Höfling Holger, Tibshirani Robert
Department of Statistics, Stanford University, Stanford, CA 94305, USA.
J Mach Learn Res. 2009 Apr 1;10:883-906.
We consider the problems of estimating the parameters as well as the structure of binary-valued Markov networks. For maximizing the penalized log-likelihood, we implement an approximate procedure based on the pseudo-likelihood of Besag (1975) and generalize it to a fast exact algorithm. The exact algorithm starts with the pseudo-likelihood solution and then adjusts the pseudo-likelihood criterion so that each additional iterations moves it closer to the exact solution. Our results show that this procedure is faster than the competing exact method proposed by Lee, Ganapathi, and Koller (2006a). However, we also find that the approximate pseudo-likelihood as well as the approaches of Wainwright et al. (2006), when implemented using the coordinate descent procedure of Friedman, Hastie, and Tibshirani (2008b), are much faster than the exact methods, and only slightly less accurate.
我们考虑估计二值马尔可夫网络的参数以及结构的问题。为了最大化惩罚对数似然，我们基于Besag（1975）的伪似然实现了一种近似方法，并将其推广为一种快速精确算法。精确算法从伪似然解开始，然后调整伪似然准则，使得每次额外的迭代都使其更接近精确解。我们的结果表明，该过程比Lee、Ganapathi和Koller（2006a）提出的竞争精确方法更快。然而，我们也发现，当使用Friedman、Hastie和Tibshirani（2008b）的坐标下降过程实现时，近似伪似然以及Wainwright等人（2006）的方法比精确方法快得多，并且准确性只是略低。
