We consider the problem of identity testing of Markov chains based on a single trajectory of observations under the distance notion introduced by Daskalakis et al. [2018a] and further analyzed by Cherapanamjeri and Bartlett [2019]. Both works made the restrictive assumption that the Markov chains under consideration are symmetric. In this work we relax the symmetry assumption to the more natural assumption of reversibility, still assuming that both the reference and the unknown Markov chains share the same stationary distribution.
翻译:我们根据Daskalakis等人[2018a]提出并由Cherapanamejeri和Bartlett[2019]进一步分析的距离概念下的单一观测轨迹来考虑Markov链的身份测试问题,这两项工程都设定了所考虑的Markov链是对称的限制性假设,在这项工作中,我们将对称假设放松到更自然的可逆假设,仍然假设参考和未知的Markov链都具有相同的固定分布。