293 citations · 737 across the 36 of their papers we have counts for
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The Markov basis of
Johannes Rauh, Seth Sullivant
This document explains how to obtain a Markov basis of the graphical model of the complete bipartite graph with binary nodes. The computations illustrate the theory devel…
Expressive Power and Approximation Errors of Restricted Boltzmann Machines
Guido Montufar, Johannes Rauh, Nihat Ay
We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which a…
Reconsidering unique information: Towards a multivariate information decomposition
Johannes Rauh, Nils Bertschinger, Eckehard Olbrich +1
The information that two random variables , contain about a third random variable can have aspects of shared information (contained in both and ), of complementar…
Lifting Markov Bases and Higher Codimension Toric Fiber Products
Johannes Rauh, Seth Sullivant
We study how to lift Markov bases and Gröbner bases along linear maps of lattices. We give a lifting algorithm that allows to compute such bases iteratively provided a certain asso…
On the Fisher Metric of Conditional Probability Polytopes
Guido Montufar, Johannes Rauh, Nihat Ay
We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these p…
The Blackwell relation defines no lattice
Nils Bertschinger, Johannes Rauh
Blackwell's theorem shows the equivalence of two preorders on the set of information channels. Here, we restate, and slightly generalize, his result in terms of random variables. F…