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We consider the problem of detecting a planted clique of size $k$ in a random graph on $n$ vertices. When the size of the clique exceeds $\Theta(\sqrt{n})$, polynomial-time algorithms for detection proliferate. We study faster -- namely,…

Data Structures and Algorithms · Computer Science 2024-02-09 Jay Mardia , Kabir Aladin Verchand , Alexander S. Wein

Spectral algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…

Data Structures and Algorithms · Computer Science 2022-10-13 Souvik Dhara , Julia Gaudio , Elchanan Mossel , Colin Sandon

Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile.…

Statistics Theory · Mathematics 2025-10-10 Debsurya De , Dmitriy Kunisky

The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…

Data Structures and Algorithms · Computer Science 2025-08-12 Kun He

In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…

Disordered Systems and Neural Networks · Physics 2022-12-07 David Gamarnik , Cristopher Moore , Lenka Zdeborová

Broadcasting on trees is a fundamental model from statistical physics that plays an important role in information theory, noisy computation and phylogenetic reconstruction within computational biology and linguistics. While this model…

Probability · Mathematics 2025-11-18 Han Huang , Elchanan Mossel

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…

Statistics Theory · Mathematics 2011-11-01 Antoine Channarond , Jean-Jacques Daudin , Stéphane Robin

We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the…

Machine Learning · Statistics 2015-12-31 Zhaoran Wang , Quanquan Gu , Han Liu

We study the community detection problem in the non-uniform hypergraph stochastic block model (HSBM), where hyperedges of varying sizes coexist. This setting captures higher-order and multi-view interactions and raises a fundamental…

Machine Learning · Statistics 2026-04-24 Manuel Fernandez , Ludovic Stephan , Yizhe Zhu

We present an efficient algorithm to solve semirandom planted instances of any Boolean constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst-case and average-case input models, where the input is generated by…

Computational Complexity · Computer Science 2023-10-02 Venkatesan Guruswami , Jun-Ting Hsieh , Pravesh K. Kothari , Peter Manohar

The analysis of Belief Propagation and other algorithms for the {\em reconstruction problem} plays a key role in the analysis of community detection in inference on graphs, phylogenetic reconstruction in bioinformatics, and the cavity…

Information Theory · Computer Science 2019-05-27 Vishesh Jain , Frederic Koehler , Jingbo Liu , Elchanan Mossel

We consider the spectral properties of balanced stochastic block models of which the average degree grows slower than the number of nodes (sparse regime) or proportional to it (dense regime). For both regimes, we prove a phase transition of…

Probability · Mathematics 2023-09-18 Yoochan Han , Ji Oon Lee , Wooseok Yang

There is a growing body of work on proving hardness results for average-case estimation problems by bounding the low-degree advantage (LDA) - a quantitative estimate of the closeness of low-degree moments - between a null distribution and a…

Computational Complexity · Computer Science 2025-05-26 Rares-Darius Buhai , Jun-Ting Hsieh , Aayush Jain , Pravesh K. Kothari

The significant progress in constructing graph spanners that are sparse (small number of edges) or light (low total weight) has skipped spanners that are everywhere-sparse (small maximum degree). This disparity is in line with other network…

Data Structures and Algorithms · Computer Science 2012-05-02 Eden Chlamtac , Michael Dinitz , Robert Krauthgamer

We introduce a novel bottom-up approach for the extraction of chart data. Our model utilizes images of charts as inputs and learns to detect keypoints (KP), which are used to reconstruct the components within the plot area. Our novelty lies…

Computer Vision and Pattern Recognition · Computer Science 2023-08-07 Saleem Ahmed , Pengyu Yan , David Doermann , Srirangaraj Setlur , Venu Govindaraju

We study the computational limits of the following general hypothesis testing problem. Let H=H_n be an \emph{arbitrary} undirected graph on n vertices. We study the detection task between a ``null'' Erd\H{o}s-R\'{e}nyi random graph G(n,p)…

Statistics Theory · Mathematics 2024-03-27 Xifan Yu , Ilias Zadik , Peiyuan Zhang

Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the…

Statistics Theory · Mathematics 2024-05-27 Anirban Chatterjee , Sagnik Nandy , Ritwik Sadhu

In this paper, we study the problem of multivariate shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we investigate the model…

Machine Learning · Statistics 2026-03-24 Zhangsong Li

In this paper, we study a spiked Wigner problem with an inhomogeneous noise profile. Our aim in this problem is to recover the signal passed through an inhomogeneous low-rank matrix channel. While the information-theoretic performances are…

Machine Learning · Statistics 2023-02-15 Aleksandr Pak , Justin Ko , Florent Krzakala

In many natural average-case problems, there are or there are believed to be critical values in the parameter space where the structure of the space of solutions changes in a fundamental way. These phase transitions are often believed to…

Computational Complexity · Computer Science 2019-12-10 Ankur Moitra , Elchanan Mossel , Colin Sandon