Dr Ruriko Yoshida
Speaker
Naval Postgraduate School, California
Dr. Ruriko Yoshida is an Associate Professor of Operations Research at the Naval Postgraduate School. Her research topics cover a wide variety of areas: applications of algebraic combinatorics to statistical problems, such as goodness of fit tests, optimized camera placement in sensor networks, phylogenetics, and phylogenomics. Dr. Yoshida received her Ph.D. (2004) in Mathematics from the University of California, Davis. She then went to the University of California, Berkeley as a postdoctoral researcher, and then Duke University for her postdoctoral research from 2004 to 2006. She was at the University of Kentucky from 2006 to 2016 as an assistant and then as associate professor. In 2016, she joined the operations research department at the Naval Postgraduate School.
Talk
Tropical Support Vector Machines
Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical metric with the max-plus algebra. In this talk, we show generalization error bounds of tropical SVMs over the tropical projective space. While the generalization error bounds attained via VC dimensions in a distribution-free manner still depend on the dimension, we also show theoretically by extreme value statistics that the tropical SVMs for classifying data points from two Gaussian distributions as well as empirical data sets of different neuron types are fairly robust against the curse of dimensionality. Extreme value statistics also underlie the anomalous scaling behaviors of the tropical distance between random vectors with additional noise dimensions.