Related papers: Towards a complete characterization of indicator v…
Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…
We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of…
A vertex colouring of a given graph $G$ can be considered as a random experiment. A discrete random variable $X$, corresponding to this random experiment, can be defined as the colour of a randomly chosen vertex of $G$ and a probability…
Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…
We propose a necessary and sufficient condition for a real-valued function on the real line to be a characteristic function of a probability measures. The statement is given in terms of harmonic functions and completely monotonic functions.
We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…
Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
Characterisations of metrizable topological spaces or metrizable uniform spaces are well known. A natural counterpart to being metrizable for topological spaces can be expressed in terms of probabilistic metrizability for approach spaces.…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…