Browsing by Author "Bhamidi, Shankar"
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- Learning attribute and homophily measures through random walksPublication . Antunes, Nelson; Banerjee, Sayan; Bhamidi, Shankar; Pipiras, VladasWe investigate the statistical learning of nodal attribute functionals in homophily networks using random walks. Attributes can be discrete or continuous. A generalization of various existing canonical models, based on preferential attachment is studied (model class P), where new nodes form connections dependent on both their attribute values and popularity as measured by degree. An associated model class U is described, which is amenable to theoretical analysis and gives access to asymptotics of a host of functionals of interest. Settings where asymptotics for model class U transfer over to model class P through the phenomenon of resolvability are analyzed. For the statistical learning, we consider several canonical attribute agnostic sampling schemes such as Metropolis-Hasting random walk, versions of node2vec (Grover and Leskovec, 2016) that incorporate both classical random walk and non-backtracking propensities and propose new variants which use attribute information in addition to topological information to explore the network. Estimators for learning the attribute distribution, degree distribution for an attribute type and homophily measures are proposed. The performance of such statistical learning framework is studied on both synthetic networks (model class P) and real world systems, and its dependence on the network topology, degree of homophily or absence thereof, (un)balanced attributes, is assessed.
- Sampling Based Estimation of In-Degree Distribution for Directed Complex NetworksPublication . Antunes, Nelson; Bhamidi, Shankar; Guo, Tianjian; Pipiras, Vladas; Wang, BangThe focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and several approaches based on random walks with possible jumps. When sampling nodes, it is assumed that only the out-edges of that node are visible, that is, the in-degree of that node is not observed. The suggested estimation of the in-degree distribution is based on two approaches. The inversion approach exploits the relation between the original and sample in-degree distributions, and can estimate the bulk of the in-degree distribution, but not the tail of the distribution. The tail of the in-degree distribution is estimated through an asymptotic approach, which itself has two versions: one assuming a power-law tail and the other for a tail of general form. The two estimation approaches are examined on synthetic and real networks, with good performance results, especially striking for the asymptotic approach. Supplementary files for this article are available online.