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A short note on learning discrete distributions

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arxiv 2002.11457 v3 pith:37DDY6NA submitted 2020-02-25 math.ST math.PRstat.TH

classification math.STmath.PRstat.TH
keywords discretelearningnoteprobabilityshortcomplexitydeltadistances
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abstract

The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error probability $\delta$.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Learning Distributions from Multiple Data Providers

    cs.DS 2026-07 accept novelty 7.0 of 10

    PAC learning from restricted conditional samples is possible iff the co-occurrence graph is complete, with optimal sample complexity ranging continuously from ~n/ε² to n²/ε² by query-family structure.

  2. Gradient-free stochastic optimization of derivatives under strong convexity

    math.ST 2026-07 accept novelty 7.0 of 10

    The minimax optimal rate for minimizing the k-th derivative of a Hölder function from noisy zero-order queries is N^{-(β-1)/(β+k)}, achieved by a kernel-based projected stochastic gradient algorithm.

  3. SPAM Tolerance for Pauli Error Estimation

    quant-ph 2025-09 conditional novelty 6.0 of 10

    An entanglement-free algorithm estimates Pauli error rates with exp(O(n^{1/3})) channel uses, tolerating strong state-preparation and measurement noise.

  4. Eliciting Fine-Tuned Transformer Capabilities via Inference-Time Techniques

    cs.LG 2025-06 reject novelty 2.0 of 10

    The paper claims that in-context learning with finite example sets can approximate supervised fine-tuning in transformers, but the proof assumes the very approximation it sets out to establish.

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