Abstract
We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of Gaussian graphical models and structure learning of discrete models. Our approach is a natural generalization of these two lines of work to the mixed case. The penalization scheme involves a novel symmetric use of the group-lasso norm and follows naturally from a particular parameterization of the model. Supplementary materials for this article are available online.
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Cheng, Levina, and Zhu (Citation2013), http://arxiv.org/abs/1304.2810, appeared on arXiv 11 months after our original article was put on arXiv, http://arxiv.org/abs/1205.5012.
If ρsj(yj) = constant, then xs and yj are also conditionally independent. However, the unpenalized term α will absorb the constant, so the estimated ρsj(yj) will never be constant for λ > 0.
Under the independence model pF is fully factorized p(x, y) = ∏ps = 1p(xs)∏qr = 1p(yr).