Author: Mingli Chen Title: Modeling Networks via Sparse-Beta Model Abstract: Data in the form of networks are increasingly available in a variety of areas. However, there is a lack of generative models to characterize notable features of a network such as degree heterogeneity and sparseness with tractable statistical properties. In this paper, we propose the Sparse ß-Model (SßM), a new network model that interpolates the celebrated Erdos-Renyi model and the more recent ß-model that assigns one different parameter to each node. By a novel reparametrization of the ß- model to distinguish global and local sparseness and assuming that many parameters therein are zero, SßM can drastically reduce the dimensionality of the ß-model and can thus model sparse networks in which the number of edges scales sub-quadratically or even linearly with that of nodes. For estimating the parameters in SßM, we derive the asymptotic distribution of the maximum likelihood estimator for sparse networks when the sparsity of the parameter is known. When the sparsity is unknown, we formulate a penalized likelihood approach with the $\ell$-0penalty. Remarkably, we show via a monotonicity lemma that the seemingly combinatorial computational problem due to the $\ell$-0 penalty can be overcome by assigning nonzero parameters to those nodes with the largest degrees. We show further that a ß-min condition guarantees our method to identify the true model and provide excess risk bounds for the estimated parameters. The estimation procedure enjoys good finite sample properties as shown by simulation studies. The usefulness of SßM is further illustrated via the analysis of a microfinance take up example. --based on a joint work with Kengo Kato (Cornell) and Chenlei Leng (Warwick).