Research map / Learning theory and algorithms / Sample complexity
Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a bias-corrected fixed-k k-NN estimator instead of plugging in a consistent k-NN density estimate (k grows with n) | k-NN functional estimators (entropy, divergence) · theoretical analysis, beta-Holder densities on [0,1]^D | MSE convergence rate | Helped |
| Fix k (no k→∞) with bias correction versus plug-in with k≍n^{β/(β+D)} | fixed-k estimators · theory, beta in (0,2] | MSE rate exponent | Helped |
| Replace compact-support boundary assumption with locally lower-bounded density (A4) | fixed-k estimator analysis · theory | applicability of finite-sample bounds | No clear effect |
| Choosing k increasing (e.g., k=n/2) vs fixed k=1 in empirical hypothesis tests | k-NN estimators in hypothesis testing · prior empirical work discussed | test performance | Mixed |
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