On Semi-parametric Inference for BART
Jul 12, 2020
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Veronika Ročková
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There has been a growing realization of the potential of Bayesian machine learning as a platform that can provide both flexible modeling, accurate predictions as well as coherent uncertainty statements. In particular, Bayesian Additive Regression Trees (BART) have emerged as one of today’s most effective general approaches to predictive modeling under minimal assumptions. Statistical theoretical developments for machine learning have been mostly concerned with approximability or rates of estimation when recovering infinite dimensional objects (curves or densities). Despite the impressive array of available theoretical results, the literature has been largely silent about uncertainty quantification. In this work, we continue the theoretical investigation of BART initiated recently by Rockova and van der Pas (2017). We focus on statistical inference questions. In particular, we study the Bernstein-von Mises (BvM) phenomenon (i.e. asymptotic normality) for smooth linear functionals of the regression surface within the framework of non-parametric regression with fixed covariates. Our semi-parametric BvM results show that, beyond rate-optimal estimation, BART can be also used for valid statistical inference.There has been a growing realization of the potential of Bayesian machine learning as a platform that can provide both flexible modeling, accurate predictions as well as coherent uncertainty statements. In particular, Bayesian Additive Regression Trees (BART) have emerged as one of today’s most effective general approaches to predictive modeling under minimal assumptions. Statistical theoretical developments for machine learning have been mostly concerned with approximability or rates of estimat…
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Mathematics
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AI & Data Science
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About ICML 2020
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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