We develop a tree-based reparameterization framework that provides a new conceptual view of a large class of iterative algorithms for computing approximate marginals in graphs with cycles. It includes belief propagation (BP), which can be reformulated as a very local form of reparameterization. More generally, we consider algorithms that perform exact computations over spanning trees of the full graph. On the practical side, we find that such tree reparameterization (TRP) algorithms have convergence properties superior to BP. The reparameterization perspective also provides a number of theoretical insights into approximate inference, including a new characterization of fixed points; and an invariance intrinsic to TRP /BP.

In this paper we introduce a new sparseness inducing prior which does not involve any (hyper)parameters that need to be adjusted or estimated. Although other applications are possible, we focus here on supervised learning problems: regression and classification. Experiments with several publicly available benchmark data sets show that the proposed approach yields state-of-the-art performance. In particular, our method outperforms support vector machines and performs competitively with the best alternative techniques, both in terms of error rates and sparseness, although it involves no tuning or adjusting of sparsenesscontrolling hyper-parameters.

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 estimate 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 estimate?"

In models described by continuous functions, the infinite number of "possibilities" can

We study properties of popular near-uniform (Dirichlet) priors for learning undersampled probability distributions on discrete nonmetric spaces and show that they lead to disastrous results. However, an Occam-style phase space argument expands the priors into their infinite mixture and resolves most of the observed problems. This leads to a surprisingly good estimator of entropies of discrete distributions. Learning a probability distribution from examples is one of the basic problems in data analysis. Common practical approaches introduce a family of parametric models, leading to questions about model selection. In Bayesian inference, computing the total probability of the data arising from a model involves an integration over parameter space, and the resulting "phase space volume" automatically discriminates against models with larger numbers of parameters--hence the description of these volume terms as Occam factors [1, 2]. As we move from finite parameterizations to models that are described by smooth functions, the integrals over parameter space become functional integrals and methods from quantum field theory allow us to do these integrals asymptotically; again the volume in model space consistent with the data is larger for models that are smoother and hence less complex [3]. Further, at least under some conditions the relevant degree of smoothness can be determined self-consistently from the data, so that we approach something like a model independent method for learning a distribution [4]. The results emphasizing the importance of phase space factors in learning prompt us to look back at a seemingly much simpler problem, namely learning a distribution on a discrete, nonmetric space.

Recent approaches have used uncertainty over the vocabulary of symbols in a multinomial distribution as a means of accounting for sparsity. We present a Bayesian approach that allows weak prior knowledge, in the form of a small set of approximate candidate vocabularies, to be used to dramatically improve the resulting estimates. We demonstrate these improvements in applications to text compression and estimating distributions over words in newsgroup data.

However, online RL algorithms such as SARSA(A) have been shown experimentally to have difficulty converging when applied with function approximators. Theoretical analysis has not been able to prove convergence, even in the case-of linear function approximators.

This paper presents an unsupervised learning algorithm that can derive the probabilistic dependence structure of parts of an object (a moving human body in our examples) automatically from unlabeled data. The distinguished part of this work is that it is based on unlabeled data, i.e., the training features include both useful foreground parts and background clutter and the correspondence between the parts and detected features are unknown. We use decomposable triangulated graphs to depict the probabilistic independence of parts, but the unsupervised technique is not limited to this type of graph. In the new approach, labeling of the data (part assignments) is taken as hidden variables and the EM algorithm is applied. A greedy algorithm is developed to select parts and to search for the optimal structure based on the differential entropy of these variables. The success of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled real image sequences.

We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using an input-dependent adaptation of the Dirichlet Process, we implement a gating network for an infinite number of Experts. Inference in this model may be done efficiently using a Markov Chain relying on Gibbs sampling. The model allows the effective covariance function to vary with the inputs, and may handle large datasets - thus potentially overcoming two of the biggest hurdles with GP models.

Narayanan and Jurafsky (1998) proposed that human language comprehension can be modeled by treating human comprehenders as Bayesian reasoners, and modeling the comprehension process with Bayesian decision 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.