Herman Rubin Memorial Lecture
11-11-2024
Date: Friday, November 15 , 2024
Time: 10:30 – 11:20 a.m.
Location: Wilmeth Active Learning Center 1132
Distance Profiles for Random Objects, with Applications to Metric Data Analysis and Conformal Inference
Abstract:
The underlying probability measure of random objects situated in a metric measure space (such as distributions, networks, high-dimensional vectors and other complex objects) can be characterized by distance profiles that correspond to one-dimensional distributions of probability mass falling into balls of increasing radius under mild regularity conditions.
Harvesting pairwise optimal transports between distance profiles leads to a measure of centrality for random objects that is useful for data analysis in metric spaces. In the presence of Euclidean (vector) predictors, conditional average transport costs to transport a given distance profile to all other distance profiles can serve as a conditional conformity score. In conjunction with the split conformal algorithm these scores lead to conditional prediction sets with asymptotic conditional validity. This presentation is based on joint work with Yaqing Chen (Rutgers) and Paromita Dubey (USC), and with Hang Zhou (Davis).
Bio:
Hans-Georg Müller is a Professor in the Department of Statistics at the University of California, Davis. He has served as Chair of the Department of Statistics, founding chair of the Graduate Program in Biostatistics at UC Davis and co-editor of Statistica Sinica. Over the years he has been engaged in various biomedical research consortia, aiming to quantify brain and neurocognitive development from brain imaging data, to sequence the wheat genome, and to model aging, longevity and human mortality, with support from NIH, NSF and the Bill and Melinda Gates Foundation. His contributions to statistics include early work on smoothing methods for nonparametric regression and density estimation, methodology for growth curves and change-points, and semiparametric and structured modeling in regression. He then devoted major efforts to develop the theoretical and methodological foundations for functional data analysis, notably functional principal component analysis, empirical dynamics, time warping and functional regression, and also to build a bridge between functional and longitudinal data analysis, aligning these two areas. In his recent research, he is developing concepts and methods for the emerging field of statistical analysis and inference for random objects, including distributional data analysis and transport regression