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Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators
Shashank Singh · Barnabas Poczos

Tue Dec 09:00 AM -- 12:30 PM PST @ Area 5+6+7+8 #48 #None

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k → ∞ as the sample size n → ∞) into the functional of interest, the estimators we consider fix k and perform a bias correction. This can be more efficient computationally, and, as we show, statistically, leading to faster convergence rates. Our framework unifies several previous estimators, for most of which ours are the first finite sample guarantees.

Author Information

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

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