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This study introduces a mediation analysis framework when the mediator is a graph. A Gaussian covariance graph model is assumed for graph representation. Causal estimands and assumptions are discussed under this representation. With a…

Methodology · Statistics 2023-07-11 Yixi Xu , Yi Zhao

This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…

Quantum Physics · Physics 2013-05-29 Scott Aaronson

Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine…

Methodology · Statistics 2014-04-21 Anshumali Shrivastava , Ping Li

We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph…

Machine Learning · Computer Science 2019-05-09 Peter Meltzer , Marcelo Daniel Gutierrez Mallea , Peter J. Bentley

We study the perturbative approach to the Wilsonian integration of noncommutative gauge theories in the matrix representation. We begin by motivating the study of noncommutative gauge theories and reviewing the matrix formulation. We then…

High Energy Physics - Theory · Physics 2007-05-23 Eric Nicholson

We consider perturbative quantum field theory in the causal framework. Gauge invariance is, in this framework, an identity involving chronological products of the interaction Lagrangian; it express the fact that the scattering matrix must…

High Energy Physics - Theory · Physics 2017-09-13 Dan-Radu Grigore

We introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two…

Rings and Algebras · Mathematics 2024-02-14 Farkhod Eshmatov , Xabier García-Martínez , Rustam Turdibaev

In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…

Methodology · Statistics 2026-04-14 Michele Peruzzi

We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved…

Econometrics · Economics 2023-02-14 Abhishek K. Umrawal , Joshua C. C. Chan

We study the Matrix theory from a purely canonical viewpoint. In particular, we identify free particle asymptotic states of the model corresponding to the 11D supergraviton multiplet along with the split of the matrix model Hamiltonian into…

High Energy Physics - Theory · Physics 2007-05-23 Jan Plefka , Andrew Waldron

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph $G=(V,…

Statistics Theory · Mathematics 2022-10-04 Bibhas Adhikari , Elizabeth Gross , Marc Härkönen , Elias Tsigaridas

The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…

Methodology · Statistics 2023-07-03 Yueqi Qian , Xianghong Hu , Can Yang

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that…

Geometric Topology · Mathematics 2007-05-23 Jon R Links , David De Wit

We extend the gauge invariant variational approach of Phys. Rev. D52 (1995) 3719, hep-th/9408081, to theories with fermions. As the simplest example we consider the massless Schwinger model in 1+1 dimensions. We show that in this solvable…

High Energy Physics - Theory · Physics 2009-10-31 William E. Brown , Juan P. Garrahan , Ian I. Kogan , Alex Kovner

We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Antony Lewis , Chris Doran , Anthony Lasenby

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

Machine Learning · Statistics 2019-02-20 Steven Atkinson , Nicholas Zabaras

Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…

Methodology · Statistics 2025-08-28 Matthias Herp , Johannes Brachem , Michael Altenbuchinger , Thomas Kneib

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is…

High Energy Physics - Theory · Physics 2019-02-22 I. V. Chebotarev , V. A. Guskov , S. L. Ogarkov , M. Bernard

We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act…

Statistics Theory · Mathematics 2020-11-20 Osama Idais , Rainer Schwabe

We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…

Methodology · Statistics 2023-03-20 Zachary M. Pisano
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