As massive data are being generated routinely in this ?big data? era, we expect to see growingneed of powerful and reliable statistical learning tools to discover patterns in these data. The proposal focuses on the development of systematic and practical tools for discovering nonlinear and interactive patterns among a set of potentialvariables, which are important steps and tasks in many scientific research areas. While most current efforts have been focused on linear systems in high dimensional problems,the proposed approaches provide a novel way of detecting nonlinear relationships and discoveringhow certain candidate predictors interact with each other to influence the response variable. The research promises to bring the power of these new high-dimensional data analysismethods and theory to bear on many important application areas such as genetics, bioinformatics, Internet commerce, and financial data analysis.

In our theoretical and methodological studies, this grant supports us to finish developing a series theoretical results and methods for analyzing a class of non-linear high-dimensional models, i.e., the index models, which assumes that the response is related to the predictors through a low dimensional projection in a nonlinear fashion. It is a very general class of models, yet has very good interpretability. We find an interesting connection between fitting a semi-parametric index model with the regular Lasso algorithm, leading to a very efficient and effective algorithm of conducting variable selections and fitting index models. We also derive the first minimax optimality result for the sliced inverse regression in high dimensions.We found that many classification models such as multi-category logistic regression models can be unified under the index model framework, thus leading to a robust stepwise variable and interaction selection method. We further investigate how margins, entropy, and feature interactions connect to each other and develop a novel algorithm IMMIGRATE to do feature selections with interactions.

We have also developed a high-dimensional tree-based Bayesian model, called the Bayesian forests, an improved parallelizable multiple-try MCMC algorithm, and a novel way of using the Wang-Landau algorithm to accelerate MCMC computation and Bayesian model and variable selections.

In the application side, the grant supports us to develop a flexible tool (CLIC) for integrating the vast amount of gene-expression microarray data from multiple sources to predict gene-gene interactions, gene-function, and gene-module relationships. We have also developed a Monte Carlo-based tool for exploring conformational space of protein folding. We have also developed a Bayesian method for detecting convergent regulatory evolution regions in the genome and providing new and convincing explanations why and how certain remotely related animals developed very similar traits (such why emu, rhea, and ostrich all lost their flying ability during evolution. See Fig 1 for evolutionary relationships of these three and other relevant birds, and Fig 2 for some Bayesian analysis results).

Last Modified: 12/03/2020
Modified by: Jun S Liu