Near-minimax recursive density estimation on the binary hypercube

This paper describes a recursive estimation procedure for multivariate binary densities 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 sparsity 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.

• Type: Conference
• Year: 2008
• Where: NIPS
• Authors: Maxim Raginsky, Svetlana Lazebnik, Rebecca Willett, Jorge Silva
• Keywords: Certain Sparsity Condition, Computational Complexity, Information Technology, Multivariate Binary Densities, NIPS 2008