No abstract

Consider fully dynamic data, where we track data as it gets inserted and deleted. There are well developed notions of private data analyses with dynamic data, for example, using differential privacy. We want to go beyond privacy, and consider privacy together with security, formulated recently as pan-privacy by Dwork et al. (ICS 2010). Informally, pan-privacy preserves differential privacy while computing desired statistics on the data, even if the internal memory of the algorithm is compromised (say, by a malicious breakin or insider curiosity or by fiat by the government or law).We study pan-private algorithms for basic analyses, like estimating distinct count, moments, and heavy hitter count, with fully dynamic data. We present the first known panprivate algorithms for these problems in the fully dynamic model. Our algorithms rely on sketching techniques popular in streaming: in some cases, we add suitable noise to a previously known sketch, using a novel approach of calibrating noise to the underlying problem structure and the projection matrix of the sketch; in other cases, we maintain certain statistics on sketches; in yet others, we define novel sketches. We also present the first known lower bounds explicitly for pan privacy, showing our results to be nearly optimal for these problems. Our lower bounds are stronger than those implied by differential privacy or dynamic data streaming alone and hold even if unbounded memory and/or unbounded processing time are allowed. The lower bounds use a noisy decoding argument and exploit a connection between pan-private algorithms and data sanitization.

We consider the problem of making graph databases such as social networks available to researchers for knowledge discovery while providing privacy to the participating entities. We use a parametric graph model, the stochastic Kronecker graph model, to model the observed graph and construct an estimator of the "true parameter" in a way that both satisfies the rigorous requirements of differential privacy and demonstrates experimental utility on several important graph statistics. The estimator, which may then be published, defines a probability distribution on graphs. Sampling such a distribution yields a synthetic graph that mimics important properties of the original sensitive graph and consequently, could be useful for knowledge discovery.

No abstract

Understanding the graphical structure of the electric power system is important in assessing reliability, robustness, and the risk of failure of operations of this critical infrastructure network. Statistical graph models of complex networks yield much insight into the underlying processes that are supported by the network. Such generative graph models are also capable of generating synthetic graphs representative of the real network. This is particularly important since the smaller number of traditionally available test systems, such as the IEEE systems, have been largely deemed to be insufficient for supporting large-scale simulation studies and commercial-grade algorithm development. Thus, there is a need for statistical generative models of electric power network that capture both topological and electrical properties of the network and are scalable.Generating synthetic network graphs that capture key topological and electrical characteristics of real-world electric power systems is important in aiding widespread and accurate analysis of these systems. Classical statistical models of graphs, such as small-world networks or Erdős-Renyi graphs, are unable to generate synthetic graphs that accurately represent the topology of real electric power networks -networks characterized by highly dense local connectivity and clustering and sparse long-haul links.This thesis presents a parametrized model that captures the above-mentioned unique topological properties of electric power networks. Specifically, a new Clusterand-Connect model is introduced to generate synthetic graphs using these parameters.Using a uniform set of metrics proposed in the literature, the accuracy of the proposed model is evaluated by comparing the synthetic models generated for specific real electric network graphs. In addition to topological properties, the electrical properties are captured via line impedances that have been shown to be modeled reliably by well-

We consider the problem of making graph databases such as social network structures available to researchers for knowledge discovery while providing privacy to the participating entities. We show that for a specific parametric graph model, the Kronecker graph model, one can construct an estimator of the true parameter in a way that both satisfies the rigorous requirements of differential privacy and is asymptotically efficient in the statistical sense. The estimator, which may then be published, defines a probability distribution on graphs. Sampling such a distribution yields a synthetic graph that mimics important properties of the original sensitive graph and, consequently, could be useful for knowledge discovery.

No abstract

No abstract