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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…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical ${\rm AC}^0$. Among others, we derive such a lower bound for all fpt-approximations of the parameterized clique problem and…
The website reductions.network serves as a comprehensive database for exploring problems and reductions between them. It presents several complexity classes in the form of an interconnected graph where problems are represented as vertices,…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…
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…
This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We study the problem of recovering a known cluster structure in a sparse network, also known as the planted partitioning problem, by means of statistical mechanics. We find a sharp transition from un-recoverable to recoverable structure as…
Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…
Hypergraph data are often projected onto a weighted graph by constructing an adjacency matrix whose $(i,j)$ entry counts the number of hyperedges containing both nodes $i$ and $j$. This reduction is computationally convenient, but it can…
The planted random subgraph detection conjecture of Abram et al. (TCC 2023) asserts the pseudorandomness of a pair of graphs $(H, G)$, where $G$ is an Erdos-Renyi random graph on $n$ vertices, and $H$ is a random induced subgraph of $G$ on…
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…
Discovering statistically significant patterns from databases is an important challenging problem. The main obstacle of this problem is in the difficulty of taking into account the selection bias, i.e., the bias arising from the fact that…
We propose the n-clique network as a powerful tool for understanding global structures of combined highly-interconnected subgraphs, and provide theoretical predictions for statistical properties of the n-clique networks embedded in a…
The clique tree algorithm is the standard method for doing inference in Bayesian networks. It works by manipulating clique potentials - distributions over the variables in a clique. While this approach works well for many networks, it is…
Engineered infrastructure systems pose inverse problems in which hidden states, unknown parameters, and subsystem couplings must be inferred from sparse and noisy measurements. These problems are difficult because physical subsystems are…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…