Motivated by stochastic systems in which observed evidence and conditional dependencies betweenstates of the network change over time, and certain quantities of interest (marginal distributions, likelihood estimates etc.) must be updated, we study the problem of adaptive inference in tree-structured Bayesian networks. We describe an algorithm for adaptive inference that handles a broad range of changes to the network and is able to maintain marginal distributions, MAP estimates, and data likelihoods in all expected logarithmic time. We give an implementation of our algorithm and provide experiments that show that the algorithm can yield up to two orders of magnitude speedups on answering queries and responding to dynamic changesover the sum-product algorithm.

It is becoming increasingly important to learn from a partially-observed random matrix and predict its missing elements. We assume that the entire matrix is a single sample drawn from a matrix-variate t distribution and suggest a matrix-variate t model (MVTM) to predict those missing elements. We show that MVTM generalizes a range of known probabilistic models, and automatically performs model selection to encourage sparse predictive models. Due to the non-conjugacy of its prior, it is difficult to make predictions by computing the mode or mean of the posterior distribution. We suggest an optimization method that sequentially minimizes a convex upper-bound of the log-likelihood, which is very efficient and scalable. The experiments on a toy data and EachMovie dataset show a good predictive accuracy of the model.

We present an efficient generalization of the sparse pseudo-input Gaussian process (SPGP)model developed by Snelson and Ghahramani [1], applying it to binary classification problems.

We describe a novel noisy-logical distribution for representing the distribution of a binary output variable conditioned on multiple binary input variables. The distribution is represented in terms of noisy-or's and noisy-and-not's of causal features which are conjunctions of the binary inputs. The standard noisy-or and noisy-and-not models, used in causal reasoning and artificial intelligence, are special cases of the noisy-logical distribution. We prove that the noisy-logical distribution is complete in the sense that it can represent all conditional distributions provided a sufficient number of causal factors are used. We illustrate the noisy-logical distribution by showing that it can account for new experimental findings on how humans perform causal reasoning in more complex contexts. Finally, we speculate on the use of the noisy-logical distribution for causal reasoning and artificial intelligence.

We propose a Gaussian process (GP) framework for robust inference in which a GP prior on the mixing weights of a two-component noise model augments the standard process over latent function values. This approach is a generalization of the mixture likelihood used in traditional robust GP regression, and a specialization of the GP mixture models suggested by Tresp (2000) and Rasmussen and Ghahramani (2002). The value of this restriction is in its tractable expectation propagation updates, which allow for faster inference and model selection, and better convergence than the standard mixture. An additional benefit over the latter method lies in our ability to incorporate knowledge of the noise domain to influence predictions, and to recover with the predictive distribution information about the outlier distribution via the gating process. The model has asymptotic complexity equal to that of conventional robust methods, but yields more confident predictions on benchmark problems than classical heavy-tailed models and exhibits improved stability for data with clustered corruptions, for which they fail altogether. We show further how our approach can be used without adjustment for more smoothly heteroscedastic data, and suggest how it could be extended to more general noise models. We also address similarities with the work of Goldberg et al. (1998), and the more recent contributions of Tresp, and Rasmussen and Ghahramani.

Sound localization by barn owls is commonly modeled as a matching procedure where localization cues derived from auditory inputs are compared to stored templates. While the matching models can explain properties of neural responses, no model explains how the owl resolves spatial ambiguity in the localization cues to produce accurate localization near the center of gaze. Here, we examine two models for the barn owl's sound localization behavior. First, we consider a maximum likelihood estimator in order to further evaluate the cue matching model. Second, we consider a maximum a posteriori estimator to test if a Bayesian model with a prior that emphasizes directions near the center of gaze can reproduce the owl's localization behavior. We show that the maximum likelihood estimator can not reproduce the owl's behavior, while the maximum a posteriori estimator is able to match the behavior. This result suggests that the standard cue matching model will not be sufficient to explain sound localization behavior in the barn owl. The Bayesian model provides a new framework for analyzing sound localization in the barn owl and leads to predictions about the owl's localization behavior.

We present a novel Bayesian model for semi-supervised paIt-of-speech tagging.

Computational models of visual cortex, and in particular those based on sparse coding, have enjoyed much recent attention. Despite this currency, the question of how sparse or how over-complete a sparse representation should be, has gone without principled answer. Here, we use Bayesian model-selection methods to address these questions for a sparse-coding model based on a Student-t prior. Having validated our methods on toy data, we find that natural images are indeed best modelled by extremely sparse distributions; although for the Student-t prior, the associated optimal basis size is only modestly overcomplete.

Generalized linear models are the most commonly used tools to describe the stimulus selectivity of sensory neurons.

The problem of obtaining the maximum a posteriori estimate of a general discrete randomfield (i.e. a random field defined using a finite and discrete set of labels) is known to be