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2023 JMLR JMLR 2023

Posterior Contraction for Deep Gaussian Process Priors

Abstract

We study posterior contraction rates for a class of deep Gaussian process priors in the nonparametric regression setting under a general composition assumption on the regression function. It is shown that the contraction rates can achieve the minimax convergence rate (up to log n factors), while being adaptive to the underlying structure and smoothness of the target function. The proposed framework extends the Bayesian nonparametric theory for Gaussian process priors. [abs] [ pdf ][ bib ] © JMLR 2023. (edit, beta)

🌉 Interdisciplinary Bridge — Artificial Intelligence and Machine Learning
🧭 Keyword Pioneer — minimax convergence rate
🐝 Cross-Pollinator — Artificial Intelligence, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning

Authors

Gianluca Finocchio , Johannes Schmidt-Hieber

Topics

Artificial Intelligence > Bayesian & Probabilistic > Bayesian Learning Machine Learning > Core Methods > Regression Machine Learning > Optimization & Theory > Statistical Learning Machine Learning > Bayesian & Probabilistic > Bayesian Inference Machine Learning > Bayesian & Probabilistic > Gaussian Processes

Keywords

bayesian nonparametrics nonparametric regression gaussian process prior deep gaussian process posterior contraction minimax convergence rate
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