We propose a dynamic Bayesian model for motifs in biopolymer sequences whichcaptures rich biological prior knowledge and positional dependencies in motif structure in a principled way. Our model posits that the position-specific multinomial parameters for monomer distribution aredistributed as a latent Dirichlet-mixture random variable, and the position-specific Dirichlet component is determined by a hidden Markov process. Model parameters can be fit on training motifs using a variational EMalgorithm within an empirical Bayesian framework. Variational inference is also used for detecting hidden motifs. Our model improves overprevious models that ignore biological priors and positional dependence. It has much higher sensitivity to motifs during detection and a notable ability to distinguish genuine motifs from false recurring patterns.

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.

Machine learning has reached a point where many probabilistic methods canbe understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized fordifferent models. Here, we describe the AUTOBAYES system which takes a high-level statistical model specification, uses powerful symbolic techniques based on schema-based program synthesis and computer algebra to derive an efficient specialized algorithm for learning that model, and generates executable code implementing that algorithm. This capability is far beyond that of code collections such as Matlab toolboxes oreven tools for model-independent optimization such as BUGS for Gibbs sampling: complex new algorithms can be generated without newprogramming, algorithms can be highly specialized and tightly crafted for the exact structure of the model and data, and efficient and commented code can be generated for different languages or systems.

In this paper, we consider Tipping's relevance vector machine (RVM)

The responses of cortical sensory neurons are notoriously variable, with the number of spikes evoked by identical stimuli varying significantly from trial to trial. This variability is most often interpreted as'noise', purely detrimental to the sensory system. In this paper, we propose an alternative viewin which the variability is related to the uncertainty, about world parameters, which is inherent in the sensory stimulus. Specifically, theresponses of a population of neurons are interpreted as stochastic samples from the posterior distribution in a latent variable model. In addition to giving theoretical arguments supporting such a representational scheme,we provide simulations suggesting how some aspects of response variability might be understood in this framework.

In this paper, we study a special kind of learning problem in which each training instance is given a set of (or distribution over) candidate class labels and only one of the candidate labels is the correct one. Such a problem can occur, e.g., in an information retrieval setting where a set of words is associated with an image, or if classes labels are organized hierarchically. We propose a novel discriminative approach for handling the ambiguity of class labels in the training examples. The experiments with the proposed approach over five different UCI datasets show that our approach is able to find the correct label among the set of candidate labels and actually achieve performance close to the case when each training instance is given a single correct label. In contrast, naIve methods degrade rapidly as more ambiguity is introduced into the labels. 1 Introduction Supervised and unsupervised learning problems have been extensively studied in the machine learning literature. In supervised classification each training instance is associated with a single class label, while in unsupervised classification (i.e.

We present a hierarchical Bayesian model for learning efficient codes of higher-order structure in natural images. The model, a nonlinear generalization ofindependent component analysis, replaces the standard assumption of independence for the joint distribution of coefficients with a distribution that is adapted to the variance structure of the coefficients of an efficient image basis. This offers a novel description of higherorder imagestructure and provides a way to learn coarse-coded, sparsedistributed representationsof abstract image properties such as object location, scale, and texture.

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 describe a method for learning sparse multiscale image representations usinga sparse prior distribution over the basis function coefficients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coefficients to have exact zero values. Coefficients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Denoising usingthe learned image model is demonstrated for some standard test images, with results that compare favorably with other denoising methods.