Directed graphical models with one layer of observed random variables and one or more layers of hidden random variables have been the dominant modelling paradigm in many research fields. Although this approach has met with considerable success, the causal semantics of these models can make it difficult to infer the posterior distribution over the hidden variables. In this paper we propose an alternative two-layer model based on exponential family distributions and the semantics of undirected models. Inference in these "exponential family harmoniums" is fast while learning is performed by minimizing contrastive divergence. A member of this family is then studied as an alternative probabilistic model for latent semantic indexing. In experiments it is shown that they perform well on document retrieval tasks and provide an elegant solution to searching with keywords.

We present an extension to the Jojic and Frey (2001) layered sprite model which allows for layers to undergo affine transformations. This extension allows for affine object pose to be inferred whilst simultaneously learning the object shape and appearance. Learning is carried out by applying an augmented variational inference algorithm which includes a global search over a discretised transform space followed by a local optimisation. To aid correct convergence, we use bottom-up cues to restrict the space of possible affine transformations. We present results on a number of video sequences and show how the model can be extended to track an object whose appearance changes throughout the sequence.

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.

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.

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 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.

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.

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.

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.

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.