Well-known applications include part-of-speech (POS) tagging, named entity classification, information extraction,text segmentation and phoneme classification in text and speech processing [7] as well as problems like protein homology detection, secondary structure prediction or gene classification in computational biology [3]. Up to now, the predominant formalism for modeling and predicting label sequences has been based on Hidden Markov Models (HMMs) and variations thereof. Yet, despite its success, generative probabilistic models - of which HMMs are a special case - have two major shortcomings, which this paper is not the first one to point out. First, generative probabilistic models are typically trained using maximum likelihood estimation (MLE) for a joint sampling model of observation and label sequences. As has been emphasized frequently, MLE based on the joint probability model is inherently non-discriminative and thus may lead to suboptimal prediction accuracy. Secondly, efficient inference and learning in this setting often requires to make questionable conditional independence assumptions.

We introduce NashProp, an iterative and local message-passing algorithm forcomputing Nash equilibria in multi-player games represented by arbitrary undirected graphs. We provide a formal analysis and experimental evidencedemonstrating that NashProp performs well on large graphical games with many loops, often converging in just a dozen iterations ongraphs with hundreds of nodes. NashProp generalizes the tree algorithm of (Kearns et al. 2001), and can be viewed as similar in spirit to belief propagation in probabilistic inference,and thus complements the recent work of (Vickrey and Koller 2002), who explored a junction tree approach. Thus, as for probabilistic inference,we have at least two promising general-purpose approaches toequilibria computation in graphs.

A new approach to inference in belief networks has been recently proposed, which is based on an algebraic representation of belief networks using multi-linear functions. According to this approach, the key computational question is that of representing multi-linear functions compactly, since inference reduces to a simple process of ev aluating and differentiating such functions. W e show here that mainstream inference algorithms based on jointrees are a special case of this approach in a v ery precise sense. W e use this result to prov e new properties of jointree algorithms, and then discuss some of its practical and theoretical implications.

In recent years variational methods have become a popular tool for approximate inference and learning in a wide variety of probabilistic models.For each new application, however, it is currently necessary first to derive the variational update equations, and then to implement them in application-specific code. Each of these steps is both time consuming and error prone. In this paper we describe a general purpose inference engine called VIBES ('Variational Inference forBayesian Networks') which allows a wide variety of probabilistic modelsto be implemented and solved variationally without recourse to coding. New models are specified either through a simple script or via a graphical interface analogous to a drawing package. VIBES then automatically generates and solves the variational equations.We illustrate the power and flexibility of VIBES using examples from Bayesian mixture modelling.

Greedy importance sampling is an unbiased estimation technique that reduces thevariance of standard importance sampling by explicitly searching for modes in the estimation objective. Previous work has demonstrated thefeasibility of implementing this method and proved that the technique is unbiased in both discrete and continuous domains. In this paper we present a reformulation of greedy importance sampling that eliminates the free parameters from the original estimator, and introduces a new regularization strategy that further reduces variance without compromising unbiasedness.The resulting estimator is shown to be effective for difficult estimation problems arising in Markov random field inference. Inparticular, improvements are achieved over standard MCMC estimators when the distribution has multiple peaked modes.

We propose in this paper a probabilistic approach for adaptive inference of generalized nonlinear classification that combines the computational advantage of a parametric solution with the flexibility of sequential sampling techniques.We regard the parameters of the classifier as latent states in a first order Markov process and propose an algorithm which can be regarded as variational generalization of standard Kalman filtering. Thevariational Kalman filter is based on two novel lower bounds that enable us to use a non-degenerate distribution over the adaptation rate. An extensive empirical evaluation demonstrates that the proposed method is capable of infering competitive classifiers both in stationary and non-stationary environments. Although we focus on classification, the algorithm is easily extended to other generalized nonlinear models.

The application of latent/hidden variable Dynamic Bayesian Networks isconstrained by the complexity of marginalising over latent variables. For this reason either small latent dimensions or Gaussian latentconditional tables linearly dependent on past states are typically considered in order that inference is tractable. We suggest an alternative approach in which the latent variables are modelled using deterministic conditional probability tables.

We present a simple direct approach for solving the ICA problem, using density estimation and maximum likelihood. Given a candidate orthogonalframe, we model each of the coordinates using a semi-parametric density estimate based on cubic splines. Since our estimates have two continuous derivatives, we can easily run a second ordersearch for the frame parameters. Our method performs very favorably when compared to state-of-the-art techniques. 1 Introduction Independent component analysis (ICA) is a popular enhancement over principal component analysis (PCA) and factor analysis. IRP which is assumed to arise from a linear mixing of a latent random source vector S E IRP, (1) X AS; the components Sj, j 1, ...,p of S are assumed to be independently distributed.

Several authors have suggested viewing boosting as a gradient descent search for a good fit in function space. We apply gradient-based boosting methodology to the unsupervised learning problem of density estimation. We show convergence properties of the algorithm and prove that a strength of weak learnability property appliesto this problem as well. We illustrate the potential of this approach through experiments with boosting Bayesian networks to learn density models.

We study an explicit parametric model of documents, queries, and relevancy assessmentfor Information Retrieval (IR). Mean-field methods are applied to analyze the model and derive efficient practical algorithms to estimate the parameters in the problem. The hyperparameters are estimated bya fast approximate leave-one-out cross-validation procedure based on the cavity method. The algorithm is further evaluated on several benchmark databases by comparing with standard algorithms in IR.