Research

Learning structure without losing interpretability

My research connects nonparametric estimation, variable selection, and statistical inference. I am interested in methods that describe nonlinear covariate effects, distinguish patterns across a response distribution, and estimate shared structure in high-dimensional binary and count data. I study both the statistical properties of these methods and algorithms for calculating them.

01 / Which variables matter, and what form do their effects take?

A straight-line model can miss a threshold, a plateau, or a change in direction. Allowing each covariate to have an unknown smooth effect makes a model more flexible, but estimating many such effects also introduces uncertainty. My work on sparse additive and varying coefficient models addresses the joint problem of selecting relevant covariates and estimating their effects.

In our functional lasso kernel smoothing research, we penalize whole component functions and estimate them using smooth backfitting. This permits variable selection without first fixing a linear shape for every association. We also study a debiased estimator for inference, so the analysis extends beyond choosing variables to quantifying uncertainty about the estimated functions.

Representative publication

Annals of Statistics · 2024
Efficient functional lasso kernel smoothing for high-dimensional additive regression

02 / How do associations differ across people and over time?

An association at the lower end of a response distribution need not match the association near its center or upper end. Quantile regression describes these differences. Varying coefficient models allow the associations themselves to change with an index, such as age or time.

My research addresses both selecting an appropriate quantile model and estimating changing associations. In our work on the Bayesian information criterion, we establish model-selection consistency for high-dimensional linear quantile regression and extend the results to structured nonparametric quantile models. The criterion also provides a basis for choosing regularization parameters.

For multiple responses, our reduced varying coefficient model represents shared patterns through principal component functions. A nearest-neighbor fused lasso penalty identifies locally similar coefficients. This permits the study of distribution-specific associations among correlated outcomes without estimating every coefficient function independently.

Representative publications

Journal of the American Statistical Association · 2014
Model selection via Bayesian information criterion for quantile regression models

Biometrics · 2026
Reduced varying coefficient models for regional quantile regression with multiple responses

03 / How can many discrete responses be analyzed together?

Many datasets contain several binary outcomes or a large vector of counts for each observational unit. Fitting an unrelated model for every response ignores structure shared across responses. My research studies low-rank regression and dimension selection for these data.

For multiple binary responses, we combine a low-rank coefficient matrix with row sparsity to select covariates and estimate shared regression structure. Our theory gives estimation-error bounds and conditions for recovering the rank and relevant covariates, allowing dependence among responses. The method is illustrated using cancer cell-line data.

For count data, our Poisson reduced-rank model provides low-dimensional representations of high-dimensional count vectors. We establish consistency of the estimated positions and dimension-selection rules under stated dependence conditions. An application to word counts in political manifestos examines how party positions change across elections.

Representative publications

Journal of the American Statistical Association · 2024
Low-rank regression models for multiple binary responses and their applications to cancer cell-line encyclopedia data

Biometrika · 2021
Poisson reduced-rank models with an application to political text data

The illustrations explain statistical concepts using synthetic examples; they are not empirical findings from the cited papers.

Complete publication list