In this seminar, the speaker will give an overview of two recent projects he has been involved in, during which new efficient statistical inference algorithms for complex network data are developed.  A belief propagation algorithm for computing one-point marginals and other quantities of interest in probabilistic graphical models on networks with short loops will first be described. This algorithm provides a significant accuracy improvement over standard belief propagation for graphical models over highly clustered networks, which are ubiquitous in complex systems research, and runs in only a fraction of the time it takes to run standard Monte Carlo sampling. The speaker will demonstrate its capabilities using the Ising model from statistical physics as an example system. He will then move on to discuss a fast parameter-free algorithm to perform regionalization, spatially contiguous clustering, over areal units with distributional metadata such as those sampled for census analysis. The problem of regionalization is viewed as one of data compression, optimizing an objective derived using purely combinatorial arguments and the minimum description length principle. The speaker will further demonstrate how the method is capable of recovering planted spatial clusters in noisy synthetic data, and that it can meaningfully coarse-grain real demographic data to provide new insights about urban spatial segregation. Using the description length formulation, it is found that spatial ethnoracial data in metropolitan areas across the U.S. has become more difficult to compress over the period from 1980 to 2010, reflecting the rising complexity of urban segregation patterns of these metros. Increasing ethnoracial diversity at small spatial scales within these metros is identified as a major contributor to this lower data compressibility, while changes in large scale ethnoracial clustering and population are not significant factors.