Analysis of Networks via the Sparse β-Model

We propose the Sparse β-Model, a new network model that interpolates the celebrated Erdos-Renyi model and the more recent β-model that assigns one different parameter to each node. By a novel reparametrization of the β-model to distinguish global and local sparseness and assuming that many parameters therein are zero, our model can drastically reduce the dimensionality of the β-model. For estimating its parameters, we formulate a penalized likelihood approach with the l_0 penalty. Remarkably, we show via a monotonicity lemma that the seemingly combinatorial computational problem due to the l_0 penalty can be overcome by assigning nonzero parameters to those nodes with the largest degrees. We show further that a β-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 study. The usefulness of our model is further illustrated via the analysis of a microfinance take up example.

• Speaker: Chenlei Leng, University of Warwick
• Friday 01 March 2019, 16:00–17:00
• Venue: MR12.
• Series: Statistics; organiser: Dr Sergio Bacallado.