Dr Ron Meir, Department of Computer Science, Technion, Israel
(1) Nonparametric Time Series Prediction Through Adaptive Model Selection

Abstract: We consider the problem of one-step ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. We make use of recent results from the theory of empirical processes, and adapt the uniform convergence framework of Vapnik and Chervonenkis to the problem of time series prediction, obtaining finite sample bounds. Furthermore, by allowing both the model complexity and memory size to be adaptively determined by the data, we derive nonparametric rates of convergence through an extension of the method of structural risk minimization suggested by Vapnik. All our results are derived for general $L_p$ error measures, and apply to both exponentially as well as algebraically mixing processes.
(2) Nearly optimal neural network approximation using incremental algorithms

Work with Vitaly Maiorov

Abstract: The problem of approximating functions by neural networks using computationally attractive incremental algorithms is studied. For functions belonging to the very general Besov class, composed of functions characterized by certain smoothness properties with respect to the $L_p$ norm, $p\ge 2$, we compute upper bounds on the approximation error where error is measured by the $L_q$ norm, $1 \le q \le \infty$. These results extend previous work, applicable in the case $p=q$. In the range $q\le p$ near-optimal rates of convergence are demonstrated. A gap remains, however, with respect to a recently established lower bound in the case $q>p$, although the rates achieved are provably better than those obtained by optimal linear approximation.

These seminars were held at the Department of Computer Science, Royal Holloway, University of London on 7 September 1998.

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