As animals interact with their environments, they must constantly update estimates about their states. Bayesian models combine prior probabilities, adynamical model and sensory evidence to update estimates optimally. Thesemodels are consistent with the results of many diverse psychophysical studies. However, little is known about the neural representation andmanipulation 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 theapproach 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 the hierarchical Dirichlet process (HDP), a nonparametric Bayesian model for clustering problems involving multiple groups of data. Each group of data is modeled with a mixture, with the number of components being open-ended and inferred automatically by the model. Further, components can be shared across groups, allowing dependencies across groups to be modeled effectively as well as conferring generalization tonew groups. Such grouped clustering problems occur often in practice, e.g. in the problem of topic discovery in document corpora. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

GSMs pose a critical assignment problem, working out which filter responses were generated by a common multiplicative factor.

We explicitly treat two cases.

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.

Just as email traffic has increased over the years since its in ception, so has the proportion that is unsolicited; some estimations have plac ed the proportion as high as 60%, and the average cost of this to business at arou nd $2000 per year, per employee (see [29] for a range of numbers and statis tics on spam). Unsolicited emails - commonly know as spam - have thereby become a daily feature of every email user's inbox; and regardless of advan ces in email filtering, spam continues to be a problem in a similar way to comp uter viruses which constantly reemerge in new guises. This leaves the res earch community with the task of continually investigating new approac hes to sorting the welcome emails (known as ham) from the unwelcome spam. W e present just such an approach to email classification and fi ltering based on a well studied data structure, the suffix tree (see [1 6] for a brief introduction). The approach is similar to many existing one s, in that it uses training examples to construct a model or profile of the class and its features, then uses this to make decisions as to the class of new example s; but it differs in the depth and extent of the anaysis. For a good overview of a number of text classification methods, see [26, 1, 31]. Using a suffix tree, we are able to compare not only single word s, as in most current approaches, but substrings of an arbitrary len gth.

This paper is concerned with the reliable inference of optimal tree-approximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between random variables by the index called mutual information. In this paper reliability is achieved by Walley's imprecise Dirichlet model, which generalizes Bayesian learning with Dirichlet priors. Adopting the imprecise Dirichlet model results in posterior interval expectation for mutual information, and in a set of plausible trees consistent with the data. Reliable inference about the actual tree is achieved by focusing on the substructure common to all the plausible trees. We develop an exact algorithm that infers the substructure in time O(m^4), m being the number of random variables. The new algorithm is applied to a set of data sampled from a known distribution. The method is shown to reliably infer edges of the actual tree even when the data are very scarce, unlike the traditional approach. Finally, we provide lower and upper credibility limits for mutual information under the imprecise Dirichlet model. These enable the previous developments to be extended to a full inferential method for trees.

We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor M from the true distribution m by the algorithmic complexity of m. Here we assume we are at a time t>1 and already observed x=x_1...x_t. We bound the future prediction performance on x_{t+1}x_{t+2}... by a new variant of algorithmic complexity of m given x, plus the complexity of the randomness deficiency of x. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.

A general linear response method for deriving improved estimates of correlations in the variational Bayes framework is presented. Three applications are given and it is discussed how to use linear response as a general principle for improving mean field approximations.

We develop a framework based on Bayesian model averaging to explain how animals cope with uncertainty about contingencies in classical conditioning experiments. Traditional accounts of conditioning fit parameters within a fixed generative model of reinforcer delivery; uncertainty over the model structure is not considered. We apply the theory to explain the puzzling relationship between second-order conditioning and conditioned inhibition, two similar conditioning regimes that nonetheless result in strongly divergent behavioral outcomes. According to the theory, second-order conditioning results when limited experience leads animals to prefer a simpler world model that produces spurious correlations; conditioned inhibition results when a more complex model is justified by additional experience.