Related papers: Information-Theoretic Thresholds for Planted Dense…
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
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…
We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we…
We study event-triggered control for stabilization of unstable linear plants over rate-limited communication channels subject to unknown, bounded delay. On one hand, the timing of event triggering carries implicit information about the…
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly…
In analyzing the point-to-point wireless channel, insights about two qualitatively different operating regimes--bandwidth- and power-limited--have proven indispensable in the design of good communication schemes. In this paper, we propose a…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
We derive mean-field equations that describe the dynamics of a general model of rumor spreading on complex networks, and use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model…
We give a simple, greedy $O(n^{\omega+0.5})=O(n^{2.872})$-time algorithm to list-decode planted cliques in a semirandom model introduced in [CSV17] (following [FK01]) that succeeds whenever the size of the planted clique is $k\geq…
We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…
We determine the sharp threshold for the containment of all $n$-vertex trees of bounded degree in random geometric graphs with $n$ vertices. This provides a geometric counterpart of Montgomery's threshold result for binomial random graphs,…
In numerous graph signal processing applications, data is often missing for a variety of reasons, and predicting the missing data is essential. In this paper, we consider data on graphs modeled as bandlimited graph signals. Predicting or…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
Safely deploying machine learning models to the real world is often a challenging process. Models trained with data obtained from a specific geographic location tend to fail when queried with data obtained elsewhere, agents trained in a…
Consider a static wireless network that has two tiers with different priorities: a primary tier vs. a secondary tier. The primary tier consists of randomly distributed legacy nodes of density $n$, which have an absolute priority to access…
An information-theoretic framework is introduced to analyze last-layer embedding, focusing on learned representations for regression tasks. We define representation-rate and derive limits on the reliability with which input-output…
Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures…