preprint
Exact formulas for the normalizing constants of Wishart distributions for graphical models
published
Caroline
Uhler
author 49ADD78E-F248-11E8-B48F-1D18A9856A870000-0002-7008-0216
Alex
Lenkoski
author
Donald
Richards
author
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate prior for inverse covariance matrices satisfying graphical constraints. While it is straightforward to posit the unnormalized densities, the normalizing constants of these distributions have been known only for graphs that are chordal, or decomposable. Up until now, it was unknown whether the normalizing constant for a general graph could be represented explicitly, and a considerable body of computational literature emerged that attempted to avoid this apparent intractability. We close this question by providing an explicit representation of the G-Wishart normalizing constant for general graphs.
ArXiv2014
ArXiv
yes
Uhler C, Lenkoski A, Richards D. Exact formulas for the normalizing constants of Wishart distributions for graphical models. <i>ArXiv</i>. 2014.
Uhler, Caroline, et al. “ Exact Formulas for the Normalizing Constants of Wishart Distributions for Graphical Models.” <i>ArXiv</i>, ArXiv, 2014.
Uhler, C., Lenkoski, A., & Richards, D. (2014). Exact formulas for the normalizing constants of Wishart distributions for graphical models. <i>ArXiv</i>. ArXiv.
C. Uhler, A. Lenkoski, and D. Richards, “ Exact formulas for the normalizing constants of Wishart distributions for graphical models,” <i>ArXiv</i>. ArXiv, 2014.
Uhler, Caroline, Alex Lenkoski, and Donald Richards. “ Exact Formulas for the Normalizing Constants of Wishart Distributions for Graphical Models.” <i>ArXiv</i>. ArXiv, 2014.
Uhler C, Lenkoski A, Richards D. 2014. Exact formulas for the normalizing constants of Wishart distributions for graphical models. ArXiv, .
C. Uhler, A. Lenkoski, D. Richards, ArXiv (2014).
20172018-12-11T11:55:14Z2021-01-12T06:54:44Z