A general linear response method for deriving improved estimates of correlations in the variational Bayes framework is presented.

We present a Bayesian approach to color constancy which utilizes a non-Gaussian probabilistic model of the image formation process.

We present a novel method for approximate inference in Bayesian models andregularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of conditional probabilitiesin factorizing distributions, much akin to Minka's Expectation Propagation. In the jointly normal case, it coincides with the latter and belief propagation, whereas in the general case, it provides an optimization strategy containing Support Vector chunking, the Bayes Committee Machine, and Gaussian Process chunking as special cases.

Wagner [7], are wholly concerned with parameter learning.

We present an analysis of concentration-of-expectation phenomena in layered Bayesian networks that use generalized linear models as the local conditional probabilities. This framework encompasses a wide variety of probability distributions, including both discrete and continuous random variables. We utilize ideas from large deviation analysis and the delta method to devise and evaluate a class of approximate inference algorithms forlayered Bayesian networks that have superior asymptotic error bounds and very fast computation time.

When we model a higher order functions, such as learning and memory, we face a difficulty of comparing neural activities with hidden variables that depend on the history of sensory and motor signals and the dynamics ofthe network. Here, we propose novel method for estimating hidden variables of a learning agent, such as connection weights from sequences of observable variables. Bayesian estimation is a method to estimate the posterior probability of hidden variables from observable data sequence using a dynamic model of hidden and observable variables.

While the mixture approach is intriguing, neither of [8, 9] compare their model to other methods.

In this paper we present Discriminative Random Fields (DRF), a discriminative frameworkfor the classification of natural image regions by incorporating neighborhoodspatial dependencies in the labels as well as the observed data. The proposed model exploits local discriminative models and allows to relax the assumption of conditional independence of the observed data given the labels, commonly used in the Markov Random Field (MRF) framework. The parameters of the DRF model are learned using penalized maximum pseudo-likelihood method. Furthermore, the form of the DRF model allows the MAP inference for binary classification problemsusing the graph min-cut algorithms. The performance of the model was verified on the synthetic as well as the real-world images. The DRF model outperforms the MRF model in the experiments.

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space.

An accepted belief is a proposition considered likely enough by an agent, to be inferred from as if it were true. This paper bridges the gap between probabilistic and logical representations of accepted beliefs. To this end, natural properties of relations on propositions, describing relative strength of belief are augmented with some conditions ensuring that accepted beliefs form a deductively closed set. This requirement turns out to be very restrictive. In particular, it is shown that the sets of accepted belief of an agent can always be derived from a family of possibility rankings of states. An agent accepts a proposition in a given context if this proposition is considered more possible than its negation in this context, for all possibility rankings in the family. These results are closely connected to the non-monotonic 'preferential' inference system of Kraus, Lehmann and Magidor and the so-called plausibility functions of Friedman and Halpern. The extent to which probability theory is compatible with acceptance relations is laid bare. A solution to the lottery paradox, which is considered as a major impediment to the use of non-monotonic inference is proposed using a special kind of probabilities (called lexicographic, or big-stepped). The setting of acceptance relations also proposes another way of approaching the theory of belief change after the works of Gärdenfors and colleagues. Our view considers the acceptance relation as a primitive object from which belief sets are derived in various contexts.