Cooperative graphical models

We study a rich family of distributions that capture variable interactions significantly more expressive than those representable with low-treewidth or pairwise graphical models, or log-supermodular models. We call these cooperative graphical models. Yet, this family retains structure, which we care...

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Detalhes bibliográficos
Autor principal: Jegelka, Stefanie Sabrina
Outros Autores: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Formato: Artigo
Idioma:English
Publicado em: Morgan Kaufmann Publishers 2021
Acesso em linha:https://hdl.handle.net/1721.1/129327
Descrição
Resumo:We study a rich family of distributions that capture variable interactions significantly more expressive than those representable with low-treewidth or pairwise graphical models, or log-supermodular models. We call these cooperative graphical models. Yet, this family retains structure, which we carefully exploit for efficient inference techniques. Our algorithms combine the polyhedral structure of submodular functions in new ways with variational inference methods to obtain both lower and upper bounds on the partition function. While our fully convex upper bound is minimized as an SDP or via tree-reweighted belief propagation, our lower bound is tightened via belief propagation or mean-field algorithms. The resulting algorithms are easy to implement and, as our experiments show, effectively obtain good bounds and marginals for synthetic and real-world examples.