The barn owl is a nocturnal hunter, capable of capturing prey using au- ditory information alone [1]. The neural basis for this localization be- havior is the existence of auditory neurons with spatial receptive fields [2]. We provide a mathematical description of the operations performed on auditory input signals by the barn owl that facilitate the creation of a representation of auditory space. To develop our model, we first formu- late the sound localization problem solved by the barn owl as a statistical estimation problem. The implementation of the solution is constrained by the known neurobiology.

We discuss the integration of the expectation-maximization (EM) algorithm for maximum likelihood learning of Bayesian networks with belief propagation algorithms for approximate inference. Specifically we propose to combine the outer-loop step of convergent belief propagation algorithms with the M-step of the EM algorithm. This then yields an approximate EM algorithm that is essentially still double loop, with the important advantage of an inner loop that is guaranteed to converge. Simulations illustrate the merits of such an approach.

We present a novel method for approximate inference in Bayesian mod- els and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of condi- tional probabilities in factorizing distributions, much akin to Minka's Expectation Propagation. In the jointly normal case, it coincides with the latter and belief propagation, whereas in the general case, it provides an optimization strategy containing Support Vector chunking, the Bayes Committee Machine, and Gaussian Process chunking as special cases.

Rao–Blackwellization is an approximation technique for probabilistic in- ference that flexibly combines exact inference with sampling. It is useful in models where conditioning on some of the variables leaves a sim- pler inference problem that can be solved tractably. This paper presents Sample Propagation, an efficient implementation of Rao–Blackwellized approximate inference for a large class of models. Sample Propagation tightly integrates sampling with message passing in a junction tree, and is named for its simple, appealing structure: it walks the clusters of a junction tree, sampling some of the current cluster's variables and then passing a message to one of its neighbors. We discuss the application of Sample Propagation to conditional Gaussian inference problems such as switching linear dynamical systems.

Recently, relevance vector machines (RVM) have been fashioned from a sparse Bayesian learning (SBL) framework to perform supervised learn- ing using a weight prior that encourages sparsity of representation. The methodology incorporates an additional set of hyperparameters govern- ing the prior, one for each weight, and then adopts a specific approxi- mation to the full marginalization over all weights and hyperparameters. Despite its empirical success however, no rigorous motivation for this particular approximation is currently available. To address this issue, we demonstrate that SBL can be recast as the application of a rigorous vari- ational approximation to the full model by expressing the prior in a dual form. This formulation obviates the necessity of assuming any hyperpri- ors and leads to natural, intuitive explanations of why sparsity is achieved in practice.

We present a new method for calculating approximate marginals for probability distributions defined by graphs with cycles, based on a Gaus- sian entropy bound combined with a semidefinite outer bound on the marginal polytope. This combination leads to a log-determinant max- imization problem that can be solved by efficient interior point meth- ods [8]. As with the Bethe approximation and its generalizations [12], the optimizing arguments of this problem can be taken as approximations to the exact marginals. In contrast to Bethe/Kikuchi approaches, our vari- ational problem is strictly convex and so has a unique global optimum. An additional desirable feature is that the value of the optimal solution is guaranteed to provide an upper bound on the log partition function.

Belief propagation on cyclic graphs is an efficient algorithm for comput- ing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. In this paper we propose two new al- gorithms for approximating joint probabilities of arbitrary pairs of nodes and prove a number of desirable properties that these estimates fulfill. The first algorithm is a propagation algorithm which is shown to con- verge if belief propagation converges to a stable fixed point. The second algorithm is based on matrix inversion. Experiments compare a number of competing methods.

We consider the situation in semi-supervised learning, where the "label sampling" mechanism stochastically depends on the true response (as well as potentially on the features). We suggest a method of moments for estimating this stochastic dependence using the unlabeled data. This is potentially useful for two distinct purposes: a. As an input to a super- vised learning procedure which can be used to "de-bias" its results using labeled data only and b. We present several examples to illustrate the practical usefulness of our method.

We present an unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations. Our algorithm does not need markers, nor does it assume prior knowledge about object shape, the dynamics of its deformation, or scan alignment. This model enforces preservation of local mesh geometry, as well as more global constraints that capture the preservation of geodesic distance between corresponding point pairs. The algorithm applies even when one of the meshes is an incomplete range scan; thus, it can be used to automatically fill in the remaining sur- faces for this partial scan, even if those surfaces were previously only seen in a different configuration. We evaluate the algorithm on several real-world datasets, where we demonstrate good results in the presence of significant movement of articulated parts and non-rigid surface defor- mation. Finally, we show that the output of the algorithm can be used for compelling computer graphics tasks such as interpolation between two scans of a non-rigid object and automatic recovery of articulated object models. The construction of 3D object models is a key task for many graphics applications.

We use to denote the entire set of model parameters {a,b}a,b {S}. An instantiation of our probabilistic model is illustrated in Figure 1(b).