Abstract:

Complex networks are increasingly prevalent in many scientific applications. Statistical analysis of suck networks depends heavily on the model generating the network. In this project, we develop a subsampling based cross-validation algorithm for model selection in networks. Given a set of candidate models, the algorithm splits the network into multiple subnetworks with a common overlap, fits each candidate model to each subnetwork, and cross-validates the fitted models on the edges between the subnetworks using an appropriate loss function. We apply this algorithm to detect the number of communities in a blockmodel, and to estimate the rank of a random dot product graph model. This method accurately determines the correct model in various scenarios and is significantly faster than the existing methods, making it feasible for model selection in very large networks as well.

Abstract:

Optimal transport (OT) theory has long-standing connections to probability and statistics. In this talk, I will discuss some applications of OT in generative modeling and Bayesian inference. Unlike traditional distances or discrepancy measures over distributions, Wasserstein distances defined via OT can capture closeness between mutually singular probability distributions. Therefore, they are more useful in addressing modern machine learning tasks where data displayed as high-dimensional vectors usually have low-dimensional structures. Another important application of OT concerns the Wasserstein gradient flow approach to solving minimization problems over the space of all probability distributions. This makes OT naturally suitable for computing or approximating posterior distributions in Bayesian models.