Related papers: Detection-Recovery Gap for Planted Dense Cycles

We note the significance of hypergraphic planted clique (HPC) detection in the investigation of computational hardness for a range of tensor problems. We ask if more evidence for the computational hardness of HPC detection can be developed.…

We consider the task of certifying that a random $d$-dimensional subspace $X$ in $\mathbb{R}^n$ is well-spread - every vector $x \in X$ satisfies $c\sqrt{n} \|x\|_2 \leq \|x\|_1 \leq \sqrt{n}\|x\|_2$. In a seminal work, Barak et. al. showed…

With the rise of the Internet of Things, strategies for effectively processing big data are essential for discovering meaningul insights. The time series datasets produced by groups of interconnected devices contain valuable underlying…

Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the…

In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…

The Contact Process has been studied on complex networks exhibiting different kinds of quenched disorder. Numerical evidence is found for Griffiths phases and other rare region effects, in Erd\H os R\'enyi networks, leading rather…

We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are…

In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…

This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…

We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and,…

We consider restricted Boltzmann machines with a binary visible layer and a Gaussian hidden layer trained by an unlabelled dataset composed of noisy realizations of a single ground pattern. We develop a statistical mechanics framework to…

Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…

We study the problem of detecting a planted star in the Erd{\H{o}}s--R{\'e}nyi random graph $G(n,m)$, formulated as a hypothesis test. We determine the scaling window for critical detection in $m$ in terms of the star size, and characterize…

In a distinguishing problem, the input is a sample drawn from one of two distributions and the algorithm is tasked with identifying the source distribution. The performance of a distinguishing algorithm is measured by its advantage, i.e.,…

Square Wave Perceptrons (SWPs) form a class of neural network models with oscillating activation function that exhibit intriguing ``hardness'' properties in the high-dimensional limit at a fixed constraint density $\alpha = O(1)$. In this…

Causal discovery aims to infer causal relationships among variables from observational data, typically represented by a directed acyclic graph (DAG). Most existing methods assume independent and identically distributed observations, an…

Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…

The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a $O(\sqrt{\log n})$-approximation algorithm due to…

Revealing underlying relations between nodes in a network is one of the most important tasks in network analysis. Using tools and techniques from a variety of disciplines, many community recovery methods have been developed for different…

This paper deals with gene networks whose dynamics is assumed to be generated by a continuous-time, linear, time invariant, finite dimensional system (LTI) at steady state. In particular, we deal with the problem of network reconstruction…