Research map / Learning theory and algorithms / Sample complexity
The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the fixed-k KL entropy estimator without supplying the Hölder smoothness s | Differential entropy estimation over Hölder balls · H_d^s(L; [0,1]^d), 0<s≤2 | worst-case root mean squared error rate: n^{-s/(s+d)} ln(n+1) + n^{-1/2} | Helped |
| Analyze the fixed-k KL estimator without assuming the density is bounded away from zero | Differential entropy estimation over Hölder balls · H_d^s(L; [0,1]^d), 0<s≤2 | worst-case root mean squared error rate: n^{-s/(s+d)} ln(n+1) + n^{-1/2} | Helped |
| Use the vanilla KL estimator for smoothness levels s>2 | Fixed-k KL entropy estimation · Hölder smoothness s>2 | adaptation to smoothness | Hurt |
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