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In this paper, we study the problem of learning Graph Neural Networks (GNNs) with Differential Privacy (DP). We propose a novel differentially private GNN based on Aggregation Perturbation (GAP), which adds stochastic noise to the GNN's…
We study the problem of releasing a differentially private (DP) synthetic graph $G'$ that well approximates the triangle-motif sizes of all cuts of any given graph $G$, where a motif in general refers to a frequently occurring subgraph…
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…
Differential privacy is a recent notion of privacy for statistical databases that provides rigorous, meaningful confidentiality guarantees, even in the presence of an attacker with access to arbitrary side information. We show that for a…
For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial-time algorithm which finds a…
Traceroute sampling is an important technique in exploring the internet router graph and the autonomous system graph. Although it is one of the primary techniques used in calculating statistics about the internet, it can introduce bias that…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Exact subgraph matching on large-scale graphs remains a challenging problem due to high computational complexity and distributed system constraints. Existing GNN-based path embedding (GNN-PE) frameworks achieve efficient exact matching on…
We present a distributed (non-Bayesian) learning algorithm for the problem of parameter estimation with Gaussian noise. The algorithm is expressed as explicit updates on the parameters of the Gaussian beliefs (i.e. means and precision). We…
Finding min $s$-$t$ cuts in graphs is a basic algorithmic tool with applications in image segmentation, community detection, reinforcement learning, and data clustering. In this problem, we are given two nodes as terminals, and the goal is…
Graphs are the dominant formalism for modeling multi-agent systems. The algebraic connectivity of a graph is particularly important because it provides the convergence rates of consensus algorithms that underlie many multi-agent control and…
In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…
Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…
We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…
We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is the distribution on graphs with n vertices obtained by…
Graph convolutional networks (GCNs) are a powerful architecture for representation learning on documents that naturally occur as graphs, e.g., citation or social networks. However, sensitive personal information, such as documents with…
A common problem in private data analysis is the partition selection problem, where each user holds a set of partitions (e.g. keys in a GROUP BY operation) from a possibly unbounded set. The challenge here is in maximizing the set of…
Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks.…
In distributed networks, calculating the maximum element is a fundamental task in data analysis, known as the distributed maximum consensus problem. However, the sensitive nature of the data involved makes privacy protection essential.…
The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached…