Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:00 pm
Date: 9th December
Place: 3001

Pragya SUR (Harvard University​) – Spectrum-Aware Debiasing: A Modern Inference Framework with Applications to Principal Components Regression

 Abstract: 

Debiasing methodologies have emerged as powerful tools for making statistical inferences in high-dimensional problems. Since its original introduction, the methodology underwent a major development with the introduction of debiasing techniques that adjust for degrees-of-freedom (Bellec and Zhang, 2019). While overcoming limitations of initial debiasing approaches, this updated method relies on Gaussian/sub-Gaussian tailed designs and independent, identically distributed samples – a key limitation. In this talk, I will propose a novel debiasing formula that breaks this barrier by exploiting the spectrum of the sample covariance matrix. Our formula applies to a much broader class of designs, including some heavy- tailed distributions, as well as certain dependent data settings. Our correction term differs significantly from prior work but recovers the Gaussian-based formula as a special case. Notably, our approach does not require estimating the high-dimensional population covariance matrix yet can account for certain classes of dependence among both features and samples. We demonstrate the utility of our method for several statistical inference problems. As a by-product, our work also introduces the first debiased principal component regression estimator with formal guarantees in high dimensions.

Organizers:

Anna KORBA (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)

Sponsors:
CREST-CMAP