# Research

## Overview

My research sits at the intersection of statistical theory and computer science methodology and is part of the modern ascendancy of mining “big data” to produce fundamentally novel science from complicated datasets. Specifically, I seek to illuminate the role played by the nature and quantity of regularization as a tool for improved scientific understanding.

Through this lens, my research can be divided into four intersecting areas: (1) computational approximation methodology, (2) model selection, (3) high-dimensional and nonparametric theory, and (4) applications related to these. My work explores and exploits the connections between these areas rather than approaching them separately—my contributions have been developed out of the pressing need to justify methodology as implemented in applications rather than in a vacuum devoid of empirical motivation. My research program seeks to generate statistical guarantees for the procedures that applied researchers use while also developing methodology for complicated, high-dimensional problems. Within this context, much of my work involves what is referred to as regularization—the process of mathematically balancing complex but meaningful scientific models with a preference for simple fundamental structures.

## Recent papers and preprints

##### Associative White Matter Tracts Selectively Predict Sensorimotor Learning

Vinci-Booher, S, McDonald, DJ, Berquist, E, Pestilli, FTechnical Report, 2023

##### Less is More: Balancing Noise Reduction and Data Retention in fMRI with Projection Scrubbing

Pham, D, McDonald, DJ, Ding, L, Nebel, MB, et al.Neuroimage, 270, 119972, 2023

##### Empirical Macroeconomics and DSGE Modeling in Statistical Perspective

McDonald, DJ, Shalizi, CRTechnical Report, 2022

##### Sparsegl: An R Package for Estimating Sparse Group Lasso

Liang, X, Cohen, A, Heinsfeld, AS, Pestilli, F, et al.Technical Report, 2022

##### Smooth Multi-Period Forecasting with Application to Prediction of COVID-19 Cases

Tuzhilina, E, Hastie, TJ, McDonald, DJ, Tay, JK, et al.Technical Report, 2022

## Slides for recent talks

Markov switching state space models for uncovering musical interpretation

COVID-19 Modelling and Forecasting in the US and Canada: A statisticians perspective

Algorithms for Estimating Trends in Global Temperature Volatility

Regularization, optimization, and approximation: The benefits of a convex combination

Matrix sketching for alternating direction method of multipliers optimization

Predicting phenotypes from microarrays using amplified, initially marginal, eigenvector regression