalization while also allowing for tractable inference. While the method of thin junction trees can, in principle, be used for this purpose, its fully greedy nature makes it prone to overfitting, particularly when data is scarce. In this work we present a novel method for learning Bayesian networks of bounded treewidth that employs global structure modifications and that is polynomial in the size of the graph and the treewidth bound. At the heart of our method is a triangulated graph that we dynamically update in a way that facilitates the addition of chain structures that increase the bound on the model's treewidth by at most one. We demonstrate the effectiveness of our treewidth-friendly'' method on several real-life datasets.

A non-parametric Bayesian model is proposed for processing multiple images. The analysis employs image features and, when present, the words associated with accompanying annotations. The model clusters the images into classes, and each image is segmented into a set of objects, also allowing the opportunity to assign a word to each object (localized labeling). Each object is assumed to be represented as a heterogeneous mix of components, with this realized via mixture models linking image features to object types. The number of image classes, number of object types, and the characteristics of the object-feature mixture models are inferred non-parametrically.

Conventional dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption, which is too restrictive in many practical applications. Various approaches to relax the homogeneity assumption have therefore been proposed in the last few years. The present paper aims to improve the flexibility of two recent versions of non-homogeneous DBNs, which either (i) suffer from the need for data discretization, or (ii) assume a time-invariant network structure. Allowing the network structure to be fully flexible leads to the risk of overfitting and inflated inference uncertainty though, especially in the highly topical field of systems biology, where independent measurements tend to be sparse. In the present paper we investigate three conceptually different regularization schemes based on inter-segment information sharing.

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. In the clustering case, we associate to each data point a latent allocation variable. These latent variables can share the same value and this induces a partition of the data set. The CRP is a prior distribution on such partitions. In latent feature models, we associate to each data point a potentially infinite number of binary latent variables indicating the possession of some features and the IBP is a prior distribution on the associated infinite binary matrix.