Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Computing the Nearest Reversible Markov Chain Computing the Nearest Reversible Markov Chain
Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Computing the Nearest Reversible Markov Chain Computing the Nearest Reversible Markov Chain
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Konrad-zuse-zentrum F ¡ Ur Informationstechnik Berlin 计算最近的可逆马尔可夫链 计算最近的可逆马尔可夫链
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通讯作者：
Marcus Weber
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作者：
Adam Nielsen;Marcus Weber
可逆马尔可夫链是许多应用的基础。然而，通过马尔可夫链的有限采样来计算转移概率会导致截断误差。即使原始的马尔可夫链是可逆的，近似的马尔可夫链也可能是不可逆的，并且会失去重要的性质，比如实值谱。在本文中，我们展示了如何找到最接近给定转移矩阵的可逆马尔可夫链。结果表明，这个矩阵可以通过求解一个凸最小化问题来计算。
Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible , the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.