A standard method to obtain stochastic models for symbolic time series is to train state-emitting hidden Markov models (SE-HMMs) with the Baum-Welch algorithm. Based on observable operator models (OOMs), in the last few months a number of novel learning algorithms for similar purposes have been developed: (1,2) two versions of an "efficiency sharpening" (ES) algorithm, which iteratively improves the statistical efficiency of a sequence of OOM estimators, (3) a constrained gradient descent ML estimator for transition-emitting HMMs (TE-HMMs). We give an overview on these algorithms and compare them with SE-HMM/EM learning on synthetic and real-life data.

We develop an approach for estimation with Gaussian Markov processes that imposes a smoothness prior while allowing for discontinuities. In- stead of propagating information laterally between neighboring nodes in a graph, we study the posterior distribution of the hidden nodes as a whole--how it is perturbed by invoking discontinuities, or weakening the edges, in the graph. We show that the resulting computation amounts to feed-forward fan-in operations reminiscent of V1 neurons. Moreover, using suitable matrix preconditioners, the incurred matrix inverse and determinant can be approximated, without iteration, in the same compu- tational style. Simulation results illustrate the merits of this approach.

This paper describes a highly successful application of MRFs to the problem of generating high-resolution range images. A new generation of range sensors combines the capture of low-resolution range images with the acquisition of registered high-resolution camera images. The MRF in this paper exploits the fact that discontinuities in range and coloring tend to co-align. This enables it to generate high-resolution, low-noise range images by integrating regular camera images into the range data. We show that by using such an MRF, we can substantially improve over existing range imaging technology.

We study the problem of parameter estimation in continuous density hidden Markov models (CD-HMMs) for automatic speech recognition (ASR). As in support vector machines, we propose a learning algorithm based on the goal of margin maximization. Unlike earlier work on max-margin Markov networks, our approach is specifically geared to the modeling of real-valued observations (such as acoustic feature vectors) using Gaussian mixture models. Unlike previous discriminative frameworks for ASR, such as maximum mutual information and minimum classification error, our framework leads to a convex optimization, without any spurious local minima. The objective function for large margin training of CD-HMMs is defined over a parameter space of positive semidefinite matrices.

Starting with the work of Jaakkola and Haussler, a variety of approaches have been proposed for coupling domain-specific generative models with statistical learning methods. The link is established by a kernel function which provides a similarity measure based inherently on the underlying model. In computational biology, the full promise of this framework has rarely ever been exploited, as most kernels are derived from very generic models, such as sequence profiles or hidden Markov models. Here, we introduce the MTreeMix kernel, which is based on a generative model tailored to the underlying biological mechanism. We compare this novel kernel to a standard, evolution-agnostic amino acid encoding in the prediction of HIV drug resistance from genotype, using support vector regression.

We rigorously establish a close relationship between message passing algorithms and models of neurodynamics by showing that the equations of a continuous Hop- (cid:2)eld network can be derived from the equations of belief propagation on a binary Markov random (cid:2)eld. As Hop(cid:2)eld networks are equipped with a Lyapunov func- tion, convergence is guaranteed. As a consequence, in the limit of many weak con- nections per neuron, Hop(cid:2)eld networks exactly implement a continuous-time vari- ant of belief propagation starting from message initialisations that prevent from running into convergence problems. Our results lead to a better understanding of the role of message passing algorithms in real biological neural networks.

Human listeners have the extraordinary ability to hear and recognize speech even when more than one person is talking. Their machine counterparts have historically been unable to compete with this ability, until now. We present a modelbased system that performs on par with humans in the task of separating speech of two talkers from a single-channel recording. The models of speech use temporal dynamics to help infer the source speech signals, given mixed speech signals. The estimated source signals are then recognized using a conventional speech recognition system.

Computational gene prediction using generative models has reached a plateau, with several groups converging to a generalized hidden Markov model (GHMM) incorporating phylogenetic models of nucleotide sequence evolution. Further improvements in gene calling accuracy are likely to come through new methods that incorporate additional data, both comparative and species specific. Conditional Random Fields (CRFs), which directly model the conditional probability P (y x) of a vector of hidden states conditioned on a set of observations, provide a unified framework for combining probabilistic and non-probabilistic information and have been shown to outperform HMMs on sequence labeling tasks in natural language processing. We describe the use of CRFs for comparative gene prediction. We implement a model that encapsulates both a phylogenetic-GHMM (our baseline comparative model) and additional non-probabilistic features.

Scoring structures of undirected graphical models by means of evaluating the marginal likelihood is very hard. The main reason is the presence of the parti- tion function which is intractable to evaluate, let alone integrate over. We propose to approximate the marginal likelihood by employing two levels of approximation: we assume normality of the posterior (the Laplace approximation) and approxi- mate all remaining intractable quantities using belief propagation and the linear response approximation. Em- pirically, we find that our procedure has about two orders of magnitude better accuracy than standard BIC methods for small datasets, but deteriorates when the size of the dataset grows.

We present a new statistical framework called hidden Markov Dirichlet process (HMDP) to jointly model the genetic recombinations among possibly infinite number of founders and the coalescence-with-mutation events in the resulting genealogies. The HMDP posits that a haplotype of genetic markers is generated by a sequence of recombination events that select an ancestor for each locus from an unbounded set of founders according to a 1st-order Markov transition process. Conjoining this process with a mutation model, our method accommodates both between-lineage recombination and within-lineage sequence variations, and leads to a compact and natural interpretation of the population structure and inheritance process underlying haplotype data. We have developed an efficient sampling algo rithm for HMDP based on a two-level nested Polya urn scheme. On both simulated and real SNP haplotype data, our method performs competitively or significantly better than extant methods in uncovering the recombination hotspots along chromosomal loci; and in addition it also infers the ancestral genetic patterns and offers a highly accurate map of ancestral compositions of modern populations.