Abstract
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 language | English (US) |
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Pages (from-to) | 2503-2511 |
Number of pages | 9 |
Journal | Proceedings of Machine Learning Research |
Volume | 130 |
State | Published - 2021 |
Event | 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States Duration: Apr 13 2021 → Apr 15 2021 |
ASJC Scopus subject areas
- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability