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Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been…

Statistics Theory · Mathematics 2024-08-14 Yuetian Luo , Chao Gao

We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…

Discrete Mathematics · Computer Science 2010-01-14 Alexander D. Scott , Gregory B. Sorkin

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

Databases · Computer Science 2020-03-11 Mujahid Sultan

In this paper, we propose a general framework for combining evidence of varying quality to estimate underlying binary latent variables in the presence of restrictions imposed to respect the scientific context. The resulting algorithms…

Methodology · Statistics 2018-08-28 Zhenke Wu , Livia Casciola-Rosen , Antony Rosen , Scott L. Zeger

This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…

Machine Learning · Computer Science 2015-10-20 Tengyu Ma , Avi Wigderson

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…

Machine Learning · Computer Science 2016-09-20 Vincent Roulet , Fajwel Fogel , Alexandre d'Aspremont , Francis Bach

Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…

Machine Learning · Computer Science 2023-05-22 Jonas K. Falkner , Lars Schmidt-Thieme

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…

Machine Learning · Computer Science 2025-12-19 Yuriy N. Bakhvalov

Cardinality estimation and conjunctive query evaluation are two of the most fundamental problems in database query processing. Recent work proposed, studied, and implemented a robust and practical information-theoretic cardinality…

Databases · Computer Science 2025-04-04 Sungjin Im , Benjamin Moseley , Hung Q. Ngo , Kirk Pruhs

We study the fundamental tradeoffs between statistical accuracy and computational tractability in the analysis of high dimensional heterogeneous data. As examples, we study sparse Gaussian mixture model, mixture of sparse linear…

Statistics Theory · Mathematics 2018-08-22 Jianqing Fan , Han Liu , Zhaoran Wang , Zhuoran Yang

Neural network-based clustering has recently gained popularity, and in particular a constrained clustering formulation has been proposed to perform transfer learning and image category discovery using deep learning. The core idea is to…

Computer Vision and Pattern Recognition · Computer Science 2018-06-29 Yen-Chang Hsu , Zhaoyang Lv , Joel Schlosser , Phillip Odom , Zsolt Kira

The pooled data problem asks to identify the unknown labels of a set of items from condensed measurements. More precisely, given $n$ items, assume that each item has a label in $\cbc{0,1,\ldots, d}$, encoded via the ground-truth $\SIGMA$.…

Probability · Mathematics 2023-12-25 Max Hahn-Klimroth , Remco van der Hofstad , Noela Müller , Connor Riddlesden

The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…

Optimization and Control · Mathematics 2018-09-05 S. Borgwardt , F. Happach

We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for…

Data Structures and Algorithms · Computer Science 2017-10-04 Samuel B. Hopkins , David Steurer

This work studies information-computation gaps for statistical problems. A common approach for providing evidence of such gaps is to show sample complexity lower bounds (that are stronger than the information-theoretic optimum) against…

Data Structures and Algorithms · Computer Science 2025-11-25 Ilias Diakonikolas , Daniel M. Kane , Sihan Liu , Thanasis Pittas

Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…

Statistics Theory · Mathematics 2022-01-25 Zhongyuan Lyu , Dong Xia

This paper presents a new semantic method for proving lower bounds in computational complexity. We use it to prove that maxflow, a PTIME complete problem, is not computable in polylogarithmic time on parallel random access machines (PRAMs)…

Computational Complexity · Computer Science 2021-02-05 Luc Pellissier , Thomas Seiller

We consider estimation in a high-dimensional linear model with strongly correlated variables. We propose to cluster the variables first and do subsequent sparse estimation such as the Lasso for cluster-representatives or the group Lasso…

Methodology · Statistics 2015-01-14 Peter Bühlmann , Philipp Rütimann , Sara van de Geer , Cun-Hui Zhang

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

Data Structures and Algorithms · Computer Science 2017-10-17 Tamal K. Dey , Alfred Rossi , Anastasios Sidiropoulos

Clustering can be defined as the process of assembling objects into a number of groups whose elements are similar to each other in some manner. As a technique that is used in many domains, such as face clustering, plant categorization,…

Machine Learning · Computer Science 2022-04-05 Mehmet F. Demirel , Enrico Au-Yeung