Modeling the distributions of the independent sources with mixture of Gaussians allows sources to be estimated with different kurtosis and skewness. The variational Bayesian method automatically determines the dimensionality of the data and yields an accurate density model for the observed data without overfitting problems.

We propose a model for natural images in which the probability of an image isproportional to the product of the probabilities of some filter outputs. Weencourage the system to find sparse features by using a Studentt distribution to model each filter output. If the t-distribution is used to model the combined outputs of sets of neurally adjacent filters, the system learnsa topographic map in which the orientation, spatial frequency and location of the filters change smoothly across the map. Even though maximum likelihood learning is intractable in our model, the product form allows a relatively efficient learning procedure that works well even for highly overcomplete sets of filters. Once the model has been learned it can be used as a prior to derive the "iterated Wiener filter" for the purpose ofdenoising images.

We present an account of human concept learning-that is, learning of categories from examples-based on the principle of minimum description length(MDL). In support of this theory, we tested a wide range of two-dimensional concept types, including both regular (simple) and highly irregular (complex) structures, and found the MDL theory to give a good account of subjects' performance. This suggests that the intrinsic complexityofa concept (that is, its description -length) systematically influences its leamability.

We describe a method for computing provably exact maximum a posteriori (MAP)estimates for a subclass of problems on graphs with cycles. The basic idea is to represent the original problem on the graph with cycles asa convex combination of tree-structured problems. A convexity argument then guarantees that the optimal value of the original problem (i.e., the log probability of the MAP assignment) is upper bounded by the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configurationin common. An important implication is that any such shared configuration must also be the MAP configuration for the original problem. Next we develop a tree-reweighted max-product algorithm for attempting to find convex combinations of tree-structured problems that share a common optimum. We give necessary and sufficient conditions for a fixed point to yield the exact MAP estimate. An attractive feature of our analysis is that it generalizes naturally to convex combinations of hypertree-structured distributions.

The Bayesian paradigm provides a natural and effective means of exploiting priorknowledge concerning the time-frequency structure of sound signals such as speech and music--something which has often been overlooked intraditional audio signal processing approaches. Here, after constructing aBayesian model and prior distributions capable of taking into account the time-frequency characteristics of typical audio waveforms, we apply Markov chain Monte Carlo methods in order to sample from the resultant posterior distribution of interest. We present speech enhancement resultswhich compare favourably in objective terms with standard time-varying filtering techniques (and in several cases yield superior performance, bothobjectively and subjectively); moreover, in contrast to such methods, our results are obtained without an assumption of prior knowledge of the noise power.

In the Bayesian approach, regularizationis achieved by specifying a prior distribution over the parameters and subsequently averaging over the posterior distribution. This regularization provides not only smoother estimates of the parameters compared to maximum likelihood but also guides the selection of model structures. It was pointed out in [6] that a very large scale parameter of the Dirichlet prior can degrade predictive accuracy due to severe regularization of the parameter estimates. We complement this discussion here and show that a very small scale parameter can lead to poor over-regularized structures when a product of (conjugate) Dirichlet priors is used over multinomial conditional distributions (Section 3). Section 4 demonstrates the effect of the scale parameter and how it can be calibrated. We focus on the class of Bayesian network models throughout this paper.

Application of V ariational Bayesian Approach to Speech Recognition Shinji Watanabe, Y asuhiro Minami, Atsushi Nakamura and Naonori Ueda NTT Communication Science Laboratories, NTT Corporation 2-4, Hikaridai, Seika-cho, Soraku-gun, Kyoto, Japan {watanabe,minami,ats,ueda}@cslab.kecl.ntt.co.jp Abstract In this paper, we propose a Bayesian framework, which constructs shared-state triphone HMMs based on a variational Bayesian approach, and recognizes speech based on the Bayesian prediction classification; variational Bayesian estimation and clustering for speech recognition (VBEC). An appropriate model structure with high recognition performance can be found within a VBEC framework. Unlike conventional methods, including BIC or MDL criterion based on the maximum likelihood approach, the proposed model selection is valid in principle, even when there are insufficient amounts of data, because it does not use an asymptotic assumption. In isolated word recognition experiments, we show the advantage of VBEC over conventional methods, especially when dealing with small amounts of data. 1 Introduction A statistical modeling of spectral features of speech (acoustic modeling) is one of the most crucial parts in the speech recognition. In acoustic modeling, a triphone-based hidden Markov model (triphone HMM) has been widely employed.

We argue that human inductive generalization is best explained in a Bayesian framework, rather than by traditional models based on similarity computations.We go beyond previous work on Bayesian concept learning by introducing an unsupervised method for constructing flexible hypothesisspaces, and we propose a version of the Bayesian Occam's razorthat trades off priors and likelihoods to prevent under-or over-generalization in these flexible spaces. We analyze two published data sets on inductive reasoning as well as the results of a new behavioral study that we have carried out.

We present a class of algorithms for learning the structure of graphical models from data. The algorithms are based on a measure known as the kernel generalized variance (KGV), which essentially allows us to treat all variables on an equal footing as Gaussians in a feature space obtained from Mercer kernels. Thus we are able to learn hybrid graphs involving discrete and continuous variables of arbitrary type. We explore the computational properties of our approach, showing how to use the kernel trick to compute the relevant statistics in linear time. We illustrate our framework with experiments involving discrete and continuous data.

The extraction of a single high-quality image from a set of lowresolution imagesis an important problem which arises in fields such as remote sensing, surveillance, medical imaging and the extraction ofstill images from video. Typical approaches are based on the use of cross-correlation to register the images followed by the inversion of the transformation from the unknown high resolution imageto the observed low resolution images, using regularization toresolve the ill-posed nature of the inversion process. In this paper we develop a Bayesian treatment of the super-resolution problem in which the likelihood function for the image registration parametersis based on a marginalization over the unknown high-resolution image. This approach allows us to estimate the unknown point spread function, and is rendered tractable through the introduction of a Gaussian process prior over images. Results indicate a significant improvement over techniques based on MAP (maximum a-posteriori) point optimization of the high resolution image and associated registration parameters. 1 Introduction The task in super-resolution is to combine a set of low resolution images of the same scene in order to obtain a single image of higher resolution. Provided the individual low resolution images have sub-pixel displacements relative to each other, it is possible to extract high frequency details of the scene well beyond the Nyquist limit of the individual source images.