I consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. Asimple expression for the generalization error in terms of the eigenvalue decomposition of the covariance function is derived, and used as the starting point for several approximation schemes. I identify where these become exact, and compare with existing bounds on learning curves; the new approximations, which can be used for any input space dimension, generally get substantially closer to the truth. 1 INTRODUCTION: GAUSSIAN PROCESSES Within the neural networks community, there has in the last few years been a good deal of excitement about the use of Gaussian processes as an alternative to feedforward networks [lJ. The advantages of Gaussian processes are that prior assumptions about the problem to be learned are encoded in a very transparent way, and that inference-at least in the case of regression that I will consider-is relatively straightforward. One crucial question for applications is then how'fast' Gaussian processes learn, i.e., how many training examples are needed to achieve a certain level of generalization performance.

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We show the similarity between belief propagation and TAP, for decoding corrupted messages encoded by Sourlas's method.

We present a split and merge EM (SMEM) algorithm to overcome the local maximum problem in parameter estimation of finite mixture models.

Te-Won Lee, Michael S. Lewicki and Terrence Sejnowski Howard Hughes Medical Institute Computational Neurobiology Laboratory The Salk Institute 10010 N. Torrey Pines Road La Jolla, California 92037, USA {tewon,lewicki,terry}Osalk.edu Abstract We present an unsupervised classification algorithm based on an ICA mixture model. The ICA mixture model assumes that the observed data can be categorized into several mutually exclusive data classes in which the components in each class are generated by a linear mixture of independent sources. The algorithm finds the independent sources, the mixing matrix for each class and also computes the class membership probability for each data point. This approach extends the Gaussian mixture model so that the classes can have non-Gaussian structure. We demonstrate that this method can learn efficient codes to represent images of natural scenes and text.

We describe the first single microphone sound localization system and its inspiration from theories of human monaural sound localization. Reflectionsand diffractions caused by the external ear (pinna) allow humans to estimate sound source elevations using only one ear. Our single microphone localization model relies on a specially shaped reflecting structure that serves the role of the pinna. Specially designedanalog VLSI circuitry uses echo-time processing to localize the sound. A CMOS integrated circuit has been designed, fabricated, and successfully demonstrated on actual sounds. 1 Introduction The principal cues for human sound localization arise from time and intensity differences betweenthe signals received at the two ears. For low-frequency components of sounds (below 1500Hz for humans), the phase-derived interaural time difference (lTD) can be used to localize the sound source. For these frequencies, the sound wavelength is at least several times larger than the head and the amount of shadowing (whichdepends on the wavelength of the sound compared with the dimensions of the head) is negligible.

We present a new energy-minimization framework for the graph isomorphism problem which is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum cliqueproblem in terms of a standard quadratic program. To solve the program we use "replicator" equations, a class of simple continuous-and discrete-time dynamical systems developed in various branchesof theoretical biology. We show how, despite their inability to escape from local solutions, they nevertheless provide experimental results which are competitive with those obtained using moreelaborate mean-field annealing heuristics. 1 INTRODUCTION The graph isomorphism problem is one of those few combinatorial optimization problems which still resist any computational complexity characterization [6]. Despite decadesof active research, no polynomial-time algorithm for it has yet been found.

Such agent-environment systems can be modeled as partially observable Markov decision processes or POMDPs (Sondik, 1978).

We present an analog VLSI cellular architecture implementing a simpli .fied

Inference is a key component in learning probabilistic models from partially observabledata. When learning temporal models, each of the many inference phases requires a traversal over an entire long data sequence; furthermore,the data structures manipulated are exponentially large, making this process computationally expensive. In [2], we describe an approximate inference algorithm for monitoring stochastic processes, and prove bounds on its approximation error. In this paper, we apply this algorithm as an approximate forward propagation step in an EM algorithm for learning temporal Bayesian networks. We provide a related approximation forthe backward step, and prove error bounds for the combined algorithm.