Practical Methods for Scalable Bayesian and Causal Inference with Provable Quality Guarantees

Many scientific and decision-making tasks require learning complex relationships between a set of 𝑝 covariates and a target response, from 𝑁 observed datapoints with 𝑁 ≪ 𝑝. For example, in genomics and precision medicine, there may be thousands or millions of genetic and environmental covariates but just hundreds or thousands of observed individuals. Researchers would like to (1) identify a small set of factors associated with diseases, (2) quantify these factors’ effects, and (3) test for causality. Unfortunately, in this high-dimensional data regime, inference is statistically and computationally challenging due to non-linear interaction effects, unobserved confounders, and the lack of randomized experimental data. In this thesis, I start by addressing the problems of variable selection and estimation when there are non-linear interactions and fewer datapoints than covariates. Unlike previous methods whose runtimes scale at least quadratically in the number of covariates, my new method (SKIM-FA) uses a kernel trick to perform inference in linear time by exploiting special interaction structure. While SKIM-FA identifies potential risk-factors, not all of these factors need be causal. So next I aim to identify causal factors to aid in decision making. To this end, I show when we can extract causal relationships from observational data, even in the presence of unobserved confounders, non-linear effects, and a lack of randomized controlled data. In the last part of my thesis, I focus on experimental design. Specifically, if the observational data is not adequate, how do we optimally collect new experimental data to test if particular causal relationships of interest exist.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2021

Author dc:creator

• Agrawal, Raj

Advisors dc:contributor.advisor

• Broderick, Tamara
• Uhler, Caroline

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/139350

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/139350