Related papers: Permutation invariant Gaussian 2-matrix models
In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph $G$. Working with the $W_{P_G}$ family defined by Letac and Massam [Ann. Statist. 35…
This paper studies separating invariants: mappings on $D$ dimensional domains which are invariant to an appropriate group action, and which separate orbits. The motivation for this study comes from the usefulness of separating invariants in…
We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A…
Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only…
We consider multivariate centered Gaussian models for the random variable $Z=(Z_1,\ldots, Z_p)$, invariant under the action of a subgroup of the group of permutations on $\{1,\ldots, p\}$. Using the representation theory of the symmetric…
This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…
Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
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…
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…
We consider novel phylogenetic models with rate matrices that arise via the embedding of a progenitor model on a small number of character states, into a target model on a larger number of character states. Adapting representation-theoretic…
Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional…
In [Trace identities and $\bf {Z}/2\bf {Z}$-graded invariants, {\it Trans. Amer. Math. Soc. \bf309} (1988), 581--589] we generalized the first and second fundamental theorems of invariant theory from the general linear group to the general…
This article is intended to provide a pedagogical introduction to the supersymmetry method for performing ensemble-averaging in Gaussian random-matrix theory. The method is illustrated by a detailed calculation of the simplest non-trivial…
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…
Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that…
Presented approach in polynomial time calculates large number of invariants for each vertex, which won't change with graph isomorphism and should fully determine the graph. For example numbers of closed paths of length k for given starting…