A biologically motivated model of cortical self-organization is proposed. Context is combined with bottom-up information via a maximum likelihood cost function. Clusters of one or more units are modulated by a common contextual gating Signal; they thereby organize themselves into mutually supportive predictors of abstract contextual features. The model was tested in its ability to discover viewpoint-invariant classes on a set of real image sequences of centered, gradually rotating faces. It performed considerably better than supervised back-propagation at generalizing to novel views from a small number of training examples.

A CDP can always be discretized in state space and time and thus reduced to a Markov Decision Problem. Algorithms like Q-Iearning and RTDP as described in [1] can then be applied to produce controls or optimal value functions for a fixed discretization. Problems arise when the discretization needs to be refined, or when multi-grid information needs to be extracted to accelerate the algorithm. The relation of time to state space discretization parameters is crucial in both cases. Therefore 1034 S. Pareigis a mathematical model of the discretized process is introduced, which reflects the properties of the converged empirical process.

We present new results about the temporal-difference learning algorithm, as applied to approximating the cost-to-go function of a Markov chain using linear function approximators. The algorithm we analyze performs online updating of a parameter vector during a single endless trajectory of an aperiodic irreducible finite state Markov chain. Results include convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. In addition to establishing new and stronger results than those previously available, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. Furthermore, we discuss the implications of two counterexamples with regards to the Significance of online updating and linearly parameterized function approximators. 1 INTRODUCTION The problem of predicting the expected long-term future cost (or reward) of a stochastic dynamic system manifests itself in both time-series prediction and control.

We cast the problem as one of maximum likelihood density estimation, and in that framework introduce an algorithm that searches for independent components using both temporal and spatial cues. We call the resulting algorithm "Contextual ICA," after the (Bell and Sejnowski 1995) Infomax algorithm, which we show to be a special case of cICA. Because cICA can make use of the temporal structure of its input, it is able separate in a number of situations where standard methods cannot, including sources with low kurtosis, colored Gaussian sources, and sources which have Gaussian histograms. 1 The Blind Source Separation Problem Consider a set of n indepent sources

This paper shows how the prices of option contracts traded in financial markets can be tracked sequentially by means of the Extended Kalman Filter algorithm. I consider call and put option pairs with identical strike price and time of maturity as a two output nonlinear system. The Black-Scholes approach popular in Finance literature and the Radial Basis Functions neural network are used in modelling the nonlinear system generating these observations. I show how both these systems may be identified recursively using the EKF algorithm. I present results of simulations on some FTSE 100 Index options data and discuss the implications of viewing the pricing problem in this sequential manner. 1 INTRODUCTION Data from the financial markets has recently been of much interest to the neural computing community. The complexity of the underlying macroeconomic system and how traders react to the flow of information leads to highly nonlinear relationships between observations.

A hint is any piece of side information about the target function to be learned. We consider the monotonicity hint, which states that the function to be learned is monotonic in some or all of the input variables. The application of mono tonicity hints is demonstrated on two real-world problems-a credit card application task, and a problem in medical diagnosis. A measure of the monotonicity error of a candidate function is defined and an objective function for the enforcement of monotonicity is derived from Bayesian principles. We report experimental results which show that using monotonicity hints leads to a statistically significant improvement in performance on both problems.

Given a multidimensional data set and a model of its density, we consider how to define the optimal interpolation between two points. This is done by assigning a cost to each path through space, based on two competing goals-one to interpolate through regions of high density, the other to minimize arc length. From this path functional, we derive the Euler-Lagrange equations for extremal motionj given two points, the desired interpolation is found by solving a boundary value problem. We show that this interpolation can be done efficiently, in high dimensions, for Gaussian, Dirichlet, and mixture models. 1 Introduction The problem of nonlinear interpolation arises frequently in image, speech, and signal processing. Consider the following two examples: (i) given two profiles of the same face, connect them by a smooth animation of intermediate poses[l]j (ii) given a telephone signal masked by intermittent noise, fill in the missing speech.

In most treatments of the regression problem it is assumed that the distribution of target data can be described by a deterministic function of the inputs, together with additive Gaussian noise having constant variance. The use of maximum likelihood to train such models then corresponds to the minimization of a sum-of-squares error function. In many applications a more realistic model would allow the noise variance itself to depend on the input variables. However, the use of maximum likelihood to train such models would give highly biased results. In this paper we show how a Bayesian treatment can allow for an input-dependent variance while overcoming the bias of maximum likelihood.

We study the spatiotemporal correlation in natural time-varying images and explore the hypothesis that the visual system is concerned with the optimal coding of visual representation through spatiotemporal decorrelation of the input signal. Based on the measured spatiotemporal power spectrum, the transform needed to decorrelate input signal is derived analytically and then compared with the actual processing observed in psychophysical experiments.

In dimension d 2, Gibson characterized the functions computable with just one hidden layer, under the assumption that there is no "multiple intersection point" and that f