Perturbation of linear forms of singular vectors under Gaussian noise

Series
High-Dimensional Phenomena in Statistics and Machine Learning Seminar
Time
Tuesday, October 20, 2015 - 3:00pm for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Dong Xia – Georgia Inst. of Technology
Organizer
Karim Lounici
Let A be a mxn matrix with singular value decomposition A=UDV', where the columns of U are left singular vectors and columns of V are right singular vectors of A. Suppose X is a mxn noise matrix whose entries are i.i.d. Gaussian random variables and consider A'=A+X. Let u_k be the k-th left singular vector of A and u'_k be its counterpart of A'. We develop sharp upper bounds for concentration of linear forms for the right singular vectors of A'.The talk is based on a joint work with Vladimir Koltchinskii.