3 citations · 3 across the 10 of their papers we have counts for
13 papers
An edge-bicolored graph approach to the Ising model on random regular graphs
Michael Borinsky, Shiyue Ren, Maximilian Wiesmann
We give an exact solution of the ferromagnetic Ising model on a random regular graph ensemble via analytic combinatorics. Expressing the partition function as the generating functi…
Asymptotic number of edge-colored regular graphs
Michael Borinsky, Chiara Meroni, Maximilian Wiesmann
We prove a formula for the asymptotic number of edge-colored regular graphs with a prescribed set of allowed vertex-incidence structures. The formula depends on specific critical p…
Lee-Yang phenomena in edge-coloured graph counting
Maximilian Wiesmann
We study the accumulation of zeros of a polynomial arising from the enumeration of edge-coloured graphs along certain limit curves. The polynomial is a variant of an edge-chromatic…
The Maximum Likelihood Degree of Toric Models is Monotonic
Carlos Améndola, Janike Oldekop, Maximilian Wiesmann
We settle a conjecture by Coons and Sullivant stating that the maximum likelihood (ML) degree of a facial submodel of a toric model is at most the ML degree of the model itself. We…
Squared Linear Models
Hannah Friedman, Bernd Sturmfels, Maximilian Wiesmann
We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one critical point in e…
The Likelihood Correspondence
Thomas Kahle, Hal Schenck, Bernd Sturmfels +1
An arrangement of hypersurfaces in projective space is strict normal crossing (SNC) if and only if its Euler discriminant is nonzero. We study the critical loci of arbitrary Lauren…
Arrangements and Likelihood
Thomas Kahle, Lukas Kühne, Leonie Mühlherr +2
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This o…
Bivariate exponential integrals and edge-bicolored graphs
Michael Borinsky, Chiara Meroni, Maximilian Wiesmann
We show that specific exponential bivariate integrals serve as generating functions of labeled edge-bicolored graphs. Based on this, we prove an asymptotic formula for the number o…
Euler Stratifications of Hypersurface Families
Simon Telen, Maximilian Wiesmann
We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric…
Pathological Regularization Regimes in Classification Tasks
Maximilian Wiesmann, Paul Larsen
In this paper we demonstrate the possibility of a trend reversal in binary classification tasks between the dataset and a classification score obtained from a trained model. This t…
Geometry of Polynomial Neural Networks
Kaie Kubjas, Jiayi Li, Maximilian Wiesmann
We study the expressivity and learning process for polynomial neural networks (PNNs) with monomial activation functions. The weights of the network parametrize the neuromanifold. I…
Algebraic Geometry of Quantum Graphical Models
Eliana Duarte, Dmitrii Pavlov, Maximilian Wiesmann
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study…
Toric Fiber Products in Geometric Modeling
Eliana Duarte, Benjamin Hollering, Maximilian Wiesmann
An important challenge in Geometric Modeling is to classify polytopes with rational linear precision. Equivalently, in Algebraic Statistics one is interested in classifying scaled…