Abstract: Deep Gaussian processes have attracted lots of research attention in the recent years. However, it suffers the same, if not more severe, bottleneck as the (one-layer) Gaussian processes due to cubic computational complexity of evaluating a high-dimensional joint Gaussian density. In this paper, we propose Deep Vecchia Gaussian processes, a highly non-trivia marriage between Deep Gaussian process and (one-layer) Vecchia Gaussian processes. The proposed method puts Vecchia Gaussian processes on the layer-wise mappings rather than the intermediate states of the training, which cleverly circumvents the random parent sets problem that prevails in literature. The proposed Deep Vecchia Gaussian process, when served as prior for statistical problems, results valid Bayesian methods with automatic uncertainty quantification, whereas enjoying scalable computational complexity and minimax optimality over a wide range of composite functions.
Bio: Dr. Yichen Zhu is currently a tenure-track Assistant Professor at the School of Computing and Data Science, the University of Hong Kong. Prior to that, he was a postdoctoral researcher at Bocconi University, advised by Prof. Botond Szabo. He obtained Ph.D. in Statistical Science at Duke University in 2023, advised by Prof. David B. Dunson. He obtained B.S. in mathematics at Peking University in 2018, advised by Prof. Wei Lin. His research interests span the areas of Bayesian Statistics, Deep Learning, Nonparametric Statistics, Statistical Computing and Theoretical Statistics.
