Log In Sign Up

The Geometry of Gaussoids

by   Tobias Boege, et al.

A gaussoid is a combinatorial structure that encodes independence in probability and statistics, just like matroids encode independence in linear algebra. The gaussoid axioms of Lnenicka and Matús are equivalent to compatibility with certain quadratic relations among principal and almost-principal minors of a symmetric matrix. We develop the geometric theory of gaussoids, based on the Lagrangian Grassmannian and its symmetries. We introduce oriented gaussoids and valuated gaussoids, thus connecting to real and tropical geometry. We classify small realizable and non-realizable gaussoids. Positive gaussoids are as nice as positroids: they are all realizable via graphical models.


page 1

page 2

page 3

page 4


Incidence geometry in the projective plane via almost-principal minors of symmetric matrices

We present an encoding of a polynomial system into vanishing and non-van...

Decomposable context-specific models

We introduce a family of discrete context-specific models, which we call...

A non-graphical representation of conditional independence via the neighbourhood lattice

We introduce and study the neighbourhood lattice decomposition of a dist...

Markov equivalence of marginalized local independence graphs

Symmetric independence relations are often studied using graphical repre...

Approximate Implication with d-Separation

The graphical structure of Probabilistic Graphical Models (PGMs) encodes...

Using the structure of d-connecting paths as a qualitative measure of the strength of dependence

Pearls concept OF a d - connecting path IS one OF the foundations OF the...