This paper proposes an approach to classification of adjacent segments of a time series as being either of classes. We use a hierarchical model that consists of a feature extraction stage and a generative classifier which is built on top of these features. Such two stage approaches are often used in signal and image processing. The novel part of our work is that we link these stages probabilistically by using a latent feature space. To use one joint model is a Bayesian requirement, which has the advantage to fuse information according to its certainty.

Predicting the 3D structure of protein chains from the linear sequence of amino acids is a fundamental open problem in computational molecular biology [1]. Any approach to the problem must deal with the basic fact that protein structures are translation and rotation invariant. To address this invariance, we have proposed a machine learning approach to protein structure prediction [4] based on the predic- tion of topological representations of proteins, in the form of contact or distance maps. The contact or distance map is a 2D representation of neighborhood rela- tionships consisting of an adjacency matrix at some distance cuto(cid:11) (typically in the range of 6 to 12 (cid:23)A), or a matrix of pairwise Euclidean distances. Fine-grained maps are derived at the amino acid or even atomic level. Coarse maps are obtained by looking at secondary structure elements, such as helices, and the distance between their centers of gravity or, as in the simulations below, the minimal distances be- tween their C(cid:11) atoms.

Spontaneous facial expressions differ substan- tially from posed expressions, similar to how continuous, spontaneous speech differs from isolated words produced on command. Previous methods for automatic facial expression recognition assumed images were collected in controlled environments in which the subjects delib- erately faced the camera. Since people often nod or turn their heads, automatic recognition of spontaneous facial behavior requires methods for handling out-of-image-plane head rotations. Here we explore an ap- proach based on 3-D warping of images into canonical views. We eval- uated the performance of the approach as a front-end for a spontaneous expression recognition system using support vector machines and hidden Markov models.

We propose a dynamic Bayesian model for motifs in biopolymer se- quences which captures rich biological prior knowledge and positional dependencies in motif structure in a principled way. Our model posits that the position-specific multinomial parameters for monomer distribu- tion are distributed as a latent Dirichlet-mixture random variable, and the position-specific Dirichlet component is determined by a hidden Markov process. Model parameters can be fit on training motifs using a vari- ational EM algorithm within an empirical Bayesian framework. Varia- tional inference is also used for detecting hidden motifs. Our model im- proves over previous models that ignore biological priors and positional dependence.

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are intractable for large models. The in- tractability of these algorithms is due to a great extent to their generating an optimal policy over the entire belief space. However, in real POMDP problems most belief states are unlikely, and there is a structured, low-dimensional manifold of plausible beliefs embedded in the high-dimensional belief space. We introduce a new method for solving large-scale POMDPs by taking advantage of belief space sparsity. We reduce the dimensionality of the belief space by exponential family Principal Components Analysis [1], which allows us to turn the sparse, high- dimensional belief space into a compact, low-dimensional representation in terms of learned features of the belief state.

Cortical synaptic plasticity depends on the relative timing of pre- and postsynaptic spikes and also on the temporal pattern of presynaptic spikes and of postsynaptic spikes. We study the hypothesis that cortical synap- tic plasticity does not associate individual spikes, but rather whole fir- ing episodes, and depends only on when these episodes start and how long they last, but as little as possible on the timing of individual spikes. Here we present the mathematical background for such a study. Stan- dard methods from hidden Markov models are used to define what "fir- ing episodes" are. Estimating the probability of being in such an episode requires not only the knowledge of past spikes, but also of future spikes.

This paper presents a novel Hidden Markov Model architecture to model the joint probability of pairs of asynchronous sequences de(cid:173) scribing the same event. It is based on two other Markovian models, namely Asynchronous Input/ Output Hidden Markov Models and Pair Hidden Markov Models. An EM algorithm to train the model is presented, as well as a Viterbi decoder that can be used to ob(cid:173) tain the optimal state sequence as well as the alignment between the two sequences. The model has been tested on an audio-visual speech recognition task using the M2VTS database and yielded robust performances under various noise conditions.

Forward decoding kernel machines (FDKM) combine large-margin clas(cid:173) sifiers with hidden 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 par(cid:173) tially labeled data. Training over very large data sets is accomplished us(cid:173) ing a sparse probabilistic support vector machine (SVM) model based on quadratic entropy, and an on-line 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.

We examine the problem of generating state-space compressions of POMDPs in a way that minimally impacts decision quality. We analyze the impact of compres- sions on decision quality, observing that compressions that allow accurate policy evaluation (prediction of expected future reward) will not affect decision qual- ity. We derive a set of sufficient conditions that ensure accurate prediction in this respect, illustrate interesting mathematical properties these confer on lossless lin- ear compressions, and use these to derive an iterative procedure for finding good linear lossy compressions. We also elaborate on how structured representations of a POMDP can be used to find such compressions.

We examine the use of hidden Markov and hidden semi-Markov mod- els for automatically segmenting an electrocardiogram waveform into its constituent waveform features. An undecimated wavelet transform is used to generate an overcomplete representation of the signal that is more appropriate for subsequent modelling. We show that the state dura- tions implicit in a standard hidden Markov model are ill-suited to those of real ECG features, and we investigate the use of hidden semi-Markov models for improved state duration modelling.