Related papers: Stable Independence in Perfect Maps
A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among…
Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with…
Divisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph $G$ can be defined with help of a chip firing game on $G$. The stable divisorial…
The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential…
A graph is $\mathcal{R}_d$-independent (resp. $\mathcal{R}_d$-connected) if its $d$-dimensional generic rigidity matroid is free (resp. connected). A result of Maxwell from 1867 implies that every $\mathcal{R}_d$-independent graph satisfies…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
Autonomous agents rely on sensor data to construct representations of their environments, essential for predicting future events and planning their actions. However, sensor measurements suffer from limited range, occlusions, and sensor…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…
This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the \emph{robust} case, in which the…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
We consider the problem of ensuring stability in a DC microgrid by means of decentralized conditions. Such conditions are derived which are formulated as input-output properties of locally defined subsystems. These follow from various…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
We take a general approach to uncertainty on product spaces, and give sufficient conditions for the independence structures of uncertainty measures to satisfy graphoid properties. Since these conditions are arguably more intuitive than some…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
Answering questions of Y. Rabinovich, we prove "stability" versions of upper bounds on maximal independent set counts in graphs under various restrictions. Roughly these say that being close to the maximum implies existence of a large…
The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…