We present an account of human concept learning-that is, learning of categories from examples-based on the principle of minimum description length(MDL). In support of this theory, we tested a wide range of two-dimensional concept types, including both regular (simple) and highly irregular (complex) structures, and found the MDL theory to give a good account of subjects' performance. This suggests that the intrinsic complexityofa concept (that is, its description -length) systematically influences its leamability.

Forward decoding kernel machines (FDKM) combine large-margin classifiers withhidden Markov models (HMM) for maximum a posteriori (MAP) adaptive sequence estimation. State transitions in the sequence are conditioned on observed data using a kernel-based probability model trained with a recursive scheme that deals effectively with noisy and partially labeleddata. Training over very large datasets is accomplished using a sparse probabilistic support vector machine (SVM) model based on quadratic entropy, and an online stochastic steepest descent algorithm. For speaker-independent continuous phone recognition, FDKM trained over 177,080 samples of the TlMIT database achieves 80.6% recognition accuracy over the full test set, without use of a prior phonetic language model. 1 Introduction Sequence estimation is at the core of many problems in pattern recognition, most notably speech and language processing. Recognizing dynamic patterns in sequential data requires a set of tools very different from classifiers trained to recognize static patterns in data assumed i.i.d.

We describe a method for computing provably exact maximum a posteriori (MAP)estimates for a subclass of problems on graphs with cycles. The basic idea is to represent the original problem on the graph with cycles asa convex combination of tree-structured problems. A convexity argument then guarantees that the optimal value of the original problem (i.e., the log probability of the MAP assignment) is upper bounded by the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configurationin common. An important implication is that any such shared configuration must also be the MAP configuration for the original problem. Next we develop a tree-reweighted max-product algorithm for attempting to find convex combinations of tree-structured problems that share a common optimum. We give necessary and sufficient conditions for a fixed point to yield the exact MAP estimate. An attractive feature of our analysis is that it generalizes naturally to convex combinations of hypertree-structured distributions.

The Bayesian paradigm provides a natural and effective means of exploiting priorknowledge concerning the time-frequency structure of sound signals such as speech and music--something which has often been overlooked intraditional audio signal processing approaches. Here, after constructing aBayesian model and prior distributions capable of taking into account the time-frequency characteristics of typical audio waveforms, we apply Markov chain Monte Carlo methods in order to sample from the resultant posterior distribution of interest. We present speech enhancement resultswhich compare favourably in objective terms with standard time-varying filtering techniques (and in several cases yield superior performance, bothobjectively and subjectively); moreover, in contrast to such methods, our results are obtained without an assumption of prior knowledge of the noise power.

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are intractable for large models. The intractability ofthese algorithms is due to a great extent to their generating an optimal policy over the entire belief space. However, in real POMDP problems most belief states are unlikely, and there is a structured, low-dimensional manifold of plausible beliefs embedded in the high-dimensional belief space. We introduce a new method for solving large-scale POMDPs by taking advantage of belief space sparsity. We reduce the dimensionality of the belief space by exponential family Principal Components Analysis [1], which allows us to turn the sparse, highdimensional beliefspace into a compact, low-dimensional representation in terms of learned features of the belief state. We then plan directly on the low-dimensional belief features. By planning in a low-dimensional space, we can find policies for POMDPs that are orders of magnitude larger than can be handled by conventional techniques. We demonstrate the use of this algorithm on a synthetic problem and also on a mobile robot navigation task.

In the Bayesian approach, regularizationis achieved by specifying a prior distribution over the parameters and subsequently averaging over the posterior distribution. This regularization provides not only smoother estimates of the parameters compared to maximum likelihood but also guides the selection of model structures. It was pointed out in [6] that a very large scale parameter of the Dirichlet prior can degrade predictive accuracy due to severe regularization of the parameter estimates. We complement this discussion here and show that a very small scale parameter can lead to poor over-regularized structures when a product of (conjugate) Dirichlet priors is used over multinomial conditional distributions (Section 3). Section 4 demonstrates the effect of the scale parameter and how it can be calibrated. We focus on the class of Bayesian network models throughout this paper.

A standard view of memory consolidation is that episodes are stored temporarily inthe hippocampus, and are transferred to the neocortex through replay. Various recent experimental challenges to the idea of transfer, particularly for human memory, are forcing its reevaluation. However, although there is independent neurophysiological evidence for replay, short of transfer, there are few theoretical ideas for what it might be doing. We suggest and demonstrate two important computational roles associated with neocortical indices.

Application of V ariational Bayesian Approach to Speech Recognition Shinji Watanabe, Y asuhiro Minami, Atsushi Nakamura and Naonori Ueda NTT Communication Science Laboratories, NTT Corporation 2-4, Hikaridai, Seika-cho, Soraku-gun, Kyoto, Japan {watanabe,minami,ats,ueda}@cslab.kecl.ntt.co.jp Abstract In this paper, we propose a Bayesian framework, which constructs shared-state triphone HMMs based on a variational Bayesian approach, and recognizes speech based on the Bayesian prediction classification; variational Bayesian estimation and clustering for speech recognition (VBEC). An appropriate model structure with high recognition performance can be found within a VBEC framework. Unlike conventional methods, including BIC or MDL criterion based on the maximum likelihood approach, the proposed model selection is valid in principle, even when there are insufficient amounts of data, because it does not use an asymptotic assumption. In isolated word recognition experiments, we show the advantage of VBEC over conventional methods, especially when dealing with small amounts of data. 1 Introduction A statistical modeling of spectral features of speech (acoustic modeling) is one of the most crucial parts in the speech recognition. In acoustic modeling, a triphone-based hidden Markov model (triphone HMM) has been widely employed.

We argue that human inductive generalization is best explained in a Bayesian framework, rather than by traditional models based on similarity computations.We go beyond previous work on Bayesian concept learning by introducing an unsupervised method for constructing flexible hypothesisspaces, and we propose a version of the Bayesian Occam's razorthat trades off priors and likelihoods to prevent under-or over-generalization in these flexible spaces. We analyze two published data sets on inductive reasoning as well as the results of a new behavioral study that we have carried out.

We focus on the problem of efficient learning of dependency trees. It is well-known that given the pairwise mutual information coefficients, a minimum-weight spanning tree algorithm solves this problem exactly and in polynomial time. However, for large data-sets it is the construction ofthe correlation matrix that dominates the running time. We have developed a new spanning-tree algorithm which is capable of exploiting partial knowledge about edge weights. The partial knowledge we maintain isa probabilistic confidence interval on the coefficients, which we derive by examining just a small sample of the data. The algorithm is able to flag the need to shrink an interval, which translates to inspection ofmore data for the particular attribute pair. Experimental results show running time that is near-constant in the number of records, without significantloss in accuracy of the generated trees. Interestingly, our spanning-tree algorithm is based solely on Tarjan's red-edge rule, which is generally considered a guaranteed recipe for bad performance.