CAREER: High-dimensional inference and applications to modern biology

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In recent years, a burgeoning field of high-dimensional statistical inference has witnessed astounding advances, providing new theoretical tools to characterize exact distributional behavior for an increasingly large class of statistical and machine-learning methods. These advances hold the promise of improved statistical procedures with more precise quantifications of uncertainty across many fields of modern biology. This research will extend the scope of these high-dimensional inferential methods, which currently remain restricted to more stylized statistical models, to address a broader range of scientific problems having complex latent structure. The research will also enable the PI to continue his educational outreach activities in the K-12 levels in Connecticut public schools, as well as his experimentation in the teaching of introductory courses at Yale University by focusing the discussion of statistical concepts and ideas on motivating real-life examples.On the theoretical front, this research will improve our understanding of mean-field phenomena in non-i.i.d. contexts, including disordered systems and spin glass models with statistically dependent couplings, as well as variational Bayesian approximations to regression models with correlated designs. This research will also further our understanding of asymptotic freeness phenomena for random matrix models arising in statistical settings. On the applications front, this research will improve our understanding of likelihood-based inference for molecular structure determination in cryo-electron microscropy, and investigate possibilities for more robust and efficient reconstruction algorithms. This research will also develop new Bayes and empirical Bayes procedures for fine-mapping of genetic causal variants and for dimensionality reduction of genetic sequence data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.