Related papers: Private graphon estimation via sum-of-squares
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…
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…
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…
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…
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,…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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.…
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…
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…