A recursive procedure for density estimation on the binary hypercube

  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},
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… 

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