Total positivity in exponential families with application to binary variables

We study exponential families of distributions that are multivariate totally positive order 2 (MTP2), show these convex and derive conditions for existence the MLE. Quadratic familes MTP2 contain attractive Gaussian graphical models ferromagnetic Ising as special examples. defined by intersecting space canonical parameters with a polyhedral cone whose faces correspond to conditional independence relations. Hence serves an implicit regularizer quadratic leads sparsity in estimated model. prove maximum likelihood estimator (MLE) binary family exists if only both sign patterns (1,−1) (−1,1) represented sample every pair variables; particular, this implies MLE may exist n=d observations, stark contrast unrestricted where 2d observations required. Finally, we provide novel globally convergent algorithm computing similar iterative proportional scaling apply it analysis data from two psychological disorders.