In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics. The Glauber dynamics is a Markov chain that sequentially updates individual nodes (variables) in a graphical model and it is frequently used to sample from the stationary distribution (to which it converges given sufficient time). Additionally, the Glauber dynamics is a natural dynamical model in a variety of settings. This work deviates from the standard formulation of graphical model learning in the literature, where one assumes access to i.i.d. samples from the distribution. Much of the research on graphical model learning has been directed towards finding algorithms with low computational cost. As the main result of this work, we establish that the problem of reconstructing binary pairwise graphical models is computationally tractable when we observe the Glauber dynamics. Specifically, we show that a binary pairwise graphical model on $p$ nodes with maximum degree $d$ can be learned in time $f(d)p^3\log p$, for a function $f(d)$, using nearly the information-theoretic minimum possible number of samples. There is no known algorithm of comparable efficiency for learning arbitrary binary pairwise models from i.i.d. samples.

考虑从Glauber dynamics生成的数据中学习无向图模型的问题。本文证明了观察到Glauber dynamics时，重建二进制成对图模型是可计算的，并且可以在接近信息理论最小采样数量的情况下使用时间f(d)p^2logp内学习。

从Glauber动力学中学习图模型