Research map / Learning theory and algorithms / Sample complexity
Uniform Convergence Rate of the Kernel Density Estimator Adaptive to Intrinsic Volume Dimension
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use volume dimension to characterize small-ball probability decay instead of relying on ambient or support dimension | KDE uniform convergence over bandwidths h >= l_n · Arbitrary probability distributions on R^d | supremum-norm deviation rate | Helped |
| Allow weaker kernel regularity and integrability conditions | KDE uniform convergence · Arbitrary probability distributions on R^d | applicability of uniform convergence bounds | Helped |
| Extend the volume-dimension analysis to kernel derivatives | Higher-order derivatives of the KDE · Uniform convergence over bandwidths h >= l_n | supremum-norm deviation bound | Helped |
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