Research map / Learning theory and algorithms / Sample complexity
Refinement Methods for Distributed Distribution Estimation under $\ell^p$-Losses
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Derives minimax optimal rates for communication-constrained distributed estimation of discrete distributions under ℓ^p losses, identifying an elbow effect at p=2.
Problem
Communication-constrained estimation of discrete distributions under ℓ^p losses when each distributed terminal holds multiple i.i.d. samples and can send only a limited number of bits.
Approach
Obtains minimax optimal rates for most parameter regimes under ℓ^p losses, revealing an elbow effect of the optimal rates at p=2; the abstract is truncated before describing the achieving scheme.
Key results
- Obtains minimax optimal rates for communication-constrained discrete distribution estimation under ℓ^p losses for most parameter regimes.
- An elbow effect of the optimal rates at p=2 is clearly identified.
Limitations
- Full text unavailable; only the abstract was provided, so the achieving scheme and details are unknown.
- Optimal rates are obtained only for most, not all, parameter regimes.
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