293 citations · 845 across the 45 of their papers we have counts for
6 papers · 1 filter
The Information-Geometric Perspective of Compositional Data Analysis
Ionas Erb, Nihat Ay
Information geometry uses the formal tools of differential geometry to describe the space of probability distributions as a Riemannian manifold with an additional dual structure. T…
Congruent families and invariant tensors
Lorenz Schwachhöfer, Nihat Ay, Jürgen Jost +1
Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only -tensor field of a statistical model which is invariant under congruent Markov morp…
Maximal Information Divergence from Statistical Models defined by Neural Networks
Guido Montufar, Johannes Rauh, Nihat Ay
We review recent results about the maximal values of the Kullback-Leibler information divergence from statistical models defined by neural networks, including naive Bayes models, r…
Information geometry and sufficient statistics
Nihat Ay, Jürgen Jost, Hông Vân Lê +1
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In s…
Support Sets in Exponential Families and Oriented Matroid Theory
Johannes Rauh, Thomas Kahle, Nihat Ay
The closure of a discrete exponential family is described by a finite set of equations corresponding to the circuits of an underlying oriented matroid. These equations are similar…
Hierarchical Models, Marginal Polytopes, and Linear Codes
Thomas Kahle, Walter Wenzel, Nihat Ay
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear co…