Agenda

Johannes Schmidt-Hieber
University of Twente

Abstract

Deep neural networks are at the heart of the AI revolution and considerable progress has been made in building an underlying statistical foundation. Deep Gaussian process priors can be viewed as continuous analogues of Bayesian neural networks. This raises the question whether there is a closer link with deep learning and to what extend statistical convergence guarantees for deep artificial neural networks also hold for deep Gaussian process priors. For a carefully selected deep Gaussian process prior, we provide a positive answer for learning compositionally sparse functions. Similarly as the convergence rates for deep ReLU networks, deep Gaussian processes can achieve in this setting the fastest possible posterior contraction rates, which do not suffer from the curse of dimensionality. Moreover, we rigorously prove that deep Gaussian process priors can outperform Gaussian process priors in terms of contraction rates if the target function has a compositional structure.

This is joint work with Gianluca Finocchio, Matteo Giordano and Kolyan Ray.

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This lecture is included in the programme of the 2024 ISBA World Meeting

For further information please contact isba2024@unive.it