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.

We propose an efficient sequential Monte Carlo inference scheme for the recently proposed coalescent clustering model (Teh et al, 2008). Our algorithm has a quadratic runtime while those in (Teh et al, 2008) is cubic. In experiments, we were surprised to find that in addition to being more efficient, it is also a better sequential Monte Carlo sampler than the best in (Teh et al, 2008), when measured in terms of variance of estimated likelihood and effective sample size. Papers published at the Neural Information Processing Systems Conference.

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.

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.

The stochastic approximation method is behind the solution to many important, actively-studied problems in machine learning. Despite its far-reaching application, there is almost no work on applying stochastic approximation to learning problems with constraints. The reason for this, we hypothesize, is that no robust, widely-applicable stochastic approximation method exists for handling such problems. We propose that interior-point methods are a natural solution. We establish the stability of a stochastic interior-point approximation method both analytically and empirically, and demonstrate its utility by deriving an on-line learning algorithm that also performs feature selection via L1 regularization.

Identification and comparison of nonlinear dynamical systems using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our method involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible without solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods. Papers published at the Neural Information Processing Systems Conference.

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.

We describe a new algorithmic framework for inference in probabilistic models, and apply it to inference for latent Dirichlet allocation. Our framework adopts the methodology of variational inference, but unlike existing variational methods such as mean field and expectation propagation it is not restricted to tractable classes of approximating distributions. Our approach can also be viewed as a sequential Monte Carlo (SMC) method, but unlike existing SMC methods there is no need to design the artificial sequence of distributions. Notably, our framework offers a principled means to exchange the variance of an importance sampling estimate for the bias incurred through variational approximation. Experiments on a challenging inference problem in population genetics demonstrate improvements in stability and accuracy over existing methods, and at a comparable cost.

We study convex stochastic optimization problems where a noisy objective function value is observed after a decision is made. There are many stochastic optimization problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation for the joint distribution of state-outcome pairs to create weights for previous observations. Those similar to the current state are used to create a convex, deterministic approximation of the objective function.