Gaussian Processes are powerful regression models specified by parametrized mean and covariance functions. Standard approaches to estimate these parameters (known by the name Hyperparameters) are Maximum Likelihood (ML) and Maximum APosterior (MAP) approaches. In this paper, we propose and investigate predictive approaches, namely, maximization of Geisser's Surrogate Predictive Probability (GPP) and minimization of mean square error with respect to GPP (referred to as Geisser's Predictive mean square Error (GPE)) to estimate the hyperparameters. We also derive results for the standard Cross-Validation (CV) error and make a comparison. These approaches are tested on a number of problems and experimental results show that these approaches are strongly competitive to existing approaches. 1 Introduction Gaussian Processes (GPs) are powerful regression models that have gained popularity recently, though they have appeared in different forms in the literature for years.

This paper revisits the classical neuroscience paradigm of Hebbian learning. We find that a necessary requirement for effective associative memory learning is that the efficacies of the incoming synapses should be uncorrelated. This requirement is difficult to achieve in a robust manner by Hebbian synaptic learning, since it depends on network level information. Effective learning can yet be obtained by a neuronal process that maintains a zero sum of the incoming synaptic efficacies. This normalization drastically improves the memory capacity of associative networks, from an essentially bounded capacity to one that linearly scales with the network's size.

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?

In this paper we define a probabilistic computational model which generalizes many noisy neural network models, including the recent work of Maass and Sontag [5]. We identify weak ergodicjty as the mechanism responsible for restriction of the computational power of probabilistic models to definite languages, independent of the characteristics of the noise: whether it is discrete or analog, or if it depends on the input or not, and independent of whether the variables are discrete or continuous. We give examples of weakly ergodic models including noisy computational systems with noise depending on the current state and inputs, aggregate models, and computational systems which update in continuous time. 1 Introduction Noisy neural networks were recently examined, e.g.

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.

The idea of a large minimum margin [17] explains the good generalization performance of AdaBoost in the low noise regime. However, AdaBoost performs worse on noisy tasks [10, 11], such as the iris and the breast cancer benchmark data sets [1]. On the latter tasks, a large margin on all training points cannot be achieved without adverse effects on the generalization error. This experimental observation was supported by the study of [13] where the generalization error of ensemble methods was bounded by the sum of the fraction of training points which have a margin smaller than some value p, say, plus a complexity term depending on the base hypotheses and p. While this bound can only capture part of what is going on in practice, it nevertheless already conveys the message that in some cases it pays to allow for some points which have a small margin, or are misclassified, if this leads to a larger overall margin on the remaining points. To cope with this problem, it was mandatory to construct regularized variants of AdaBoost, which traded off the number of margin errors and the size of the margin 562 G. Riitsch, B. Sch6lkopf, A. J. Smola, K.-R.

We study a population decoding paradigm in which the maximum likelihood inference is 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 model is 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 when the 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.

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

Noise-induced coherent oscillations in randomly connected neural networks.

In this paper we discuss the semi parametric statistical model for blind deconvolution. First we introduce a Lie Group to the manifold of noncausal FIR filters. Then blind deconvolution problem is formulated in the framework of a semiparametric model, and a family of estimating functions is derived for blind deconvolution. A natural gradient learning algorithm is developed for training noncausal filters. Stability of the natural gradient algorithm is also analyzed in this framework.