A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs.

The technique of principal component analysis (PCA) has recently been expressed as the maximum likelihood solution for a generative latent variable model. In this paper we use this probabilistic reformulation as the basis for a Bayesian treatment of PCA. Our key result is that effective dimensionalityof the latent space (equivalent to the number of retained principal components) can be determined automatically as part of the Bayesian inference procedure. An important application of this framework is to mixtures of probabilistic PCA models, in which each component can determine its own effective complexity. 1 Introduction Principal component analysis (PCA) is a widely used technique for data analysis. Recently Tipping and Bishop (1997b) showed that a specific form of generative latent variable model has the property that its maximum likelihood solution extracts the principal subspace of the observed data set.

As a benchmark task, the spiral problem is well known in neural networks. Unlikeprevious work that emphasizes learning, we approach the problem from a generic perspective that does not involve learning. We point out that the spiral problem is intrinsically connected to the inside/outside problem.A generic solution to both problems is proposed based on oscillatory correlation using a time delay network. Our simulation resultsare qualitatively consistent with human performance, and we interpret human limitations in terms of synchrony and time delays, both biologically plausible. As a special case, our network without time delays can always distinguish these figures regardless of shape, position, size, and orientation.

Yule-Walker) are available for learning Auto-Regressive process models of simple, directly observable, dynamical processes.When sensor noise means that dynamics are observed only approximately, learning can still been achieved via Expectation-Maximisation (EM) together with Kalman Filtering. However, this does not handle more complex dynamics, involving multiple classes of motion.

The WS (Wake-Sleep) algorithm is a simple learning rule for the models with hidden variables. It is shown that this algorithm can be applied to a factor analysis model which is a linear version of the Helmholtz machine. Buteven for a factor analysis model, the general convergence is not proved theoretically. In this article, we describe the geometrical understanding ofthe WS algorithm in contrast with the EM (Expectation Maximization) algorithm and the em algorithm. As the result, we prove the convergence of the WS algorithm for the factor analysis model. We also show the condition for the convergence in general models.

On the other hand, discriminative methods such as support vector machines enable us to construct flexible decision boundaries and often result in classification performance superiorto that of the model based approaches. An ideal classifier should combine these two complementary approaches. In this paper, we develop a natural way of achieving this combination byderiving kernel functions for use in discriminative methods such as support vector machines from generative probability models.

Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reductionand independent component analysis, and has some neurophysiological plausibility. In this paper, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a shrinkage nonlinearity on the components of sparse coding so as to reduce noise. Furthermore, we show how to choose the optimal sparse coding basis for denoising.

Recent works in parameter estimation and neural coding have demonstrated that optimal performance are related to the mutual information between parameters and data. We consider the mutual information in the case where the dependency in the parameter (a vector 8) of the conditional p.d.f. of each observation (a vector

Using a recurrent neural network of excitatory spiking neurons with adapting synapses we show that both effects could be explained by a fast and a slow component inthe synaptic adaptation.

A common way to represent a time series is to divide it into shortduration blocks,each of which is then represented by a set of basis functions. A limitation of this approach, however, is that the temporal alignmentof the basis functions with the underlying structure in the time series is arbitrary. We present an algorithm for encoding a time series that does not require blocking the data. The algorithm finds an efficient representation by inferring the best temporal positions forfunctions in a kernel basis. These can have arbitrary temporal extent and are not constrained to be orthogonal.