Related papers: Bratteli--Vershik models and graph covering models
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models…
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…
We study some sorts of dimensionally-deconstructed models for supersymmetric (Euclidean) quantum mechanics, or zero-dimensional field theory. In these models, we assign bosonic and fermionic variables to vertices and edges of a graph. We…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…
Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept…
We give a formula for generalized Eulerian numbers, prove monotonicity of sequences of certain ratios of the Eulerian numbers, and apply these results to obtain a new proof that the natural symmetric measure for the Bratteli-Vershik…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class,…
The aim of this paper is to study measure-theoretical rigidity and partial rigidity for classes of Cantor dynamical systems including Toeplitz systems and enumeration systems. We use Bratteli diagrams to control invariant measures that are…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
Real ecosystems are characterized by sparse and asymmetric interactions, posing a major challenge to theoretical analysis. We introduce a new method to study the generalized Lotka-Volterra model with stochastic dynamics on sparse graphs. By…
Transductive tasks on graphs differ fundamentally from typical supervised machine learning tasks, as the independent and identically distributed (i.i.d.) assumption does not hold among samples. Instead, all train/test/validation samples are…
We define non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and establish a quantum version of the Sandwich Theorem of Gr\"{o}tschel, Lov\'{a}sz and…
A total weighting of a graph $G$ is a mapping $f$ which assigns to each element $z \in V(G) \cup E(G)$ a real number $f(z)$ as its weight. The vertex sum of $v$ with respect to $f$ is $\phi_f(v)=\sum_{e \in E(v)}f(e)+f(v)$. A total…
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…
Consider a triple of "Bartnik data" $(\Sigma, \gamma,H)$, where $\Sigma$ is a topological 2-sphere with Riemannian metric $\gamma$ and positive function $H$. We view Bartnik data as a boundary condition for the problem of finding a compact…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…