A recursive procedure for density estimation on the binary hypercube

作者：Raginky Maxim^*; Sliva Jorge G; Lazebnik Svetlana; Willett Rebecca

来源：Electronic Journal of Statistics, 2013, 7(0): 820-858.

DOI：10.1214/13-EJS787

• Minimax estimation
• density estimation
• adaptive estimation
• binary hypercube
• Walsh basis
• sparsity

This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For d covariates, there are 2(d) 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 for moderate sample sizes, 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.

• 出版日期2013