Recent work has exploited boundedness of data in the unsupervised learning of new types of generative model. For nonnegative data it was recently shown that the maximum-entropy generative model is a Non(cid:173) negative Boltzmann Distribution not a Gaussian distribution, when the model is constrained to match the first and second order statistics of the data. Learning for practical sized problems is made difficult by the need to compute expectations under the model distribution. The computa(cid:173) tional cost of Markov chain Monte Carlo methods and low fidelity of naive mean field techniques has led to increasing interest in advanced mean field theories and variational methods. Here I present a second(cid:173) order mean-field approximation for the Nonnegative Boltzmann Machine model, obtained using a "high-temperature" expansion.

Bayesian networks are graphical representations of probability distributions. In virtually all of the work on learning these networks, the assumption is that we are presented with a data set consisting of randomly generated instances from the underlying distribution. In many situations, however, we also have the option of active learning, where we have the possibility of guiding the sampling process by querying for certain types of samples. This paper addresses the problem of estimating the parameters of Bayesian networks in an active learning setting. We provide a theoretical framework for this problem, and an algorithm that chooses which active learning queries to generate based on the model learned so far.

Multisensory response enhancement (MRE) is the augmentation of the response of a neuron to sensory input of one modality by si(cid:173) multaneous input from another modality. The maximum likelihood (ML) model presented here modifies the Bayesian model for MRE (Anastasio et al.) by incorporating a decision strategy to maximize the number of correct decisions. Thus the ML model can also deal with the important tasks of stimulus discrimination and identifi(cid:173) cation in the presence of incongruent visual and auditory cues. It accounts for the inverse effectiveness observed in neurophysiolog(cid:173) ical recording data, and it predicts a functional relation between uni- and bimodal levels of discriminability that is testable both in neurophysiological and behavioral experiments.

The mutual information of two random variables z and J with joint probabilities {7rij} is commonly used in learning Bayesian nets as well as in many other fields. The chances 7rij are usually estimated by the empirical sampling frequency nij In leading to a point es(cid:173) timate J(nij In) for the mutual information. To answer questions like "is J (nij In) consistent with zero?" or "what is the probability that the true mutual information is much larger than the point es(cid:173) timate?" one has to go beyond the point estimate. In the Bayesian framework one can answer these questions by utilizing a (second order) prior distribution p( 7r) comprising prior information about 7r. From the prior p(7r) one can compute the posterior p(7rln), from which the distribution p(Iln) of the mutual information can be cal(cid:173) culated.

We describe the g-factor, which relates probability distributions on image features to distributions on the images themselves. The g-factor depends only on our choice of features and lattice quanti(cid:173) zation and is independent of the training image data. We illustrate the importance of the g-factor by analyzing how the parameters of Markov Random Field (i.e. Gibbs or log-linear) probability models of images are learned from data by maximum likelihood estimation. In particular, we study homogeneous MRF models which learn im(cid:173) age distributions in terms of clique potentials corresponding to fea(cid:173) ture histogram statistics (d.

Bayesian belief propagation in graphical models has been recently shown to have very close ties to inference methods based in statis- tical physics. After Yedidia et al. demonstrated that belief prop- agation (cid:12)xed points correspond to extrema of the so-called Bethe free energy, Yuille derived a double loop algorithm that is guar- anteed to converge to a local minimum of the Bethe free energy. Yuille's algorithm is based on a certain decomposition of the Bethe free energy and he mentions that other decompositions are possi- ble and may even be fruitful. In the present work, we begin with the Bethe free energy and show that it has a principled interpre- tation as pairwise mutual information minimization and marginal entropy maximization (MIME). Next, we construct a family of free energy functions from a spectrum of decompositions of the original Bethe free energy.

Narayanan and Jurafsky (1998) proposed that human language compre- hension can be modeled by treating human comprehenders as Bayesian reasoners, and modeling the comprehension process with Bayesian de- cision trees. In this paper we extend the Narayanan and Jurafsky model to make further predictions about reading time given the probability of difference parses or interpretations, and test the model against reading time data from a psycholinguistic experiment.

We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying state-transition matrix, and the expected num- ber of distinct hidden states in a finite sequence. In this framework it is also natural to allow the alphabet of emitted symbols to be infinite-- consider, for example, symbols being possible words appearing in En- glish text.

The marriage of Renyi entropy with Parzen density estimation has been shown to be a viable tool in learning discriminative feature transforms. However, it suffers from computational complexity proportional to the square of the number of samples in the training data. This sets a practical limit to using large databases. We suggest immediate divorce of the two methods and remarriage of Renyi entropy with a semi-parametric density estimation method, such as a Gaussian Mixture Models (GMM). This al- lows all of the computation to take place in the low dimensional target space, and it reduces computational complexity proportional to square of the number of components in the mixtures. Furthermore, a conve- nient extension to Hidden Markov Models as commonly used in speech recognition becomes possible.

It is desirable that a complex decision-making problem in an uncer(cid:173) tain world be adequately modeled by a Markov Decision Process (MDP) whose structural representation is adaptively designed by a parsimonious resources allocation process. Resources include time and cost of exploration, amount of memory and computational time allowed for the policy or value function representation. Concerned about making the best use of the available resources, we address the problem of efficiently estimating where adding extra resources is highly needed in order to improve the expected performance of the resulting policy. Possible application in reinforcement learning (RL), when real-world exploration is highly costly, concerns the de(cid:173) tection of those areas of the state-space that need primarily to be explored in order to improve the policy. Another application con(cid:173) cerns approximation of continuous state-space stochastic control problems using adaptive discretization techniques for which highly efficient grid points allocation is mandatory to survive high dimen(cid:173) sionality.