Seminar - Prof. Jianqing Fan

Event Date: 

Wednesday, March 10, 2021 - 3:30pm to 4:30pm

Event Location: 

  • Zoom Webinar

Title: An ℓp theory of PCA and spectral clustering theory of PCA and spectral clustering

Abstract:

We develop an ℓp perturbation theory for a hollowed version of PCA in Hilbert spaces which provably improves upon the vanilla PCA in the presence of heteroscedastic noises. Through a novel ℓp analysis of eigenvectors, we investigate entrywise behaviors of principal component score vectors and show that they can be approximated by linear functionals of the Gram matrix in ℓp norm. For sub-Gaussian mixture models, the choice of p in the theoretical analysis depends on the signal-to-noise ratio, which further yields optimality guarantees for spectral clustering. For contextual community detection, the ℓp theory leads to a simple spectral algorithm that achieves the information threshold for exact recovery. This provides optimal recovery results for the stochastic block model and Gaussian mixture model as special cases.

(Joint work with Emmanual Abbe and Kaizheng Wang)

 
Bio:
 
Jianqing Fan, is a statistician, financial econometrician, and data scientist. He is Frederick L. Moore '18 Professor of Finance, Professor of Statistics, and Professor of Operations Research and Financial Engineering at the Princeton University where he chaired the department from 2012 to 2015. He is the winner of the 2000 COPSS Presidents' Award, Morningside Gold Medal for Applied Mathematics (2007), Guggenheim Fellow (2009), Pao-Lu Hsu Prize (2013) and Guy Medal in Silver (2014). He got elected to Academician from Academia Sinica in 2012.
 

 

Prof. Jianqing Fan