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Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for…

Community detection is the problem of identifying dense communities in networks. Motivated by transitive behavior in social networks ("thy friend is my friend"), an emerging line of work considers spatially-embedded networks, which…

We consider the problem of clustering (or reconstruction) in the stochastic block model, in the regime where the average degree is constant. For the case of two clusters with equal sizes, recent results by Mossel, Neeman and Sly, and by…

Community detection is an important content in complex network analysis. The existing community detection methods in attributed networks mostly focus on only using network structure, while the methods of integrating node attributes is…

In recent years there has been an increased interest in statistical analysis of data with multiple types of relations among a set of entities. Such multi-relational data can be represented as multi-layer graphs where the set of vertices…

We consider a dynamic version of the stochastic block model, in which the nodes are partitioned into latent classes and the connection between two nodes is drawn from a Bernoulli distribution depending on the classes of these two nodes. The…

We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the…

We consider a spiked random matrix model obtained by applying a function entrywise to a signal-plus-noise symmetric data matrix. We prove that the largest eigenvalue of this model, which we call a transformed spiked Wigner matrix, exhibits…

The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network…

We investigate the widely encountered problem of detecting communities in multiplex networks, such as social networks, with an unknown arbitrary heterogeneous structure. To improve detectability, we propose a generative model that leverages…

In this paper, the key objects of interest are the sequential covariance matrices $\mathbf{S}_{n,t}$ and their largest eigenvalues. Here, the matrix $\mathbf{S}_{n,t}$ is computed as the empirical covariance associated with observations…

In this work, we investigate quantum phase transition (QPT) in a generic family of spin chains using the ground-state energy, the energy gap, and the geometric measure of entanglement (GE). In many of prior works, GE per site was used.…

The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…

We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually…

Dynamic networks, especially those representing social networks, undergo constant evolution of their community structure over time. Nodes can migrate between different communities, communities can split into multiple new communities,…

In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. To this end, we develop spectral estimators for both unobserved blocks and the effect of…

The discovery of the "hidden population", whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

The Stochastic Block Model (Holland et al., 1983) is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the…

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden…