Seminar

Please Note: This seminar will be given online.

Is the integral the most important object in all of mathematics?

Please Note: This seminar will be given online.

Reconstructing Encrypted Signals: Optimization with input from Spin Glasses and RMT.

Please Note: This seminar will be given online.

First-Order Correction of Statistical Significance for Screening Two-Way Epistatic Interactions

Please Note: This seminar will be given online.

Predictive Comparisons for Screening and Interpreting Inputs in Machine Learning

Please Note: This seminar will be given online.

Large Values of the Riemann Zeta Function in Short Intervals

Please Note: This seminar will be given online.

Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency

Please Note: This seminar will be given online.

Data-Adaptive Regression Modeling in High Dimensions

Please Note: This seminar will be given online.

On univoque and strongly univoque sets

A new framework for modeling sparse networks that makes sense (and can actually be fit!)

Latent position models are a versatile tool when working with network data. Applications include clustering entities, network visualization, and controlling for unobserved causal confounding. In traditional treatments of the latent position model, the nodes’ latent positions are viewed as independent and identically distributed random variables. This assumption implies that the average node degree grows linearly with the number of nodes in the network, making it inappropriate when the network is sparse. In the first part of this talk, I will propose an alternative assumption—that the latent positions are generated according to a Poisson point process—and show that it is compatible with various levels of network sparsity. I will also provide theory establishing that the nodes’ latent positions can be consistently estimated, provided that the network isn't too sparse.  In the second part of the talk, I will consider the computational challenge of fitting latent position models to large datasets. I will describe a new Markov chain Monte Carlo strategy—based on a combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo—that is much more efficient than the standard Metropolis-within-Gibbs algorithm for inferring the latent positions. Throughout the talk, I will use an advice-sharing network of elementary school teachers within a school district as a running example.

Please note: This talk will be hosted on Webex. To join please click on the following link: Department seminar by Neil Spencer.

Network Response Regression for Modeling Population of Networks with Covariates

Multiple-network data are fast emerging in recent years, where a separate network over a common set of nodes is measured for each individual subject, along with rich subject covariates information. Existing network analysis methods have primarily focused on modeling a single network, and are not directly applicable to multiple networks with subject covariates.

In this talk, we present a new network response regression model, where the observed networks are treated as matrix-valued responses, and the individual covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the parsimonious effects of subject covariates on the network through a sparse slope tensor. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating gradient descent algorithm. We establish the non-asymptotic error bound for the actual estimator from our optimization algorithm. Built upon this error bound, we derive the strong consistency for network community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through intensive simulations and two brain connectivity studies.

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Meeting ID: 844 283 6948
Passcode: 318995