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 problem of super-resolution involves generating feasible higher resolution images, which are pleasing to the eye and realistic, from a given low resolution image. This might be attempted by using simplefilters for smoothing out the high resolution blocks or through applications where substantial prior information is used to imply the textures and shapes which will occur in the images. In this paper we describe an approach which lies between the two extremes. It is a generic unsupervised method which is usable in all domains, but goes beyond simple smoothing methods in what it achieves. We use a dynamic treelike architecture to model the high resolution data. Approximate conditioning on the low resolution image is achieved through a mean field approach.

In the Bayesian approach, regularization is 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 can be 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 for different models.

We propose a framework for classifier design based on discriminative densities for representation of the differences of the class-conditional distributions in a way that is optimal for classification. The densities are selected from a parametrized set by constrained maximization of some objective function which measures the average (bounded) difference, i.e. the contrast between discriminative densities. We show that maximization of the contrast is equivalent to minimization of an approximation of the Bayes risk.

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.

We consider Bayesian mixture approaches, where a predictor is constructed by forming a weighted average of hypotheses from some space of functions. While such procedures are known to lead to optimal predictors in several cases, where sufficiently accurate prior information is available, it has not been clear how they perform when some of the prior assumptions are violated. In this paper we establish data-dependent bounds for such procedures, extending previous randomized approaches such as the Gibbs algorithm to a fully Bayesian setting. The finite-sample guarantees established in this work enable the utilization of Bayesian mixture approaches in agnostic settings, where the usual assumptions of the Bayesian paradigm fail to hold. Moreover, the bounds derived can be directly applied to non-Bayesian mixture approaches such as Bagging and Boosting.

An essential step in understanding the function of sensory nervous systems is to characterize as accurately as possible the stimulus-response function (SRF) of the neurons that relay and process sensory information. One increasingly common experimental approach is to present a rapidly varying complex stimulus to the animal while recording the responses of one or more neurons, and then to directly estimate a functional transformation of the input that accounts for the neuronal firing. The estimation techniques usually employed, such as Wiener filtering or other correlation-based estimation of the Wiener or Volterra kernels, are equivalent to maximum likelihood estimation in a Gaussian-output-noise regression model. We explore the use of Bayesian evidence-optimization techniques to condition these estimates. We show that by learning hyperparameters that control the smoothness and sparsity of the transfer function it is possible to improve dramatically the quality of SRF estimates, as measured by their success in predicting responses to novel input.

The Bayesian paradigm provides a natural and effective means of exploiting prior knowledge concerning the time-frequency structure of sound signals such as speech and music--something which has often been overlooked in traditional audio signal processing approaches. Here, after constructing a Bayesian 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 results which compare favourably in objective terms with standard time-varying filtering techniques (and in several cases yield superior performance, both objectively and subjectively); moreover, in contrast to such methods, our results are obtained without an assumption of prior knowledge of the noise power.

In this paper, we consider Tipping's relevance vector machine (RVM) [1] and formalize an incremental training strategy as a variant of the expectation-maximization (EM) algorithm that we call Subspace EM (SSEM). Working with a subset of active basis functions, the sparsity of the RVM solution will ensure that the number of basis functions and thereby the computational complexity is kept low. We also introduce a mean field approach to the intractable classification model that is expected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case.