English(EN) Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds

新方法估算用于人工智能应用的马尔可夫链谱隙

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-15 04:00

研究人员开发了一种新方法，仅用一条观测轨迹即可估算连续马尔可夫链的伪谱隙。该估计器在具有 Lipschitz 密度转移的链上接近 minimax 最优。这项新技术与 Bernstein 不等式结合，可以推导出马尔可夫链的经验集中不等式，这在主动学习和泛化界等领域有广泛应用。 AI

影响能够改进利用马尔可夫链的人工智能系统的泛化界和主动学习策略。

排序理由学术论文，详细介绍了一种用于连续马尔可夫链的新估算方法。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.LG TIER_1 English(EN) · Vahe Karagulyan, Miko{\l}aj Kasprzak, Pierre Alquier · 2026-10-15 04:00

连续马尔可夫链伪谱隙的Minimax估计及其在经验集中界上的应用

arXiv:2610.20007v1 Announce Type: cross Abstract: We study the minimax estimation of the pseudo-spectral gap $\gamma_{ps}$ of a Markov chain from the observation of a single trajectory. Extending earlier works on finite-state space chains by Wolfer and Kontorovich (2024), we prov…