Department of Statistics pres.
Livestream: Statistics Department Seminar Series: Tamara Broderick, Associate Professor, Department Electrical Engineering and Computer Science, Massachusetts Institute of Technology
"Fast Discovery of Pairwise Interactions in High Dimensions using Bayes"
Discovering interaction effects on a response of interest is a fundamental problem in biology, medicine, economics, and many other scientific disciplines. In theory, Bayesian methods for discovering pairwise interactions enjoy many benefits such as coherent uncertainty quantification, the ability to incorporate background knowledge, and desirable shrinkage properties. In practice, however, Bayesian methods are often computationally intractable for even moderate-dimensional problems. Our key insight is that many hierarchical models of practical interest admit a particular Gaussian process (GP) representation; the GP allows us to capture the posterior with a vector of O(p) kernel hyper-parameters rather than O(p^2) interactions and main effects. With the implicit representation, we can run Markov chain Monte Carlo (MCMC) over model hyper-parameters in time and memory linear in p per iteration. We focus on sparsity-inducing models and show on datasets with a variety of covariate behaviors that our method: (1) reduces runtime by orders of magnitude over naive applications of MCMC, (2) provides lower Type I and Type II error relative to state-of-the-art LASSO-based approaches, and (3) offers improved computational scaling in high dimensions relative to existing Bayesian and LASSO-based approaches.
This Seminar will be livestreamed using Zoom. When you click the meeting link on your PC or mobile device, it will direct you to the Zoom app (which you may wish to download in advance).
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Webinar ID: 402 943 422
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