We introduce topological mixture estimation, a completely nonparametric and computationally efficient solution to the problem of estimating a one-dimensional mixture with generic unimodal components. We repeatedly perturb the unimodal decomposition of Baryshnikov and Ghrist to produce a topologically and information-theoretically optimal unimodal mixture. We also detail a smoothing process that optimally exploits topological persistence of the unimodal category in a natural way when working directly with sample data. Finally, we illustrate these techniques through examples.
Steve Huntsman (BAE Systems FAST Labs)
Steve Huntsman is a mathematician whose work focuses on discrete geometric and probabilistic themes in physics, computation, and communication. Before joining BAE Systems, he initiated a data science program for a government organization. Previously he founded a network security startup applying methods from nonequilibrium statistical physics and was co-PI on the DARPA Scalable Network Monitoring program. He began his career as a researcher at the Institute for Defense Analyses and the Naval Postgraduate School.
Related Events (a corresponding poster, oral, or spotlight)
2018 Oral: Topological mixture estimation »
Fri Jul 13th 09:40 -- 09:50 AM Room A6