About Jian Cao Jian Cao Ph.D., Statistics data science spatio-temporal statistics statistics Jian Cao obtained his Ph.D. degree in Statistics from King Abdullah University of Science and Technology (KAUST), under the supervision of Professor Marc Genton at the "spatio-temporal statistics and data science" research group. His research focused on Monte Carlo simulation, hierarchical matrices, tile-low-rank matrices, and solving high dimensional multivariate normal or Student-t probabilities. Education and Early Career Ph.D. degree from King Abdullah University of Science and Technology Master from Shanghai Jiaotong University Bachelor from University of Science and Technology of China Events Presented Events Apr 5 - Apr 11, 2020 Computation of High-Dimensional Multivariate Normal and Student-t Probabilities Based on Matrix Compression Schemes Jian Cao, Ph.D., Statistics Apr 6, 16:00 - 18:00 KAUST The thesis focuses on the computation of high-dimensional multivariate normal (MVN) and multivariate Student-t (MVT) probabilities. Firstly, a generalization of the conditioning method for MVN probabilities is proposed and combined with the hierarchical matrix representation. Next, I revisit the Quasi-Monte Carlo (QMC) method and improve the state-of-the-art QMC method for MVN probabilities with block reordering, resulting in a ten-time-speed improvement. The thesis proceeds to discuss a novel matrix compression scheme using Kronecker products. This novel matrix compression method has a memory footprint smaller than the hierarchical matrices by more than one order of magnitude. A Cholesky factorization algorithm is correspondingly designed and shown to accomplish the factorization in 1 million dimensions within 600 seconds. To make the computational methods for MVN probabilities more accessible, I introduce an R package that implements the methods developed in this thesis and show that the package is currently the most scalable package for computing MVN probabilities in R. Finally, as an application, I derive the posterior properties of the probit Gaussian random field and show that the R package I introduce makes the model selection and posterior prediction feasible in high dimensions.
Computation of High-Dimensional Multivariate Normal and Student-t Probabilities Based on Matrix Compression Schemes Jian Cao, Ph.D., Statistics Apr 6, 16:00 - 18:00 KAUST The thesis focuses on the computation of high-dimensional multivariate normal (MVN) and multivariate Student-t (MVT) probabilities. Firstly, a generalization of the conditioning method for MVN probabilities is proposed and combined with the hierarchical matrix representation. Next, I revisit the Quasi-Monte Carlo (QMC) method and improve the state-of-the-art QMC method for MVN probabilities with block reordering, resulting in a ten-time-speed improvement. The thesis proceeds to discuss a novel matrix compression scheme using Kronecker products. This novel matrix compression method has a memory footprint smaller than the hierarchical matrices by more than one order of magnitude. A Cholesky factorization algorithm is correspondingly designed and shown to accomplish the factorization in 1 million dimensions within 600 seconds. To make the computational methods for MVN probabilities more accessible, I introduce an R package that implements the methods developed in this thesis and show that the package is currently the most scalable package for computing MVN probabilities in R. Finally, as an application, I derive the posterior properties of the probit Gaussian random field and show that the R package I introduce makes the model selection and posterior prediction feasible in high dimensions.
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