On Learning Continuous Pairwise Markov Random Fields
On Learning Continuous Pairwise Markov Random Fields
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发表时间：
2020-10
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通讯作者：
Abhin Shah;Devavrat Shah;G. Wornell
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作者：
Abhin Shah;Devavrat Shah;G. Wornell
我们考虑从i.i.d样本中学习具有连续值变量的稀疏成对马尔可夫随机场（MRF）。我们调整了Vuffray等人的算法。（2019）在这种情况下，并提供有限样本分析，揭示样本复杂性随变量数量的变化规律，如离散和高斯设置。我们的方法是适用于一个大类的成对MRF连续变量，也有理想的渐近性质，包括在温和的条件下的一致性和正态性。此外，我们确定Vuffray等人（2019）中采用的优化标准的群体版本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的稳健变化，这可能本身就很有趣。
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.