Related papers: Topological Conditional Separation
We introduce soft bitopological spaces from the standpoint of soft elements. A soft bitopological space is a soft set equipped with two soft topologies. Following the classical construction of Goldar--Ray, each soft topology on $F$ induces…
The graphical structure of Probabilistic Graphical Models (PGMs) encodes the conditional independence (CI) relations that hold in the modeled distribution. Graph algorithms, such as d-separation, use this structure to infer additional…
We show that the set of $d$-variate symmetric stable tail dependence functions, uniquely associated with exchangeable $d$-dimensional extreme-value copulas, is a simplex and determine its extremal boundary. The subset of elements which…
We give a sufficient condition on totally disconnected topological graphs such that their associated topological graph algebras are purely infinite.
We develop an asymptotic theory for extremes in decomposable graphical models by presenting results applicable to a range of extremal dependence types. Specifically, we investigate the weak limit of the distribution of suitably normalised…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
Conditional Independence (CI) graphs are a type of probabilistic graphical models that are primarily used to gain insights about feature relationships. Each edge represents the partial correlation between the connected features which gives…
For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a…
We introduce binomial edge ideals attached to a simple graph $G$ and study their algebraic properties. We characterize those graphs for which the quadratic generators form a Gr\"obner basis in a lexicographic order induced by a vertex…
We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly…
In this article we propose an extension to the typed natural deduction calculus TNDPQ to model verification of individual fairness and intersectionality in probabilistic classifiers. Their interpretation is obtained by formulating specific…
We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the…
We establish topological necessary and sufficient conditions under which a pair of statistical hypotheses can be consistently distinguished when i.i.d. observations are recorded only to finite precision. To accommodate finite-precision…
We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The former quantifies the discrepancy between multiparameter and…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence that is weaker than exchangeability, but is equivalent to exchangeability for stationary sequences. In this article we…