Near-minimax recursive density estimation on the binary hypercube

Details Near-minimax recursive density estimation on the binary hypercube Near-minimax recursive density estimation on the binary hypercube

2011-12-07

arxiv.org/abs/1112.1450v1

Mathematics

Statistics Theory

submitted to Electronic Journal of Statistics

Scientific paper

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, 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.

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