On Using Graph Distances to Estimate Euclidean and Related Distances

Abstract:  Graph distances have proven quite useful in machine learning/statistics, particularly in the estimation of Euclidean or geodesic distances. The talk will include a partial review of the literature, and then present more recent developments on the estimation of curvature-constrained distances on a surface, as well as on the estimation of Euclidean distances based on an unweighted and noisy neighborhood graph.

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About the Speaker:  Ery Arias-Castro received his Ph.D. in Statistics from Stanford University in 2004. He then took a postdoctoral position at the Institute for Pure and Applied Mathematics (IPAM), where he participated in the program on Multiscale Geometry and Analysis in High Dimensions. After that, he took a postdoctoral position at the Mathematical Sciences Research Institute (MSRI), where he participated in the program on Mathematical, Computational and Statistical Aspects of Image Analysis. He joined the faculty in the mathematics department at UCSD in 2005. His research interests are in high-dimensional statistics, machine learning, spatial statistics, image processing, and applied probability.