Huiming Zhang, Haoyu Wei, Guang Cheng
arXiv 13 Mar 2023 · Statistics — Machine Learning · 1 citations (OpenAlex)
arXiv:2303.07287 · PDF · DOI · OpenAlex · Extracted main text
In non-asymptotic learning, variance-type parameters of sub-Gaussian distributions are of paramount importance. However, directly estimating these parameters using the empirical moment generating function (MGF) is infeasible. To address this, we suggest using the sub-Gaussian intrinsic moment norm [Buldygin and Kozachenko (2000), Theorem 1.3] achieved by maximizing a sequence of normalized moments. Significantly, the suggested norm can not only reconstruct the exponential moment bounds of MGFs but also provide tighter sub-Gaussian concentration inequalities. In practice, we provide an intuitive method for assessing whether data with a finite sample size is sub-Gaussian, utilizing the sub-Gaussian plot. The intrinsic moment norm can be robustly estimated via a simple plug-in approach. Our theoretical findings are also applicable to reinforcement learning, including the multi-armed bandit scenario.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | B. Hao, Y. A. Yadkori, Z. Wen, and G. Cheng, Bootstrapping upper con… (2019) pp. 12123–12133 | 1.000 | 9 | 4 | 100% |
| 2 | P. Auer, N. Cesa-Bianchi, and P. Fischer, Finite-time analysis of th… (2002) pp. 235–256 | 0.928 | 4 | 3 | 100% |
| 3 | V. V. Buldygin and I. V. Kozachenko, Metric characterization of rand… (2000) | 0.811 | 4 | 2 | 100% |
| 4 | J. Lieber, Estimating concentration parameters for bandit algorithms (2022) | 0.811 | 4 | 2 | 100% |
| 5 | P. J. Rousseeuw and S. Verboven, Robust estimation in very small sam… (2002) pp. 741–758 | 0.737 | 3 | 2 | 100% |
| 6 | M. J. Wainwright, High-dimensional statistics: A non-asymptotic view… (2019) | 0.737 | 3 | 2 | 100% |
| 7 | H. Zhang and S. X. Chen, Concentration inequalities for statistical… (2021) pp. 1–85 | 0.737 | 3 | 2 | 100% |
| 8 | S. Boucheron, G. Lugosi, and P. Massart, Concentration inequalities:… (2013) | 0.644 | 2 | 2 | 100% |
| 9 | S. Arlot, G. Blanchard, E. Roquain, et al., Some nonasymptotic resul… (2010) pp. 51–82 | 0.511 | 2 | 1 | 100% |
| 10 | N. Bettache, C. Butucea, and M. Sorba, Fast nonasymptotic testing an… (2021) p. 104883 | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 43 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | 2412.02251 | 1.000 | 7 | 3 |
| 2 | Zero-Inflated Bandits | 0.000 | 1 | 1 |