Regularization and approximation: statistical inference, model selection, and large data

点击翻译按钮获取中文摘要

Extracting information from large data requires computational tractability and statistical efficiency. These are typically achieved through approximation or regularization, either of which heuristically balances fidelity to the data with scientific goals like parsimony, smoothness, sparsity, or interpretability. My long-term objective is to enable fundamental scientific progress by developing and characterizing the connections between computational approximation and statistical regularization, thereby facilitating improved inference. In particular, my research program investigates how statistically optimal decisions depend on the amount of regularization or approximation and their structures, both of which must be tied to the scientific questions at stake and calibrated according to the data. Research in computer science has focused on improving algorithms to enable computation with a minimum of approximation. Meanwhile, statisticians have developed regularization techniques in order to take advantage of simple structures that, if representative of the truth, will improve inference and prediction. My work seeks to bridge the gap between these perspectives. My research program aims to deepen the theoretical links between approximation algorithms and inference for estimation and prediction by: (1) developing and justifying approximation techniques for dependent data; (2) enabling application through reasoned tuning parameter selection; (3) precisely characterizing the effect of approximations in nonparametric statistics; and (4) ensuring scientific applicability through synergistic development and collaboration with domain experts.