The application of latent/hidden variable Dynamic Bayesian Net- works is constrained by the complexity of marginalising over latent variables. For this reason either small latent dimensions or Gaus- sian latent conditional 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. This specialisa- tion has the advantage of tractable inference even for highly com- plex non-linear/non-Gaussian visible conditional probability tables. This approach enables the consideration of highly complex latent dynamics whilst retaining the bene(cid:12)ts of a tractable probabilistic model.

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.

Missing data is common in real-world datasets and is a problem for many estimation techniques. We have developed a variational Bayesian method to perform Independent Component Analysis (ICA) on high-dimensional data containing missing entries. Missing data are handled naturally in the Bayesian framework by integrating the generative density model. Mod- eling the distributions of the independent sources with mixture of Gaus- sians allows sources to be estimated with different kurtosis and skewness. The variational Bayesian method automatically determines the dimen- sionality of the data and yields an accurate density model for the ob- served data without overfitting problems.

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.

An essential step in understanding the function of sensory nervous sys- tems is to characterize as accurately as possible the stimulus-response function (SRF) of the neurons that relay and process sensory informa- tion. One increasingly common experimental approach is to present a rapidly varying complex stimulus to the animal while recording the re- sponses of one or more neurons, and then to directly estimate a func- tional transformation of the input that accounts for the neuronal firing. The estimation techniques usually employed, such as Wiener filtering or other correlation-based estimation of the Wiener or Volterra kernels, are equivalent to maximum likelihood estimation in a Gaussian-output-noise regression model. We explore the use of Bayesian evidence-optimization techniques to condition these estimates. We show that by learning hyper- parameters that control the smoothness and sparsity of the transfer func- tion it is possible to improve dramatically the quality of SRF estimates, as measured by their success in predicting responses to novel input.

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 present an analysis of concentration-of-expectation phenomena in layered Bayesian networks that use generalized linear models as the local conditional probabilities. This framework encompasses a wide variety of probability distributions, including both discrete and continuous random variables. We utilize ideas from large deviation analysis and the delta method to devise and evaluate a class of approximate inference algo- rithms for layered Bayesian networks that have superior asymptotic error bounds and very fast computation time.

Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent after- current. This model is a biophysically plausible alternative to models with Poisson (memory-less) spiking, and has been shown to effectively reproduce various spiking statistics of neurons in vivo. However, the problem of estimating the model from extracellular spike train data has not been examined in depth. We formulate the problem in terms of max- imum likelihood estimation, and show that the computational problem of maximizing the likelihood is tractable.