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.

The correction of bias in magnetic resonance images is an important problem in medical image processing. Most previous approaches have used a maximum likelihood method to increase the likelihood of the pixels in a single image by adaptively estimating a correction to the unknown image bias field. The pixel likelihoods are defined either in terms of a preexisting tissue model, or non-parametrically in terms of the image's own pixel values. In both cases, the specific location of a pixel in the image is not used to calculate the likelihoods. We suggest a new approach in which we simultaneously eliminate the bias from a set of images of the same anatomy, but from different patients. We use the statistics from the same location across different images, rather than within an image, to eliminate bias fields from all of the images simultaneously. The method builds a "multi-resolution" nonparametric tissue model conditioned on image location while eliminating the bias fields associated with the original image set.

It has been demonstrated that basic aspects of human visual motion perception are qualitatively consistent with a Bayesian estimation framework, where the prior probability distribution on velocity favors slow speeds. Here, we present a refined probabilistic model that can account for the typical trial-to-trial variabilities observed in psychophysical speed perception experiments. We also show that data from such experiments can be used to constrain both the likelihood and prior functions of the model. Specifically, we measured matching speeds and thresholds in a two-alternative forced choice speed discrimination task. Parametric fits to the data reveal that the likelihood function is well approximated by a LogNormal distribution with a characteristic contrast-dependent variance, and that the prior distribution on velocity exhibits significantly heavier tails than a Gaussian, and approximately follows a power-law function.

Areas of the brain involved in various forms of memory exhibit patterns of neural activity quite unlike those in canonical computational models. We show how to use well-founded Bayesian probabilistic autoassociative recall to derive biologically reasonable neuronal dynamics in recurrently coupled models, together with appropriate values for parameters such as the membrane time constant and inhibition. We explicitly treat two cases. One arises from a standard Hebbian learning rule, and involves activity patterns that are coded by graded firing rates. The other arises from a spike timing dependent learning rule, and involves patterns coded by the phase of spike times relative to a coherent local field potential oscillation. Our model offers a new and more complete understanding of how neural dynamics may support autoassociation.

Statistical approaches to language learning typically focus on either short-range syntactic dependencies or long-range semantic dependencies between words. We present a generative model that uses both kinds of dependencies, and can be used to simultaneously find syntactic classes and semantic topics despite having no representation of syntax or semantics beyond statistical dependency. This model is competitive on tasks like part-of-speech tagging and document classification with models that exclusively use short-and long-range dependencies respectively.

We consider the semi-supervised learning problem, where a decision rule is to be learned from labeled and unlabeled data. In this framework, we motivate minimum entropy regularization, which enables to incorporate unlabeled data in the standard supervised learning. Our approach includes other approaches to the semi-supervised problem as particular or limiting cases. A series of experiments illustrates that the proposed solution benefits from unlabeled data. The method challenges mixture models when the data are sampled from the distribution class spanned by the generative model. The performances are definitely in favor of minimum entropy regularization when generative models are misspecified, and the weighting of unlabeled data provides robustness to the violation of the "cluster assumption". Finally, we also illustrate that the method can also be far superior to manifold learning in high dimension spaces.

As animals interact with their environments, they must constantly update estimates about their states. Bayesian models combine prior probabilities, a dynamical model and sensory evidence to update estimates optimally. These models are consistent with the results of many diverse psychophysical studies. However, little is known about the neural representation and manipulation of such Bayesian information, particularly in populations of spiking neurons. We consider this issue, suggesting a model based on standard neural architecture and activations. We illustrate the approach on a simple random walk example, and apply it to a sensorimotor integration task that provides a particularly compelling example of dynamic probabilistic computation. Bayesian models have been used to explain a gamut of experimental results in tasks which require estimates to be derived from multiple sensory cues.

We propose a probabilistic, generative account of configural learning phenomena in classical conditioning. Configural learning experiments probe how animals discriminate and generalize between patterns of simultaneously presented stimuli (such as tones and lights) that are differentially predictive of reinforcement. Previous models of these issues have been successful more on a phenomenological than an explanatory level: they reproduce experimental findings but, lacking formal foundations, provide scant basis for understanding why animals behave as they do. We present a theory that clarifies seemingly arbitrary aspects of previous models while also capturing a broader set of data.