Novelty detection involves modeling the normal behaviour of a system hence enabling detection of any divergence from normality. It has potential applications in many areas such as detection of machine damage or highlighting abnormal features in medical data. One approach is to build a hypothesis estimating the support of the normal data i.e. constructing a function which is positive in the region where the data is located and negative elsewhere. Recently kernel methods have been proposed for estimating the support of a distribution and they have performed well in practice - training involves solution of a quadratic programming problem. In this paper we propose a simpler kernel method for estimating the support based on linear programming. The method is easy to implement and can learn large datasets rapidly. We demonstrate the method on medical and fault detection datasets.

We investigate a new kernel-based classifier: the Kernel Fisher Discriminant (KFD). A mathematical programming formulation based on the observation that KFD maximizes the average margin permits an interesting modification of the original KFD algorithm yielding the sparse KFD. We find that both, KFD and the proposed sparse KFD, can be understood in an unifying probabilistic context. Furthermore, we show connections to Support Vector Machines and Relevance Vector Machines. From this understanding, we are able to outline an interesting kernel-regression technique based upon the KFD algorithm.

It has been shown that the receptive fields of simple cells in VI can be explained by assuming optimal encoding, provided that an extra constraint of sparseness is added. This finding suggests that there is a reason, independent of optimal representation, for sparseness. However this work used an ad hoc model for the noise. Here I show that, if a biologically more plausible noise model, describing neurons as Poisson processes, is used sparseness does not have to be added as a constraint. Thus I conclude that sparseness is not a feature that evolution has striven for, but is simply the result of the evolutionary pressure towards an optimal representation.

The principle of maximizing mutual information is applied to learning overcomplete and recurrent representations. The underlying model consists of a network of input units driving a larger number of output units with recurrent interactions. In the limit of zero noise, the network is deterministic and the mutual information can be related to the entropy of the output units.

People are active experimenters, not just passive observers, constantly seeking new information relevant to their goals. A reasonable approach to active information gathering is to ask questions and conduct experiments that maximize the expected information gain, given current beliefs (Fedorov 1972, MacKay 1992, Oaksford & Chater 1994). In this paper we present results on an exploratory experiment designed to study people's active information gathering behavior on a concept learning task (Tenenbaum 2000). The results of the experiment are analyzed in terms of the expected information gain of the questions asked by subjects. In scientific inquiry and in everyday life, people seek out information relevant to perceptual and cognitive tasks.

Our al exploits the special structure of the sum of squared error measure in Equation (1); hence, the other objective functions are outside the scope of this paper. The gradient vector and Hessian matrix are given by g g(9) JT rand H H(9) JT J S, where J is the m x n Jacobian matrix of r, and S denotes the matrix of second-derivative terms. If S is simply omitted based on the "small residual" assumption, then the Hessian matrix reduces to the Gauss-Newton model Hessian: i.e., JT J. Furthermore, a family of quasi-Newton methods can be applied to approximate term S alone, leading to the augmented Gauss-Newton model Hessian (see, for example, Mizutani [2] and references therein).

We present efficient algorithms for all-point-pairs problems, or'Nbody'-like problems, which are ubiquitous in statistical learning. We focus on six examples, including nearest-neighbor classification, kernel density estimation, outlier detection, and the two-point correlation.

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.

In this paper, we discuss some new research directions in automatic speech recognition (ASR), and which somewhat deviate from the usual approaches. More specifically, we will motivate and briefly describe new approaches based on multi-stream and multi/band ASR. These approaches extend the standard hidden Markov model (HMM) based approach by assuming that the different (frequency) channels representing the speech signal are processed by different (independent) "experts", each expert focusing on a different characteristic of the signal, and that the different stream likelihoods (or posteriors) are combined at some (temporal) stage to yield a global recognition output. As a further extension to multi-stream ASR, we will finally introduce a new approach, referred to as HMM2, where the HMM emission probabilities are estimated via state specific feature based HMMs responsible for merging the stream information and modeling their possible correlation.

Using statistical mechanics results, I calculate learning curves (average generalization error) for Gaussian processes (GPs) and Bayesian neural networks (NNs) used for regression. Applying the results to learning a teacher defined by a two-layer network, I can directly compare GP and Bayesian NN learning.