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Related papers: Private graphon estimation via sum-of-squares

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We consider extensions of the Shannon relative entropy, referred to as $f$-divergences.Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing…

Information Theory · Computer Science 2023-09-19 Francis Bach

Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…

Data Structures and Algorithms · Computer Science 2018-12-24 Hannu Reittu , Lasse Leskelä , Tomi Räty , Marco Fiorucci

We design the first node-differentially private algorithm for approximating the number of connected components in a graph. Given a database representing an $n$-vertex graph $G$ and a privacy parameter $\varepsilon$, our algorithm runs in…

Data Structures and Algorithms · Computer Science 2023-04-17 Iden Kalemaj , Sofya Raskhodnikova , Adam Smith , Charalampos E. Tsourakakis

Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…

Optimization and Control · Mathematics 2024-06-14 Richard L. Zhu , Mathias Oster , Yuehaw Khoo

Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…

Data Structures and Algorithms · Computer Science 2019-08-07 Prasad Raghavendra , Tselil Schramm , David Steurer

We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…

Data Structures and Algorithms · Computer Science 2013-12-24 Boaz Barak , Jonathan Kelner , David Steurer

Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein-Chen method to derive Poisson approximations for the distribution of the number of subgraphs in the stochastic block model which are…

Probability · Mathematics 2017-03-21 Matthew Coulson , Robert E. Gaunt , Gesine Reinert

We study differentially private stochastic convex optimization (DP-SCO) under user-level privacy, where each user may hold multiple data items. Existing work for user-level DP-SCO either requires super-polynomial runtime [Ghazi et al.…

Machine Learning · Computer Science 2023-11-08 Hilal Asi , Daogao Liu

Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…

Machine Learning · Computer Science 2025-07-01 Marco Bressan , Victor Chepoi , Emmanuel Esposito , Maximilian Thiessen

We study differentially private algorithms for graph cut sparsification, a fundamental problem in algorithms, privacy, and machine learning. While significant progress has been made, the best-known private and efficient cut sparsifiers on…

Data Structures and Algorithms · Computer Science 2025-07-03 Anders Aamand , Justin Y. Chen , Mina Dalirrooyfard , Slobodan Mitrović , Yuriy Nevmyvaka , Sandeep Silwal , Yinzhan Xu

In monitoring applications, recent data is more important than distant data. How does this affect privacy of data analysis? We study a general class of data analyses - computing predicate sums - with privacy. Formally, we study the problem…

Data Structures and Algorithms · Computer Science 2013-08-05 Jean Bolot , Nadia Fawaz , S. Muthukrishnan , Aleksandar Nikolov , Nina Taft

Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…

Social and Information Networks · Computer Science 2020-07-14 Kazuki Nakajima , Kazuyuki Shudo

Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models…

Methodology · Statistics 2024-01-11 Arthur Verdeyme , Sofia C. Olhede

We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant…

Machine Learning · Statistics 2022-12-02 Kristian Georgiev , Samuel B. Hopkins

We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…

Machine Learning · Computer Science 2020-02-25 Huy L. Nguyen , Jonathan Ullman , Lydia Zakynthinou

Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…

Cryptography and Security · Computer Science 2024-06-06 Dung Nguyen , Anil Vullikanti

A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem.…

Optimization and Control · Mathematics 2013-03-07 Peter Seiler , Qian Zheng , Gary Balas

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…

Machine Learning · Computer Science 2024-04-25 Gavin Brown , Jonathan Hayase , Samuel Hopkins , Weihao Kong , Xiyang Liu , Sewoong Oh , Juan C. Perdomo , Adam Smith

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

Combinatorics · Mathematics 2015-08-04 Alexander Barvinok , Pablo Soberón

Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is…

Social and Information Networks · Computer Science 2022-11-09 Arpit Merchant , Michael Mathioudakis , Yanhao Wang