Hoeffding's inequality for general Markov chains with its applications to statistical learning.
Hoeffding's inequality for general Markov chains with its applications to statistical learning.
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发表时间：
2021-08
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通讯作者：
Sun Q
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作者：
Fan J;Jiang B;Sun Q
本文建立了一般状态空间和不一定可逆马氏链的有界函数的Hoeffding引理和不等式。这些结果的锐度的特点是在马尔可夫依赖和独立设置的方差代理之间的比率的最优性。函数的有界性是必要的，这样的结果一般举行。为了展示新结果的有用性，我们将其应用于MCMC估计，响应驱动采样和高维协方差矩阵估计的马尔可夫性质的时间序列数据的非渐近分析。除了统计问题，我们还将其应用于研究计量经济模型中的时间折扣奖励和机器学习领域中产生的马尔可夫奖励的多臂强盗问题。
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.