## On Learning Discrete Graphical Models using Group-Sparse

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@MISC{Jalali_onlearning,

author = {Ali Jalali and Pradeep Ravikumar and Vishvas Vasuki and Sujay Sanghavi},

title = {On Learning Discrete Graphical Models using Group-Sparse},

year = {}

}

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### Abstract

We study the problem of learning the graph structure associated with a general discrete graphical models (each variable can take any of m> 1 values, the clique factors have maximum size c ≥ 2) from samples, under high-dimensional scaling where the number of variables p could be larger than the number of samples n. We provide a quantitative consistency analysis of a procedure based on node-wise multi-class logistic regression with group-sparse regularization. We first consider general m-ary pairwise models – where each factor depends on at most two variables. We show that when

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Citation Context ...for all t ∈ N (r). Accordingly, let ¯ Θ∗ P c represent all non-zero nonpairwise entries. Hierarchical Models. A common assumption imposed on such higher-order MRFs is that they be hierarchical models =-=[16]-=-. Specifically, any MRF of the form (2) is hierarchical if for any clique C, θ∗ C = 0 implies that θ∗ B = 0 for any clique B ⊇ A containing A. This has an importance consequence: the set of pairwise e... |

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Citation Context ...ing approaches. Methods for estimating such graph structure include those based on constraint and hypothesis testing [29], and those that estimate restricted classes of graph structures such as trees =-=[5]-=-, polytrees [11], and hypertrees [30]. Another class of approaches estimate the local neighborhood of each node via exhaustive search for the special case of bounded degree graphs. Abbeel et al.[1] pr... |

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Citation Context ... an ℓ1/ℓ2-regularized 380On Learning Discrete Graphical Models using Group-Sparse Regularization multiclass logistic regression problem, and is thus the multiclass logistic analog of the group Lasso =-=[36]-=-. The solution to the program (6) yields an estimate ̂N (r) of the neighborhood of node r by ̂N (r) = {t ∈ V : t ̸= r; ∥ ˆ θrt∥2 ̸= 0}. We are interested in the event that all the node neighboorhoods ... |

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