research
My research develops statistical and machine learning methods for complex biomedical data, with particular interests in multimodal data integration, geometric and functional data analysis, and inverse problems.
Geometric & Functional Data Analysis
Many biomedical data objects, such as surfaces representing cortical morphology and covariance matrices representing functional connectivity, do not naturally live in Euclidean space. We develop statistical and machine-learning methods that respect this geometry and provide interpretable representations of their variation. One example is the classification model shown below, which combines cortical morphology and thickness to identify a joint signature of Alzheimer’s disease.
Lila, Zhang, Levendovszky (2024) Interpretable discriminant analysis for functional data supported on random nonlinear domains with an application to Alzheimer’s disease, JRSS-B.
Lila, Aston (2020) Statistical Analysis of Functions on Surfaces, With an Application to Medical Imaging, JASA.
Multimodal Data Integration
We develop statistical methods for integrating complex imaging data with behavioral, genetic, and clinical data. While data integration is a component of much of our work, one example that specifically focuses on integration methodology is our work on characterizing relationships between dynamic functional connectivity and behavioral features through dominant modes of cross-sectional variation.
Motwani, Shojaie, Rokem, Lila (2026) Genetic Regression Analysis of Human Brain Connectivity Using an Efficient Estimator of Genetic Covariance, Preprint.
Buenfil, Lila (2026) A correlation analysis approach to finding interpretable latent representations via conditional generative models. AISTATS.
Buenfil, Lila (2025) Asymmetric Canonical Correlation Analysis of Riemannian and High-Dimensional Data, EJS.
Statistical Inverse Problems
In many biomedical imaging problems, the quantities of interest are not observed directly but must be inferred from noisy or indirect measurements. We develop methods for recovering these latent signals by combining statistical, machine-learning, and physics-based models. One example is the physics-informed model shown below, which combines deep learning with the physics of signal propagation in MEG to obtain more accurate reconstructions of brain activity.
Lila, Peterson, Bosseler, Kutz, Taulu (2026) Biophysics-informed deep operator learning for inverse problems with application to electrophysiological source reconstruction, Preprint.
Lila, Arridge, Aston (2020) Representation and reconstruction of covariance operators in linear inverse problems, Inverse Problems.