A generative probabilistic model for objects in images is presented. An object consists of a constellation of features. Feature appearance and pose are modeled probabilistically. Scene images are generated by draw- ing a set of objects from a given database, with random clutter sprinkled on the remaining image surface. We study the case where features from the same object share a common reference frame. Moreover, parameters for shape and appearance den- sities are shared across features.

We propose a new interpretation of spiking neurons as Bayesian integra- tors accumulating evidence over time about events in the external world or the body, and communicating to other neurons their certainties about these events. In this model, spikes signal the occurrence of new infor- mation, i.e. what cannot be predicted from the past activity. As a result, firing statistics are close to Poisson, albeit providing a deterministic rep- resentation of probabilities. We proceed to develop a theory of Bayesian inference in spiking neural networks, recurrent interactions implement- ing a variant of belief propagation. Many perceptual and motor tasks performed by the central nervous system are probabilis- tic, and can be described in a Bayesian framework [4, 3].

Spike sorting involves clustering spike trains recorded by a micro- electrode according to the source neuron. It is a complicated problem, which requires a lot of human labor, partly due to the non-stationary na- ture 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 descrip- tions 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 so- lution of the resulting probabilistic model. Transition probabilities are computed using local stationarity assumptions and are based on a Gaus- sian version of the Jensen-Shannon divergence.

Two players, Black and White, take turns to place stones on the intersections of an N N grid (usually N 19 but smaller boards are in use as well). All the stones of each player are identical. Players place their stones in order to create territory by occupying or surrounding areas of the board. The player with the most territory at the end of the game is the winner. A stone is captured if it has been completely surrounded (in the horizontal and vertical directions) by stones of the opponent's colour.

As animals interact with their environments, they must constantly update estimates about their states. Bayesian models combine prior probabil- ities, a dynamical model and sensory evidence to update estimates op- timally. These models are consistent with the results of many diverse psychophysical studies. However, little is known about the neural rep- resentation 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.

Belief propagation (BP) is an increasingly popular method of perform- ing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether from quantization or other simplified message representations or from stochastic approxima- tion methods. Introducing such errors into the BP message computations has the potential to adversely affect the solution obtained. We analyze this effect with respect to a particular measure of message error, and show bounds on the accumulation of errors in the system. This leads both to convergence conditions and error bounds in traditional and approximate BP message passing.

Alternative splicing (AS) is an important and frequent step in mammalian gene expression that allows a single gene to specify multiple products, and is crucial for the regulation of fundamental biological processes. The extent of AS regulation, and the mechanisms involved, are not well un- derstood. We have developed a custom DNA microarray platform for surveying AS levels on a large scale. We present here a generative model for the AS Array Platform (GenASAP) and demonstrate its utility for quantifying AS levels in different mouse tissues. Learning is performed using a variational expectation maximization algorithm, and the parame- ters are shown to correctly capture expected AS trends.

This paper analyzes generalization of the classic Rescorla-Wagner (R- W) learning algorithm and studies their relationship to Maximum Like- lihood 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 gener- icity 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. We describe how to determine convergence conditions and calculate conver- gence rates for the GLRW algorithms under these conditions.

It has been demonstrated that basic aspects of human visual motion per- ception are qualitatively consistent with a Bayesian estimation frame- work, 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 vari- ance, and that the prior distribution on velocity exhibits significantly heavier tails than a Gaussian, and approximately follows a power-law function.

In this paper we present a framework for using multi-layer per- ceptron (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 neu- rons. The method can be used to derive nonlinear coun- terparts for linear algorithms such as factor analysis, independent component/factor analysis and state-space models. This is demon- strated with a nonlinear factor analysis experiment in which even 20 sources can be estimated from a real world speech data set.