Related papers: Planar Graphical Models which are Easy
We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes. Many real-world models exhibit unfair discriminatory behavior due to biases in data. Such discrimination is known to be…
We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in…
Several statistical models used in genome-wide prediction assume independence of marker allele substitution effects, but it is known that these effects might be correlated. In statistics, graphical models have been identified as a useful…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are…
In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional fermion algebra, and we investigate the properties of this category. The categorical…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
We investigate a class of random graph ensembles based on the Feynman graphs of multidimensional integrals, representing statistical-mechanical partition functions. We show that the resulting ensembles of random graphs strongly resemble…
In this article we will present a graph partitioning algorithm which partitions a graph into two different types of components: the well-known `strongly connected components' as well as another type of components we call `connected acyclic…
In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages of this technology it has been known that nature points to correlated effects. In statistics, graphical models…
The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…
This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity $\mathcal{O}(n^3)$ in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical…
We introduce a graphical calculus, consisting of a set of fermionic tensors with tensor-network equations, which can be used to perform various computations in fermionic many-body physics purely diagrammatically. The indices of our tensors…
We prove a complexity dichotomy theorem for counting planar graph homomorphisms of domain size 3. Given any 3 by 3 real valued symmetric matrix $H$ defining a graph homomorphism from all planar graphs $G \mapsto Z_H(G)$, we completely…
In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily…
A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using…
In multivariate statistics, the question of finding direct interactions can be formulated as a problem of network inference - or network reconstruction - for which the Gaussian graphical model (GGM) provides a canonical framework.…