In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x, y) k(x.

These include face detection [14], face pose discrimination [12] and face recognition [16]. Although facial sex classification has attracted much attention in the psychological literature [1, 4, 8, 15], relatively few computatinal learning methods have been proposed. We will briefly review and summarize the prior art in facial sex classification.

We present evidence that several higher-order statistical properties of natural images and signals can be explained by a stochastic model which simply varies scale of an otherwise stationary Gaussian process. We discuss two interesting consequences. The first is that a variety of natural signals can be related through a common model of spherically invariant random processes, which have the attractive property that the joint densities can be constructed from the one dimensional marginal. The second is that in some cases the non-stationarity assumption and only second order methods can be explicitly exploited to find a linear basis that is equivalent to independent components obtained with higher-order methods. This is demonstrated on spectro-temporal components of speech. 1 Introduction Recently, considerable attention has been paid to understanding and modeling the non-Gaussian or "higher-order" properties of natural signals, particularly images. Several non-Gaussian properties have been identified and studied.

Incorporating prior knowledge of a particular task into the architecture of a learning algorithm can greatly improve generalization performance. We study here a case where we know that the function to be learned is non-decreasing in two of its arguments and convex in one of them. For this purpose we propose a class of functions similar to multi-layer neural networks but (1) that has those properties, (2) is a universal approximator of continuous functions with these and other properties. We apply this new class of functions to the task of modeling the price of call options. Experiments show improvements on regressing the price of call options using the new types of function classes that incorporate the a priori constraints.

The naive mean-field approach fails in this case whereas linear response theory-which gives an improved estimate of covariances-is very efficient. The examples given are for sources without temporal correlations .

Algebraic geometry is essential to learning theory. In hierarchical learning machines such as layered neural networks and gaussian mixtures, the asymptotic normality does not hold, since Fisher information matrices are singular. In this paper, the rigorous asymptotic form of the stochastic complexity is clarified based on resolution of singularities and two different problems are studied.

We show how a wavelet basis may be adapted to best represent natural images in terms of sparse coefficients. The wavelet basis, which may be either complete or overcomplete, is specified by a small number of spatial functions which are repeated across space and combined in a recursive fashion so as to be self-similar across scale. These functions are adapted to minimize the estimated code length under a model that assumes images are composed of a linear superposition of sparse, independent components. When adapted to natural images, the wavelet bases take on different orientations and they evenly tile the orientation domain, in stark contrast to the standard, non-oriented wavelet bases used in image compression. When the basis set is allowed to be overcomplete, it also yields higher coding efficiency than standard wavelet bases. 1 Introduction The general problem we address here is that of learning efficient codes for representing natural images.

Bayesian networks are graphical representations of probability distributions. In virtually all of the work on learning these networks, the assumption is that we are presented with a data set consisting of randomly generated instances from the underlying distribution. In many situations, however, we also have the option of active learning, where we have the possibility of guiding the sampling process by querying for certain types of samples. This paper addresses the problem of estimating the parameters of Bayesian networks in an active learning setting. We provide a theoretical framework for this problem, and an algorithm that chooses which active learning queries to generate based on the model learned so far. We present experimental results showing that our active learning algorithm can significantly reduce the need for training data in many situations.

Adaptive boosting methods are simple modular algorithms that operate as follows. Let 9: X -t Y be the function to be learned, where the label set Y is finite, typically binary-valued. The algorithm uses a learning procedure, which has access to n training examples, {(Xl, Y1),..., (xn, Yn)}, drawn randomly from X x Yaccording to distribution D; it outputs a hypothesis I:

Prior knowledge about video structure can be used both as a means to improve the peiformance of content analysis and to extract features that allow semantic classification. We introduce statistical models for two important components of this structure, shot duration and activity, and demonstrate the usefulness of these models by introducing a Bayesian formulation for the shot segmentation problem. The new formulations is shown to extend standard thresholding methods in an adaptive and intuitive way, leading to improved segmentation accuracy.