We describe an approach to building brain-computer interfaces (BCI) based on graphical models for probabilistic inference and learning. We show how a dynamic Bayesian network (DBN) can be used to infer probability distributions over brain-and body-states during planning and execution of actions. The DBN is learned directly from observed data and allows measured signals such as EEG and EMG to be interpreted in terms of internal states such as intent to move, preparatory activity, and movement execution. Unlike traditional classification-based approaches to BCI, the proposed approach (1) allows continuous tracking and prediction of internal states over time, and (2) generates control signals based on an entire probability distribution over states rather than binary yes/no decisions. We present preliminary results of brain-and body-state estimation using simultaneous EEG and EMG signals recorded during a self-paced left/right hand movement task.

We propose a "soft greedy" learning algorithm for building small conjunctions of simple threshold functions, called rays, defined on single real-valued attributes. We also propose a PAC-Bayes risk bound which is minimized for classifiers achieving a nontrivial tradeoff between sparsity (the number of rays used) and the magnitude of the separating margin of each ray. Finally, we test the soft greedy algorithm on four DNA micro-array data sets.

In this paper we present a framework for using multi-layer perceptron (MLP) networks in nonlinear generative models trained by variational Bayesian learning. The nonlinearity is handled by linearizing it using a Gauss-Hermite quadrature at the hidden neurons.

In the analysis of natural images, Gaussian scale mixtures (GSM) have been used to account for the statistics of filter responses, and to inspire hierarchical cortical representational learning schemes. GSMs pose a critical assignment problem, working out which filter responses were generated by a common multiplicative factor. We present a new approach to solving this assignment problem through a probabilistic extension to the basic GSM, and show how to perform inference in the model using Gibbs sampling. We demonstrate the efficacy of the approach on both synthetic and image data. Understanding the statistical structure of natural images is an important goal for visual neuroscience. Neural representations in early cortical areas decompose images (and likely other sensory inputs) in a way that is sensitive to sophisticated aspects of their probabilistic structure. This structure also plays a key role in methods for image processing and coding. A striking aspect of natural images that has reflections in both top-down and bottom-up modeling is coordination across nearby locations, scales, and orientations. From a topdown perspective, this structure has been modeled using what is known as a Gaussian Scale Mixture model (GSM).

We present a novel method for learning with Gaussian process regression in a hierarchical Bayesian framework. In a first step, kernel matrices on a fixed set of input points are learned from data using a simple and efficient EM algorithm. This step is nonparametric, in that it does not require a parametric form of covariance function. In a second step, kernel functions are fitted to approximate the learned covariance matrix using a generalized Nystr om method, which results in a complex, data driven kernel. We evaluate our approach as a recommendation engine for art images, where the proposed hierarchical Bayesian method leads to excellent prediction performance.

We establish learning rates to the Bayes risk for support vector machines (SVMs) with hinge loss. In particular, for SVMs with Gaussian RBF kernels we propose a geometric condition for distributions which can be used to determine approximation properties of these kernels. Finally, we compare our methods with a recent paper of G. Blanchard et al..

This paper analyzes generalization of the classic Rescorla-Wagner (R-W) learning algorithm and studies their relationship to Maximum Likelihood estimation of causal parameters. We prove that the parameters of two popular causal models, P and P C, can be learnt by the same generalized linear Rescorla-Wagner (GLRW) algorithm provided genericity conditions apply. We characterize the fixed points of these GLRW algorithms and calculate the fluctuations about them, assuming that the input is a set of i.i.d.

Spike sorting involves clustering spike trains recorded by a microelectrode according to the source neuron. It is a complicated problem, which requires a lot of human labor, partly due to the non-stationary nature of the data. We propose an automated technique for the clustering of non-stationary Gaussian sources in a Bayesian framework. At a first search stage, data is divided into short time frames and candidate descriptions of the data as a mixture of Gaussians are computed for each frame. At a second stage transition probabilities between candidate mixtures are computed, and a globally optimal clustering is found as the MAP solution of the resulting probabilistic model. Transition probabilities are computed using local stationarity assumptions and are based on a Gaussian version of the Jensen-Shannon divergence. The method was applied to several recordings. The performance appeared almost indistinguishable from humans in a wide range of scenarios, including movement, merges, and splits of clusters.

Classification algorithms typically induce population-wide models that are trained to perform well on average on expected future instances. We introduce a Bayesian framework for learning instance-specific models from data that are optimized to predict well for a particular instance. Based on this framework, we present a lazy instance-specific algorithm called ISA that performs selective model averaging over a restricted class of Bayesian networks. On experimental evaluation, this algorithm shows superior performance over model selection. We intend to apply such instance-specific algorithms to improve the performance of patient-specific predictive models induced from medical data.

First-order Markov models have been successfully applied to many problems, for example in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model's parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for many problems, the firstorder conditional independence assumptions are not satisfied, and as a result the higher order transition probabilities may be poorly approximated. Motivated by the problem of learning an MDP's parameters for control, we propose an algorithm for learning a first-order Markov model that explicitly takes into account higher order interactions during training. Our algorithm uses an optimization criterion different from maximum likelihood, and allows us to learn models that capture longer range effects, but without giving up the benefits of using first-order Markov models. Our experimental results also show the new algorithm outperforming conventional maximum likelihood estimation in a number of control problems where the MDP's parameters are estimated from data.