We present a class of approximate inference algorithms for graphical models of the QMR-DT type. We give convergence rates for these algorithms and for the Jaakkola and Jordan (1999) algorithm, and verify these theoretical predictions empirically.

Reinforcement learning in nonstationary environments is generally regarded as an important and yet difficult problem. This paper partially addresses the problem by formalizing a subclass of nonstationary environments.The environment model, called hidden-mode Markov decision process (HM-MDP), assumes that environmental changes are always confined to a small number of hidden modes.

We study a population decoding paradigm in which the maximum likelihood inferenceis based on an unfaithful decoding model (UMLI). This is usually the case for neural population decoding because the encoding process of the brain is not exactly known, or because a simplified decoding modelis preferred for saving computational cost. We consider an unfaithful decoding model which neglects the pairwise correlation between neuronal activities, and prove that UMLI is asymptotically efficient whenthe neuronal correlation is uniform or of limited-range. The performance of UMLI is compared with that of the maximum likelihood inference based on a faithful model and that of the center of mass decoding method.It turns out that UMLI has advantages of decreasing the computational complexity remarkablely and maintaining a high-level decoding accuracy at the same time. The effect of correlation on the decoding accuracy is also discussed.

This learning function is based on recent experimental findings .

In this paper, we consider the problem of active learning in trigonometric polynomialnetworks and give a necessary and sufficient condition of sample points to provide the optimal generalization capability. By analyzing thecondition from the functional analytic point of view, we clarify the mechanism of achieving the optimal generalization capability. We also show that a set of training examples satisfying the condition does not only provide the optimal generalization but also reduces the computational complexityand memory required for the calculation of learning results. Finally, examples of sample points satisfying the condition are given and computer simulations are performed to demonstrate the effectiveness ofthe proposed active learning method. 1 Introduction Supervised learning is obtaining an underlying rule from training examples, and can be formulated as a function approximation problem. If sample points are actively designed, then learning can be performed more efficiently. In this paper, we discuss the problem of designing sample points, referred to as active learning, for optimal generalization. Active learning is classified into two categories depending on the optimality. One is global optimal, where a set of all training examples is optimal (e.g.

We propose a new Markov Chain Monte Carlo algorithm which is a generalization ofthe stochastic dynamics method. The algorithm performs exploration of the state space using its intrinsic geometric structure, facilitating efficientsampling of complex distributions. Applied to Bayesian learning in neural networks, our algorithm was found to perform at least as well as the best state-of-the-art method while consuming considerably less time. 1 Introduction

We describe a new incremental algorithm for training linear threshold functions:the Relaxed Online Maximum Margin Algorithm, or ROMMA. ROMMA can be viewed as an approximation to the algorithm that repeatedly chooses the hyperplane that classifies previously seen examples correctlywith the maximum margin. It is known that such a maximum-margin hypothesis can be computed by minimizing the length of the weight vector subject to a number of linear constraints. ROMMA works by maintaining a relatively simple relaxation of these constraints that can be efficiently updated. We prove a mistake bound for ROMMA that is the same as that proved for the perceptron algorithm. Our analysis implies that the more computationally intensive maximum-margin algorithm alsosatisfies this mistake bound; this is the first worst-case performance guaranteefor this algorithm. We describe some experiments using ROMMA and a variant that updates its hypothesis more aggressively as batch algorithms to recognize handwritten digits. The computational complexity and simplicity of these algorithms is similar to that of perceptron algorithm,but their generalization is much better. We describe a sense in which the performance of ROMMA converges to that of SVM in the limit if bias isn't considered.

I present a simple variation of importance sampling that explicitly searches forimportant regions in the target distribution. I prove that the technique yieldsunbiased estimates, and show empirically it can reduce the variance of standard Monte Carlo estimators. This is achieved by concentrating samplesin more significant regions of the sample space. 1 Introduction It is well known that general inference and learning with graphical models is computationally hard[1] and it is therefore necessary to consider restricted architectures [13], or approximate algorithms to perform these tasks [3, 7]. Among the most convenient and successful techniques are stochastic methods which are guaranteed to converge to a correct solution in the limit oflarge samples [10, 11, 12, 15]. These methods can be easily applied to complex inference problems that overwhelm deterministic approaches.

The reliability and accuracy of spike trains have been shown to depend on the nature of the stimulus that the neuron encodes.

This question was recently shown in [9] to be a special case of a much more fundamental problem:What are the features of the variable X that are relevant for the prediction of another, relevance, variable Y?