Speaker: Shuoyang Wang (University of Louisville, Department of Bioinformatics and Biostatistics)

 

Title: Deep Learning for Complex Functional Data Analysis

 

Abstract: Functional data are realizations of random functions observed over a continuum, such as signals and images. In many modern applications, including neuroscience and biomedical research, observations are more naturally represented as random functions rather than finite dimensional vectors. The intrinsic complexity of such data stems from high dimensional functional domains, cross cohort heterogeneity, and unknown data generating distributions, which together complicate principled modeling and performance guarantees. Although deep learning has shown strong empirical performance in biomedical studies, its methodological and theoretical foundations for complex functional data settings remain limited.

 

In this talk, I will present two methodological contributions that develop principled deep learning frameworks for complex functional data. First, I will introduce a federated deep learning approach for functional data classification across multiple heterogeneous cohorts. The learner visits each cohort once, performs local updates, and transmits only compressed model weights, thereby preserving privacy and reducing communication and computational costs. To address cross cohort heterogeneity, we develop an adaptive sequential weight updating strategy that progressively corrects distributional shifts and improves performance on a target cohort. We establish minimax optimal excess risk bounds and characterize a sharp sampling threshold governing learnability under both densely and sparsely observed functional data. Second, I will present a deep learning based functional graphical modeling framework for learning conditional independence structures in multivariate functional data. Each node’s neighborhood is estimated via flexible functional regression with embedded feature selection, allowing a fully nonparametric specification, and the overall graph is recovered by aggregating the neighborhood estimates. The method avoids restrictive distributional assumptions and does not rely on a well-defined functional precision operator. We prove global model selection consistency and establish convergence rates that attain the classical nonparametric regression rate up to a logarithmic factor, with a fundamental sampling threshold determining the estimator’s convergence behavior. Empirical performance is demonstrated through simulations and real data applications, including analyses of ADNI dataset and the ADHD-200 Consortium.