• DOI:10.1214/13-EJS787
• Corpus ID: 18647962

A recursive procedure for density estimation on the binary hypercube

@article{Raginsky2011ARP,
  title={A recursive procedure for density estimation on the binary hypercube},
  author={Maxim Raginsky and Jorge G. Silva and Svetlana Lazebnik and Rebecca M. Willett},
  journal={arXiv: Statistics Theory},
  year={2011}
}

• M. Raginsky, Jorge G. Silva, +1 author R. Willett
• Published 7 December 2011
• Mathematics, Computer Science
• arXiv: Statistics Theory

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.