Adaptive density estimation under low-rank constraints

Music City Center 

In this talk, we address the challenge of bivariate probability density
estimation under low-rank constraints for both discrete and continuous
distributions. For discrete distributions, we model the target as a
low-rank probability matrix. In the continuous case, we assume the
density function is Lipschitz continuous over an unknown compact
rectangular support and can be decomposed into a sum of K separable
components, each represented as a product of two one-dimensional
functions. We introduce an estimator that leverages these low-rank
constraints, achieving significantly improved convergence rates. We
also derive lower bounds for both discrete and continuous cases,
demonstrating that our estimators achieve minimax optimal convergence
rates within logarithmic factors.

Low-rank models

Density estimation

Adaptive estimation