Research map / Learning theory and algorithms / Sample complexity
Optimal Rates for Nonparametric Density Estimation under Communication Constraints
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a wavelet-based noninteractive estimator with vector quantization and distributed simulation | Besov density estimation under per-sample communication constraints · Besov classes, L_r loss for r ≤ p | minimax expected L_r^r loss rate | Helped |
| Use the adaptive multi-level wavelet estimator without knowing p and q | Besov density estimation under per-sample communication constraints · Besov classes, all stated parameter regimes | minimax expected L_r^r loss rate | Helped |
| Apply the wavelet-based estimator to Sobolev spaces instead of relying on a Fourier representation | Sobolev density estimation under communication constraints · Sobolev spaces | minimax estimation rate | Helped |
| Use a Fourier basis for Sobolev density estimation | Sobolev density estimation under communication constraints · Sobolev spaces | minimax estimation rate | Hurt |
| Use coordinate-wise quantization instead of the sparse vector-quantization alphabet | Wavelet coefficient communication · Besov density estimation | minimax estimation rate | No clear effect |
| Use Hoeffding-based thresholds instead of exploiting sparse, mostly zero wavelet estimates | Adaptive multi-level wavelet estimator · Besov density estimation | minimax estimation rate | Hurt |
| Allow interactive communication protocols | Communication-constrained Besov density estimation · Besov classes | minimax expected L_r^r loss rate | No clear effect |
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