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Efficient Nonparametric Smoothness Estimation
Shashank Singh · Simon Du · Barnabas Poczos

Mon Dec 05 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #9

Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They also include, as special cases, L^2 quantities which are used in many applications. We propose and analyze a family of estimators for Sobolev quantities of unknown probability density functions. We bound the finite-sample bias and variance of our estimators, finding that they are generally minimax rate-optimal. Our estimators are significantly more computationally tractable than previous estimators, and exhibit a statistical/computational trade-off allowing them to adapt to computational constraints. We also draw theoretical connections to recent work on fast two-sample testing and empirically validate our estimators on synthetic data.

Author Information

Shashank Singh (Carnegie Mellon University)
Simon Du (Carnegie Mellon University)
Barnabas Poczos (Carnegie Mellon University)

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