On Learning Continuous Pairwise Markov Random Fields
This work addresses the challenge of modeling continuous variables in graphical models for researchers in machine learning and statistics, though it is incremental as it adapts a prior method.
The authors tackled the problem of learning sparse pairwise Markov Random Fields with continuous-valued variables from independent samples, adapting an existing algorithm to this setting and achieving sample complexity that scales logarithmically with the number of variables, similar to discrete and Gaussian cases.
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.