Near-minimax recursive density estimation on the binary hypercube
Maxim Raginsky, Jorge Silva, Svetlana Lazebnik, Rebecca M. Willett · arXiv (Cornell University) · 2011
This paper describes a recursive estimation procedure for multivariate binary den-sities using orthogonal expansions. For d covariates, there are 2d basis coefficients to estimate, which renders conventional approaches computationally prohibitive when d is large. However, for a wide class of densities that satisfy a certain spar-sity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error, and (2) the computational complexity is lower for sparser densities. Our method also allows for flexible control of the trade-off between mean-squared error and computational complexity. 1