Covariance Estimation in light of the Spiked Covariance Model & 50 Years of
Covariance Estimation in light of the Spiked Covariance Model:
Since Charles Stein's pioneering work in 1956, we know that high-dimensional covariance estimation requires shrinkage. Owing to recent progress in the so-called spiked covariance model, we can now precisely determine the structure of optimal orthogonally-equivariant estimates of covariance matrices, under each of many different metrics. I will describe the optimal procedures and some of their interesting properties.
The talk will review the article Optimal Shrinkage of Eigenvalues in the Spiked Covariance Model
currently available on-line at the 'papers to appear in future issues' website of the Annals of Statistics. It will also review subsequent work.
This is joint work with Iain Johnstone, Matan Gavish, Behrooz Ghorbani.
50 Years of Data Science:
I will review the article by the same title appearing in the December 2017 issue of "Journal of Computational and Graphical Statistics"
Some passages from the abstract of that paper:
More than 50 years ago, John Tukey called for a reformation of academic statistics. In "The Future of Data Analysis" he pointed to the existence of an as-yet unrecognized science, whose subject of interest was learning from data, or "data analysis."...
This article reviews some ingredients of the current “data science moment,” including recent commentary about data science in the popular media, and about how/whether data science is really different from statistics.
Drawing on work by Tukey, Cleveland, Chambers, and Breiman, I present a vision of data science based on the activities of people who are "learning from data," and I describe an academic field dedicated to improving that activity in an evidence-based manner.
Prof. Jiashun Jin (Carnegie Mellon) and collaborators have been working on translating this article into Mandarin.
David Donoho is Anne T. and Robert M. Bass Professor in the Humanities and Sciences at Stanford University. He is a member of the US National Academy of Sciences and a Foreign Associate of the French Academy of Sciences. He was awarded the 2013 Shaw Prize in Mathematical Sciences. Some of the Ph.D. students he has advised on theses include Jianqing Fan (Princeton) (advised jointly with P. Bickel), Jiashun Jin (Carnegie Mellon), and Emmanuel Candes (Stanford).