Sergey Kirshner

University of Illinois at Chicago, Chicago, Illinois, United States

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Publications (6)0 Total impact

  • Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining, Chicago, Illinois, USA; 01/2013
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    Lin Yuan, Sergey Kirshner, Robert Givan
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    ABSTRACT: We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-parametric model similar to kernel density estimators. We show that under mild conditions, the resulting model uses only the sufficient statistics if the density is within the chosen exponential family, and asymptotically, it approximates densities outside of the chosen exponential family. Using the proposed approach, we modify the exponential random graph model, commonly used for modeling small-size graph distributions, to address the well-known issue of model degeneracy.
    06/2012;
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    Dalton Lunga, Sergey Kirshner
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    ABSTRACT: We propose a novel model for generating graphs similar to a given example graph. Unlike standard approaches that compute features of graphs in Euclidean space, our approach obtains features on a surface of a hypersphere. We then utilize a von Mises-Fisher distribution, an exponential family distribution on the surface of a hypersphere, to define a model over possible feature values. While our approach bears similarity to a popular exponential random graph model (ERGM), unlike ERGMs, it does not suffer from degeneracy, a situation when a significant probability mass is placed on unrealistic graphs. We propose a parameter estimation approach for our model, and a procedure for drawing samples from the distribution. We evaluate the performance of our approach both on the small domain of all 8-node graphs as well as larger real-world social networks.
    Computing Research Repository - CORR. 05/2011;
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    ABSTRACT: Much of the past work on mining and modeling networks has focused on understanding the observed properties of single example graphs. However, in many real-life applications it is important to characterize the structure of populations of graphs. In this work, we investigate the distributional properties of Kronecker product graph models (KPGMs). Specifically, we examine whether these models can represent the natural variability in graph properties observed across multiple networks and find surprisingly that they cannot. By considering KPGMs from a new viewpoint, we can show the reason for this lack of variance theoretically - which is primarily due to the generation of each edge independently from the others. Based on this understanding we propose a generalization of KPGMs that uses tied parameters to increase the variance of the model, while preserving the expectation. We then show experimentally, that our mixed-KPGM can adequately capture the natural variability across a population of networks.
    Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on; 11/2010
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    ABSTRACT: Several works are focused in the analysis of just one network, trying to repli-cate, match and understanding the most possible characteristics of it, however, in these days it becomes more important to match the distribution of the networks rather than just one graph. In this work we will theoretically demonstrate that the Kronecker product graph models (KPGMs) [1] is unable to model the natu-ral variability in graph properties observed across multiple networks. Moreover after different approaches to improve this deficiency, we show a generalization of KPGM that uses tied parameters to increase the variance of the model, while preserving the expectation. We then show experimentally, that our new model can adequately capture the natural variability across a population of networks.
  • Dalton Lunga, Okan Ersoy, Sergey Kirshner
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    ABSTRACT: In this discussion we present assessments and valuable insights on random graph generating models. Of particular interest, we focus on the exponential random graph models (ERGMs) with sufficient statistics that consists of the number of edges and the number of triangles for each given undirected graph of 8 nodes. These models have so far been mainly applied in studying the statistical properties of social networks. Issues that arise when working with ERGMs have been shown to relate to the geometry of discrete polyhedral convex sets. These issues include model degeneracy, inferential complexity and model misfit. Using the results from applied geometry the parameter space can be shown to have a very complex structure that hinders many optimization algorithms from obtaining local or global solutions to MLE estimates. We propose a whitening transform onto the graph feature space to reduce the correlation of observed features because MLE estimates are linear combinations of the observed features as such any dependency in the observed features will contribute to degeneracy of the estimated model. We show that the geometry of the transformed space has a much smoother surface for the objective function as compared to the original space. Gobal solution searching and convergence of the gradient based optimization algorithm is observed to be very fast in the transfored space. We carry out assessments for model fitting by constructing a likelihood surface in the transform space: this is done by searching for the transformed mean features that match the mode of their distribution. since the transformation does not change the form of the distribution we show that the entropy objective function can characterize both the canonical and mean value parameter spaces of the transformed feature space. From the new feature space, we also highlight a region in which even reasonable models with true parameter values will result in unrealistic observations. We note that although the transformation introduces smoothness in the natural parameter space, there is still a region of feature statistics whose pmfs have modes placed on other regions of the feature space.
    ECE Technical Reports.