arXiv:2601.07074stat.MLcs.LG2026-01被引 7
提出两种鲁棒均值估计方法，抗量化和对抗性干扰。
Robust Mean Estimation under Quantization
- 设计双场景鲁棒估计器，适配单比特与部分无量化数据
- 在两种设定下均达到最优（对数因子内）
- 适合高噪声、低精度数据环境下的统计推断
我们研究在量化和对抗性污染下的均值估计问题。构建了两种多维鲁棒估计器，在两种不同设定下性能接近最优，仅差对数因子。第一种是单比特设定，每个比特仅依赖单一样本；第二种是部分量化设定，估计器可使用少量未量化数据。
原文摘要 · Abstract (English)
We consider the problem of mean estimation under quantization and adversarial corruption. We construct multivariate robust estimators that are optimal up to logarithmic factors in two different settings. The first is a one-bit setting, where each bit depends only on a single sample, and the second is a partial quantization setting, in which the estimator may use a small fraction of unquantized data.
均值估计量化鲁棒性统计推断
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