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**Estimation of sparse binary pairwise Markov networks using pseudo-likelihoods.**
*(English)*
Zbl 1245.62121

Summary: 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 approximation procedure based on the pseudo-likelihood of J. Besag [Proc. 21 Nat. Conf. Artificial Intell. (AAAI-06), 24, 179–195 (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 iteration moves it closer to the exact solution. Our results show that this procedure is faster than the competing exact method proposed byS.-I. Lee et al. [Advances Neural Inform. Process. Syst. (2006)]. However, we also find that the approximate pseudo-likelihood as well as the approaches of M.J. Wainwright et al. [ibid., Vancouver (2006)], when implemented using the coordinate descent procedure of J. Friedman et al. [Tech. Rep., Stanford Univ. (2008)] are much faster than the exact methods, and only slightly less accurate.

### MSC:

62M99 | Inference from stochastic processes |

60J99 | Markov processes |

68T99 | Artificial intelligence |

05C90 | Applications of graph theory |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

62J12 | Generalized linear models (logistic models) |