论文标题
学习连续成对马尔可夫随机字段
On Learning Continuous Pairwise Markov Random Fields
论文作者
论文摘要
我们考虑学习具有来自I.I.D样本的连续值变量的稀疏成对Markov随机场（MRF）。我们适应Vuffray等人的算法。 （2019年）到此设置，并提供有限样本分析，揭示了样品复杂性比对数缩放的变量数量，如离散和高斯设置所示。我们的方法适用于具有连续变量的大型成对MRF，并且具有理想的渐近特性，包括在轻度条件下的一致性和正态性。此外，我们确定Vuffray等人采用的优化标准的种群版本。 （2019）可以解释为局部最大似然估计（MLE）。作为我们分析的一部分，我们引入了稀疏线性回归A La Lasso的鲁棒变化，这本身可能引起人们的关注。
We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a` la Lasso, which may be of interest in its own right.
