Related papers: Information-Theoretic Thresholds for Bipartite Lat…
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
This manuscript studies the unsupervised change point detection problem in time series of graphs using a decoder-only latent space model. The proposed framework consists of learnable prior distributions for low-dimensional graph…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…
We consider the problem of community detection from the joint observation of a high-dimensional covariate matrix and $L$ sparse networks, all encoding noisy, partial information about the latent community labels of $n$ subjects. In the…
We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erd\H{o}s-Renyi…
We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges…
The correlation matrix of massive biomedical data (e.g. gene expression or neuroimaging data) often exhibits a complex and organized, yet latent graph topological structure. We propose a two step procedure that first detects the latent…
This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the…
Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…
Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…
The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
Informational parsimony provides a useful inductive bias for learning representations that achieve better generalization by being robust to noise and spurious correlations. We propose \textit{information gating} as a way to learn…
Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and…
Scientific fields such as insider-threat detection and highway-safety planning often lack sufficient amounts of time-series data to estimate statistical models for the purpose of scientific discovery. Moreover, the available limited data…