Polynomial-Time Algorithms for Accurate Approximation and Estimation of Functions by Neural Nets

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9410760 Barron The goal of the project is the development and proof of computationally feasible algorithms for training artificial neural networks that provide accurate approximation, estimation, and classification for general classes of functions in high dimensions. The analysis involves Markov chain convergence theory, based on a decomposition of the neural net likelihood function as a mixture of log-concave functions, and an information-theoretic analysis of Bayes estimators of neural nets. Practical computer implementation will also be investigated.