Vishesh Karwa

Private Analysis of Graph Structure

We present efficient algorithms for releasing useful statistics about graph data while providing rigorous privacy guarantees. Our algorithms work on datasets that consist of relationships between individuals, such as social ties or email communication. The algorithms satisfy edge differential privacy, which essentially requires that the presence or absence of any particular relationship be hidden. Our algorithms output approximate answers to subgraph counting queries. Given a query graph H, for example, a triangle, k-star, or k-triangle, the goal is to return the number of edge-induced isomorphic copies of H in the input graph. The special case of triangles was considered by Nissim et al. [2007] and a more general investigation of arbitrary query graphs was initiated by Rastogi et al. [2009]. We extend the approach of Nissim et al. to a new class of statistics, namely k-star queries. We also give algorithms for k-triangle queries using a different approach based on the higher-order local sensitivity. For the specific graph statistics we consider (i.e., k-stars and k-triangles), we significantly improve on the work of Rastogi et al.: our algorithms satisfy a stronger notion of privacy that does not rely on the adversary having a particular prior distribution on the data, and add less noise to the answers before releasing them. We evaluate the accuracy of our algorithms both theoretically and empirically, using a variety of real and synthetic datasets. We give explicit, simple conditions under which these algorithms add a small amount of noise. We also provide the average-case analysis in the Erdős-Rényi-Gilbert G(n,p) random graph model. Finally, we give hardness results indicating that the approach Nissim et al. used for triangles cannot easily be extended to k-triangles (hence justifying our development of a new algorithmic approach).

Differentially private graphical degree sequences and synthetic graphs

We present an algorithm for releasing graphical degree sequences of simple undirected graphs under the framework of differential privacy. The algorithm is designed to provide utility for statistical inference in random graph models whose sufficient statistics are functions of degree sequences. Specifically, we focus on the tasks of existence of maximum likelihood estimates, parameter estimation and goodness-of-fit testing for the beta model of random graphs. We show the usefulness of our algorithm by evaluating it empirically on simulated and real-life datasets. As the released degree sequence is graphical, our algorithm can also be used to release synthetic graphs under the beta model.

Inference using noisy degrees: Differentially private

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-model and synthetic graphs

-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the

Causal inference in transportation safety studies: Comparison of potential outcomes and causal diagrams

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Predicting Pavement Marking Retroreflectivity Using Artificial Neural Networks: Exploratory Analysis

-model, and show that the MLE never exists for the degree partition

Analysis of Effects of Pavement Marking Retroreflectivity on Traffic Crash Frequency on Highways in North Carolina: Application of Artificial Neural Networks and Generalized Estimating Equations

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Differentially Private Exponential Random Graphs

-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of

Use of Pavement Marking Degradation Models to Develop a Pavement Marking Management System

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