Research

My research develops statistical methods for complex, structured data, including functional data, matrices, and tensors, motivated by questions in neuroimaging and precision medicine.

Bayesian methods for neuroimaging data

Brain networks and connectivity matrices

Functional connectivity describes how activity in different brain regions co-varies, giving each subject a symmetric positive-definite matrix. I develop regression models that use these matrices as predictors of cognitive or clinical outcomes while respecting their geometry, and that identify the sub-networks of brain regions driving the association. A related line of work clusters subjects by their connectivity or covariance matrices.

Brain slices for 15 network nodes above a heatmap of node loadings on four latent sub-networks — Four estimated sub-networks (rows) of 15 brain network nodes, learned while predicting cognitive scores from Human Connectome Project connectivity data. Brain slices above show the regions of each node.

Functional and time–frequency data

EEG experiments record brain activity as surfaces over time and frequency, measured for each subject under several experimental conditions. I develop Bayesian mixed-effects models for such multilevel two-way functional data, which separate population-level effects of conditions and covariates from subject- and trial-level variation.

Five time-frequency heatmaps showing Y equals A plus B plus C plus E — An EEG time–frequency response decomposed into a fixed effect of condition and covariates (A), a subject-level random effect (B), a subject-by-condition random effect (C), and residual noise (E).

Multi-way tensor data

Many neuroimaging studies produce data indexed along several dimensions at once, which are naturally represented as multi-way arrays, or tensors. I am developing probabilistic models that summarize such data through a small number of interpretable components, with full uncertainty quantification.

Schematic of a three-way array approximated by a sum of components, each the product of three factors — Schematic: a multi-way array approximated by a sum of a few components.

Boosting for complex data

Gradient boosting builds flexible prediction models by combining many simple learners, such as small regression trees, one step at a time. My work develops boosting algorithms that are robust to outliers and that handle functional predictors, with implementations in open-source R packages.

Left: scatter plot with outliers where a dashed least-squares fit bends toward the outliers and a solid robust fit follows the main trend. Right: several curves feeding into a sum of small regression trees. — Schematic of the two ideas. Left: robust boosting tracks the bulk of the data, while least-squares boosting is pulled toward a few outliers. Right: functional predictors enter an ensemble of regression trees built stage by stage.

Software

Package	Description
BMEF	Bayesian mixed-effects models for multilevel two-way functional data (R)
RRBoost	Robust gradient boosting algorithms (R)
RTFBoost	Tree-based boosting for functional regression and robust variations (R)