Total positivity in exponential families with application to binary variables

On the geometry of discrete exponential families with application to exponential random graph models

There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum likelihood estimates. The issues associated with these difficulties relate to the broader structure of discrete exponential families. This paper re-examines the i...

Satisfiability with Exponential Families

Fix a set S ⊆ {0, 1}∗ of exponential size, e.g. |S ∩ {0, 1}n| ∈ Ω(αn), α > 1. The S-SAT problem asks whether a propositional formula F over variables v1, . . . , vn has a satisfying assignment (v1, . . . , vn) ∈ {0, 1}n ∩S. Our interest is in determining the complexity of S-SAT. We prove that S-SAT is NP-complete for all context-free sets S. Furthermore, we show that if S-SAT is in P for some e...

To “ Estimation in Exponential Families on Permutations ”

1. Proofs of main results. This section carries out the proof of all results of the main paper. Subsection 1.1 gives a brief description of the notion of permutation limits, mostly adapted from [8]. Subsection 1.2 states the large deviation principle for permutations in Theorem 1.1, and uses it to prove the results of this paper. Finally, subsection 1.3 gives a proof of Theorem 1.1 using permut...

Exponential families

The Exponential Nature and Positivity

In the present article, a basis of the coordinate algebra of the multi-parameter quantized matrix is constructed by using an elementary method due to Lusztig. The construction depends heavily on an antiautomorphism, the bar action. The exponential nature of the bar action is derived which provides an inductive way to compute the basis elements. By embedding the basis into the dual basis of Lusz...