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2013 A recursive procedure for density estimation on the binary hypercube
Maxim Raginsky, Jorge G. Silva, Svetlana Lazebnik, Rebecca Willett
Electron. J. Statist. 7: 820-858 (2013). DOI: 10.1214/13-EJS787


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.


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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.


Published: 2013
First available in Project Euclid: 25 March 2013

zbMATH: 1337.62070
MathSciNet: MR3040561
Digital Object Identifier: 10.1214/13-EJS787

Primary: 62G07
Secondary: 62C20, 62G20

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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