This paper presents a unified probabilistic framework for denoising and dereverberation of speech signals. The framework transforms the denois(cid:173) ing and dereverberation problems into Bayes-optimal signal estimation. The key idea is to use a strong speech model that is pre-trained on a large data set of clean speech. Computational efficiency is achieved by using variational EM, working in the frequency domain, and employing conjugate priors. The framework covers both single and multiple micro(cid:173) phones.

Jensen's inequality is a powerful mathematical tool and one of the workhorses in statistical learning. Its applications therein include the EM algorithm, Bayesian estimation and Bayesian inference. Quite often (i.e. in discriminative learning) upper bounds are needed as well. We derive and prove an efficient analytic inequality that provides such variational upper bounds. This inequality holds for latent variable mixtures of exponential family distributions and thus spans a wide range of contemporary statis(cid:173) tical models.

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.

Many algorithms for approximate reinforcement learning are not known to converge. In fact, there are counterexamples showing that the adjustable weights in some algorithms may oscillate within a region rather than converging to a point. This paper shows that, for two popular algorithms, such oscillation is the worst that can happen: the weights cannot diverge, but instead must converge to a bounded region. The algorithms are SARSA(O) and V(O); the latter algorithm was used in the well-known TD-Gammon program.

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.

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.

We address two open theoretical questions in Policy Gradient Reinforce- ment Learning. The first concerns the efficacy of using function approx- imation to represent the state action value function, . Theory is pre- sented showing that linear function approximation representations of can degrade the rate of convergence of performance gradient estimates by a factor of relative to when no function approximation of is used, where is the number of basis functions in the function approximation representation. The sec- ond concerns the use of a bias term in estimating the state action value function. Theory is presented showing that a non-zero bias term can improve the rate of convergence of performance gradient estimates by is the number of possible actions.

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.

Recently, Jaakkola and Haussler proposed a method for construct(cid:173) ing kernel functions from probabilistic models. Their so called "Fisher kernel" has been combined with discriminative classifiers such as SVM and applied successfully in e.g. Whereas the Fisher kernel (FK) is calculated from the marginal log-likelihood, we propose the TOP kernel derived from Tangent vectors Of Posterior log-odds. Furthermore we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing FK and TOP. In experiments our new discriminative TOP kernel compares favorably to the Fisher kernel.