Source separation is an important problem at the intersection of several fields, including machine learning, signal processing, and speech technology. Herewe describe new separation algorithms which are based on probabilistic graphical models with latent variables. In contrast with existing methods, these algorithms exploit detailed models to describe source properties. They also use subband filtering ideas to model the reverberant environment, and employ an explicit model for background and sensor noise. We leverage variational techniques to keep the computational complexityper EM iteration linear in the number of frames.

Forward decoding kernel machines (FDKM) combine large-margin classifiers withhidden Markov models (HMM) for maximum a posteriori (MAP) adaptive sequence estimation. State transitions in the sequence are conditioned on observed data using a kernel-based probability model trained with a recursive scheme that deals effectively with noisy and partially labeleddata. Training over very large datasets is accomplished using a sparse probabilistic support vector machine (SVM) model based on quadratic entropy, and an online stochastic steepest descent algorithm. For speaker-independent continuous phone recognition, FDKM trained over 177,080 samples of the TlMIT database achieves 80.6% recognition accuracy over the full test set, without use of a prior phonetic language model. 1 Introduction Sequence estimation is at the core of many problems in pattern recognition, most notably speech and language processing. Recognizing dynamic patterns in sequential data requires a set of tools very different from classifiers trained to recognize static patterns in data assumed i.i.d.

Given a set of hidden variables with an a-priori Markov structure, we derive an online algorithm which approximately updates the posterior as pairwise measurements between the hidden variables become available. The update is performed using Assumed Density Filtering: to incorporate each pairwise measurement, we compute the optimal Markov structure which represents the true posterior and use it as a prior for incorporating the next measurement. We demonstrate the resulting algorithm by calculating globallyconsistent trajectories of a robot as it navigates along a 2D trajectory. To update a trajectory of length t, the update takes O(t). When all conditional distributions are linear-Gaussian, the algorithm can be thought of as a Kalman Filter which simplifies the state covariance matrix after incorporating each measurement.

We derive multiplicative updates for solving the nonnegative quadratic programming problem in support vector machines (SVMs). The updates have a simple closed form, and we prove that they converge monotonically tothe solution of the maximum margin hyperplane. The updates optimize the traditionally proposed objective function for SVMs. They do not involve any heuristics such as choosing a learning rate or deciding which variables to update at each iteration. They can be used to adjust all the quadratic programming variables in parallel with a guarantee of improvement ateach iteration. We analyze the asymptotic convergence of the updates and show that the coefficients of nonsupport vectors decay geometrically to zero at a rate that depends on their margins.

We present a class of algorithms for learning the structure of graphical models from data. The algorithms are based on a measure known as the kernel generalized variance (KGV), which essentially allows us to treat all variables on an equal footing as Gaussians in a feature space obtained from Mercer kernels. Thus we are able to learn hybrid graphs involving discrete and continuous variables of arbitrary type. We explore the computational properties of our approach, showing how to use the kernel trick to compute the relevant statistics in linear time. We illustrate our framework with experiments involving discrete and continuous data.

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.

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.