Abstract
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.
Citation
Maxim Raginsky. Jorge G. Silva. Svetlana Lazebnik. Rebecca Willett. "A recursive procedure for density estimation on the binary hypercube." Electron. J. Statist. 7 820 - 858, 2013. https://doi.org/10.1214/13-EJS787
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