Abstract: As tensor-valued data become increasingly common in time series analysis, there is a growing need for flexible and interpretable models that can handle high-dimensional predictors and responses across multiple modes. We propose a unified framework for high-dimensional tensor stochastic regression based on CANDECOMP/PARAFAC (CP) decomposition, which encompasses vector, matrix, and tensor responses and predictors as special cases. Tensor autoregression naturally arises as a special case within this framework. By leveraging CP decomposition, the proposed models interpret the interactive roles of any two distinct tensor modes, enabling dynamic modeling of input-output mechanisms. We develop both CP low-rank and sparse CP low-rank estimators, establish their non-asymptotic error bounds, and propose an efficient alternating minimization algorithm for estimation. Simulation studies confirm the theoretical properties and demonstrate the computational advantage. Applications to mixed-frequency macroeconomic data and spatio-temporal air pollution data reveal interpretable low-dimensional structures and meaningful dynamic dependencies. We will also discuss possible applications of the method to medical/neuroimaging at the end of the talk.

Abstract: Multisite studies offer several advantages including increased statistical power and enabling the generalization of research outcomes; however, data harmonization and standardization across different clinical domains including Positron Emission Tomography (PET) imaging and blood biomarkers continue to hinder our ability to accurately estimate differences across different clinical groups. In this study we present different harmonizations methods for PET imaging and blood biomarkers outcomes in Alzheimer’s Disease studies and show variability in effect sizes across different groups before and after harmonization methods.

Abstract: Estimation of biomarkers related to disease classification and modeling of its progression is essential for treatment development for Alzheimer’s Disease (AD). The task is more daunting for characterizing relatively rare AD subtypes such as the early-onset AD. In this talk, I will describe the Longitudinal Alzheimer’s Disease Study (LEADS) intending to collect and publicly distribute clinical, imaging, genetic, and other types of data from people with EOAD, as well as cognitively normal (CN) controls and people with early-onset non-amyloid positive (EOnonAD) dementias. I will discuss manifold estimation methods for estimation of surfaces of shapes in the brain using data clouds, factor-analytic methods for estimation of clinical biomarkers of AD and their use for modeling differences in longitudinal trajectories of clinical deterioration between CN, EOAD, and EOnonAD groups. Finally, I will discuss our work in leveraging magnetic resonance imaging and positron emission tomography data to characterize distributions of white matter hyperintensities in people with EOAD and to obtain imaging-based biomarkers of disease trajectories of AD subtypes.