一般马尔可夫链的Hoeffding不等式及其在统计学习中的应用。

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2021-08-01
Jianqing Fan, Bai Jiang, Qiang Sun
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引用次数: 0

摘要

本文建立了一般状态空间非可逆马尔可夫链有界函数的Hoeffding引理和不等式。这些结果的清晰度是由方差代理在马尔可夫依赖和独立设置之间的比率的最优性来表征的。对于一般的结果,函数的有界性是成立的必要条件。为了展示新结果的实用性,我们将其应用于具有马尔可夫性质的时间序列数据的MCMC估计,受访者驱动抽样和高维协方差矩阵估计的非渐近分析。除了统计问题外,我们还将其应用于研究计量经济模型中的时间贴现奖励和机器学习领域中出现的带有马尔可夫奖励的多臂强盗问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hoeffding's inequality for general Markov chains with its applications to statistical learning.

This paper establishes Hoeffding's lemma and inequality for bounded functions of general-state-space and not necessarily reversible Markov chains. The sharpness of these results is characterized by the optimality of the ratio between variance proxies in the Markov-dependent and independent settings. The boundedness of functions is shown necessary for such results to hold in general. To showcase the usefulness of the new results, we apply them for non-asymptotic analyses of MCMC estimation, respondent-driven sampling and high-dimensional covariance matrix estimation on time series data with a Markovian nature. In addition to statistical problems, we also apply them to study the time-discounted rewards in econometric models and the multi-armed bandit problem with Markovian rewards arising from the field of machine learning.

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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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