Spring 2022 Colloquia
- Wednesday, January 12th: Rounak Dey (Harvard T.H. Chan School of Public Health) - 10:00 a.m. via Zoom
- Friday, January 14th: Michael Jauch (Cornell University) - 10:00 a.m. via Zoom
- Tuesday, January 18th: Toryn Schafer (Cornell University) - 10:00 a.m. via Zoom
- Wednesday, January 19th: Lu Zhang (Columbia University) - 10:00 a.m. via Zoom
- Friday, January 21st: Weijing Tang (University of Michigan) - 10:00 a.m. via Zoom
- Wednesday, January 26th: Michael Law (University of Michigan) - 10:00 a.m. via Zoom
- Monday, January 24th: Abhishek Roy (University of California, Davis) - 10:00 a.m. via Zoom
10:00 a.m. via Zoom
Title: High-order Joint Embedding for Multi-Level Link Prediction
Abstract: Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a novel tensor-based joint network embedding approach on simultaneously encoding pairwise links and hyperlinks onto a latent space, which captures the dependency between pairwise and multi-way links in inferring potential unobserved hyperlinks. The major advantage of the proposed embedding procedure is that it incorporates both the pairwise relationships and subgroup-wise structure among nodes to capture richer network information. In addition, the proposed method introduces a hierarchical dependency among links to infer potential hyperlinks, and leads to better link prediction. In theory we establish the estimation consistency for the proposed embedding approach, and provide a faster convergence rate compared to link prediction utilizing pairwise links or hyperlinks only. Numerical studies on both simulation settings and Facebook ego-networks indicate that the proposed method improves both hyperlink and pairwise link prediction accuracy compared to existing link prediction algorithms.
This is a joint work with Prof. Annie Qu in UC-Irvine
10:00 a.m. via Zoom
Title: Modeling Extremal Dependence in Trend Analysis of in Situ Measurements of Daily Precipitation Extremes
Abstract: The detection of changes over time in the distribution of precipitation extremes is significantly complicated by noise at the spatial scale of daily weather systems. This so-called "storm dependence" is non-negligible for extreme precipitation and makes detecting changes over time very difficult. To appropriately separate spatial signals from spatial noise due to storm dependence, we first utilize a well-developed Gaussian scale mixture model that directly incorporates extremal dependence. Our method uses a data-driven approach to determine the dependence strength of the observed proces (either asymptotic independence or dependence) and is generalized to analyze changes over time and increase the scalability of computations. We apply the model to daily measurements of precipitation over the central United States and compare our results with single-station and conditional independence methods. Our main finding is that properly accounting for storm dependence leads to increased detection of statistically significant trends in the climatology of extreme daily precipitation. Next, in order to extend our analysis to much larger spatial domains, we propose a mixture component model that achieves flexible dependence properties and allows truly high-dimensional inference for extremes of spatial processes. We modify the popular random scale construction via adding non-stationarity to the Gaussian process while allowing the radial variable to vary smoothly across space. As the level of extremeness increases, this single model exhibits both long-range asymptotic independence and short-range weakening dependence strength that leads to either asymptotic dependence or independence. To make inference on the model parameters, we construct global Bayesian hierarchical models and run adaptive Metropolis algorithms concurrently via parallelization. For future work to allow efficient computation, we plan to explore local likelihood and dimension reduction approaches.
10:00 a.m. via Zoom
Title: An Eigenmodel for Dynamic Multilayer Networks
Abstract: Network (or graph) data is at the heart of many modern data science problems: disease transmission, community dynamics on social media, international relations, and others. In this talk, I will elaborate on my research in statistical inference for complex time-varying networks. I will focus on dynamic multilayer networks, which frequently represent the structure of multiple co-evolving relations. Despite their prevalence, statistical models are not well-developed for this network type. Here, I propose a new latent space model for dynamic multilayer networks. The key feature of this model is its ability to identify common time-varying structures shared by all layers while also accounting for layer-wise variation and degree heterogeneity. I establish the identifiability of the model's parameters and develop a structured mean-field variational inference approach to estimate the model's posterior, which scales to networks previously intractable to dynamic latent space models. I apply the model to two real-world problems: discerning regional conflicts in a data set of international relations and quantifying infectious disease spread throughout a school based on the student's daily contact patterns.