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Webinar: Fast Discovery of Pairwise Interactions in High Dimensions using Bayes

This post is by Eric.

This Wednesday, at 12 pm ET, Tamara Broderick is stopping by to talk to us about pairwise interactions in high dimensions. You can register here.

Abstract

Discovering interaction effects on a response of interest is a fundamental problem in medicine, economics, and many other 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 problems of even moderate dimension p. 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; on datasets with a variety of covariate behaviors, we show 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.

About the speaker

Tamara Broderick is an Associate Professor in the Department of Electrical Engineering and Computer Science at MIT. She is a member of the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL), the MIT Statistics and Data Science Center, and the Institute for Data, Systems, and Society (IDSS). She completed her Ph.D. in Statistics at the University of California, Berkeley in 2014.

The video is available here.

One Comment

  1. Andrew says:

    Cool!

    The discussion of sparsity reminds me of some of our past blog posts, including:

    “Economic predictions with big data” using partial pooling.

    Whither the “bet on sparsity principle” in a nonsparse world?.

    The king must die (This one’s from Dan Simpson).

    The anthropic principle in statistics.

    It’s a topic we keep coming back to.

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