Frontiers in Mathematical Sciences - 8th Conference


TITLE  
Modern Statistical Inference: From High-Dimensional to Infinite-Dimensional


SPEAKER  
Ali Shojaie
Department of Biostatistics, University of Washington





ABSTRACT

Statistical inference --- that is, characterizing the uncertainty of estimators in the form of $p$-values and confidence intervals --- plays a crucial role in scientific research across many disciplines and is at the core of statistical science.
Emerging statistical machine learning and artificial intelligence methods involve models with many parameters, either due to the large number of covariates being modeled, or because of the complexity and flexibility of the approaches. Moreover, many scientific problems involve infinite-dimensional (or function-valued) parameters.
Unfortunately, classical statistical inference procedures fail in such settings.
In this talk, we will discuss recent developments in statistical inference for regularized estimation strategies for high-dimensional models, i.e. models with more parameters than observations. We then discuss the challenges of extending these ideas to the setting of infinite-dimensional (or function-valued) parameters and present a new inference framework that facilitates statistical inference in previously intractable problems.