## Hans-Georg Müller

University of California, Davis

3:45 PM

127 Hayes-Healy Center

A reception will precede the event at 3:15 pm in 101A Crowley Hall

### Metric Profiles for the Geometric Exploration of Complex Data and Random Objects

For random objects, i.e., data taking values in a general totally bounded metric space (X,d) with a probability measure, we inrtoduce metric profiles. The metric profile of an element x of X refers to the distribution of the distances between x and the random elements of X. Since metric profiles are one-dimensional distributions, optimal transports between them are easily obtained and can be harnessed to define transport ranks, which capture the centrality of each element in X with respect to the entire data cloud. These transport ranks provide an effective device for detecting and visualizing patterns in samples of random objects and they also entail a notion of quantiles for metric space valued data. The convergence of sample based estimates to their population targets provides theoretical justification. Specific examples for the utility of transport ranks include distributional data, compositional data and network data. This talk is based on joint work with Yaqing Chen (Rutgers) and Paromita Dubey (USC).

*Dr. Hans-Georg Müller is a Distinguished Professor of Statistics at the University of California, Davis, where he has served as chair of the Department of Statistics and founding chair of the Graduate Program in Biostatistics at UC Davis. He is an elected member of ISI, and a fellow of IMS, ASA and the American Association for the Advancement of Science.*

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