Although one can derive the Gaussian noise assumption based on a maximum entropy approach, the main reason for this assumption is practicability: under the Gaussian noise assumption the maximum likelihood parameter estimate can simply be found by minimization of the squared error. Despite its common use it is far from clear that the Gaussian noise assumption is a good choice for many practical problems. A reasonable approach therefore would be a noise distribution which contains the Gaussian as a special case but which has a tunable parameter that allows for more flexible distributions.

We present a new technique for time series analysis based on dynamic probabilistic networks. In this approach, the observed data are modeled in terms of unobserved, mutually independent factors, as in the recently introduced technique of Independent Factor Analysis (IFA). However, unlike in IFA, the factors are not Li.d.; each factor has its own temporal statistical characteristics. We derive a family of EM algorithms that learn the structure of the underlying factors and their relation to the data. These algorithms perform source separation and noise reduction in an integrated manner, and demonstrate superior performance compared to IFA. 1 Introduction The technique of independent factor analysis (IFA) introduced in [1] provides a tool for modeling L'-dim data in terms of L unobserved factors. These factors are mutually independent and combine linearly with added noise to produce the observed data.

In particular, Mackay showed that by approximating the distributions of the weights with Gaussians and adopting smoothing priors, it is possible to obtain estimates of the weights and output variances and to automatically set the regularisation coefficients. Neal (1996) cast the net much further by introducing advanced Bayesian simulation methods, specifically the hybrid Monte Carlo method, into the analysis of neural networks [3]. Bayesian sequential Monte Carlo methods have also been shown to provide good training results, especially in time-varying scenarios [4]. More recently, Rios Insua and Muller (1998) and Holmes and Mallick (1998) have addressed the issue of selecting the number of hidden neurons with growing and pruning algorithms from a Bayesian perspective [5,6]. In particular, they apply the reversible jump Markov Chain Monte Carlo (MCMC) algorithm of Green [7] to feed-forward sigmoidal networks and radial basis function (RBF) networks to obtain joint estimates of the number of neurons and weights. We also apply the reversible jump MCMC simulation algorithm to RBF networks so as to compute the joint posterior distribution of the radial basis parameters and the number of basis functions. However, we advance this area of research in two important directions. Firstly, we propose a full hierarchical prior for RBF networks.

Recently, sample complexity bounds have been derived for problems involving linear functions such as neural networks and support vector machines. In this paper, we extend some theoretical results in this area by deriving dimensional independent covering number bounds for regularized linear functions under certain regularization conditions. We show that such bounds lead to a class of new methods for training linear classifiers with similar theoretical advantages of the support vector machine. Furthermore, we also present a theoretical analysis for these new methods from the asymptotic statistical point of view. This technique provides better description for large sample behaviors of these algorithms.

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.

One of the open questions that remains is how to set the'tunable' parameters of an SVM algorithm: While methods for choosing the width of the kernel function and the noise parameter C (which controls how closely the training data are fitted) have been proposed [4, 5] (see also, very recently, [6]), the effect of the overall shape of the kernel function remains imperfectly understood [1]. Error bars (class probabilities) for SVM predictions - important for safety-critical applications, for example - are also difficult to obtain. In this paper I suggest that a probabilistic interpretation of SVMs could be used to tackle these problems. It shows that the SVM kernel defines a prior over functions on the input space, avoiding the need to think in terms of high-dimensional feature spaces. It also allows one to define quantities such as the evidence (likelihood) for a set of hyperparameters (C, kernel amplitude Ko etc). I give a simple approximation to the evidence which can then be maximized to set such hyperparameters. The evidence is sensitive to the values of C and Ko individually, in contrast to properties (such as cross-validation error) of the deterministic solution, which only depends on the product CKo. It can thfrefore be used to assign an unambiguous value to C, from which error bars can be derived.

Effective methods of capacity control via uniform convergence bounds for function expansions have been largely limited to Support Vector machines, where good bounds are obtainable by the entropy number approach. We extend these methods to systems with expansions in terms of arbitrary (parametrized) basis functions and a wide range of regularization methods covering the whole range of general linear additive models. This is achieved by a data dependent analysis of the eigenvalues of the corresponding design matrix.

In this article we study the effects of introducing structure in the input distribution of the data to be learnt by a simple perceptron. We determine the learning curves within the framework of Statistical Mechanics. Stepwise generalization occurs as a function of the number of examples when the distribution of patterns is highly anisotropic. Although extremely simple, the model seems to capture the relevant features of a class of Support Vector Machines which was recently shown to present this behavior.

Simply changing the potential function allows one to create new algorithms related to AdaBoost. However, these new algorithms are generally not known to have the formal boosting property. This paper examines the question of which potential functions lead to new algorithms that are boosters. The two main results are general sets of conditions on the potential; one set implies that the resulting algorithm is a booster, while the other implies that the algorithm is not. These conditions are applied to previously studied potential functions, such as those used by LogitBoost and Doom II.

We show that the recently proposed variant of the Support Vector machine (SVM) algorithm, known as v-SVM, can be interpreted as a maximal separation between subsets of the convex hulls of the data, which we call soft convex hulls. The soft convex hulls are controlled by choice of the parameter v. If the intersection of the convex hulls is empty, the hyperplane is positioned halfway between them such that the distance between convex hulls, measured along the normal, is maximized; and if it is not, the hyperplane's normal is similarly determined by the soft convex hulls, but its position (perpendicular distance from the origin) is adjusted to minimize the error sum. The proposed geometric interpretation of v-SVM also leads to necessary and sufficient conditions for the existence of a choice of v for which the v-SVM solution is nontrivial. 1 Introduction Recently, SchOlkopf et al. [I) introduced a new class of SVM algorithms, called v-SVM, for both regression estimation and pattern recognition. The basic idea is to remove the user-chosen error penalty factor C that appears in SVM algorithms by introducing a new variable p which, in the pattern recognition case, adds another degree of freedom to the margin.