Related papers: ERGMs are Hard
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
We consider a family of quantum spin systems which includes as special cases the ferromagnetic XY model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any…
Traditional network analysis focuses on binary edges, while real-world relationships are more nuanced, encompassing cooperation, neutrality, and conflict. The rise of negative edges in social media discussions spurred interest in analyzing…
Random geometric graphs defined on Euclidean subspaces, also called Gilbert graphs, are widely used to model spatially embedded networks across various domains. In such graphs, nodes are located at random in Euclidean space, and any two…
We will amalgamate the Rash model (for rectangular binary tables) and the newly introduced $\alpha$-$\beta$ models (for random undirected graphs) in the framework of a semiparametric probabilistic graph model. Our purpose is to give a…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…
The paper demonstrates the use of LASSO-based estimation in network models. Taking the Exponential Random Graph Model (ERGM) as a flexible and widely used model for network data analysis, the paper focuses on the question of how to specify…
While many classical notions of learnability (e.g., PAC learnability) are distribution-free, utilizing the specific structures of an input distribution may improve learning performance. For example, a product distribution on a…
The NP-hard EFFECTORS problem on directed graphs is motivated by applications in network mining, particularly concerning the analysis of probabilistic information-propagation processes in social networks. In the corresponding model the arcs…
We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves the metric…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
We extend the classical edge-triangle Exponential Random Graph Model (ERGM) to an inhomogeneous setting in which vertices carry types determined by an underlying partition. This leads to a block-structured ERGM where interaction parameters…
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning…
As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection, probabilistic generative models (PGMs) have become the…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model builds on the random geometric graphs…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…