Efficient Interpolation of Density Estimators

Paxton Turner, Jingbo Liu, Philippe Rigollet

Research output: Contribution to journalConference articlepeer-review


We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation scheme to give a computationally efficient construction that converts the original estimator to a new estimator that can be queried efficiently and has low space requirements, all without adversely deteriorating the original approximation quality. Our result gives a new statistical perspective on the problem of fast evaluation of kernel density estimators in the presence of underlying smoothness. As a corollary, we give a succinct derivation of a classical result of Kolmogorov-Tikhomirov on the metric entropy of Hölder classes of smooth functions.

Original languageEnglish (US)
Pages (from-to)2503-2511
Number of pages9
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States
Duration: Apr 13 2021Apr 15 2021

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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