Old Clark Road, Old Clark Rd, Hanover, MD 21076, USA
Title: My Adventured with Bayes: In search of optimal solutions in machine learning, computervision and beyond
Abstract: The Bayes criterion is generally regarded as the holy grail in classification because, for known distributions, it leads to the smallest possible classification error. Unfortunately, the Bayes classification boundary is generally nonlinear and its associated error can only be calculated under unrealistic assumptions. In this talk, we will show how these obstacles can be readily and efficiently averted yielding Bayes optimal algorithms in machine learning, statistics, computer visionand other areas of scientific inquiry. In this journey, we will extend the notion of homoscedasticity (meaning of the same variance) to spherical-homoscedasticity (meaning of the same variance up to a rotation) and show howthis allows us to generalize the Bayes criterion under more realistic assumptions. This will lead to a new concept of kernel mappings with applications in classification (machine learning), shape analysis (statistics), structure from motion (computer vision), brain alignment (neuroscience), andothers. We will then define other optimization criteria where Bayes cannotbe readily applied and define the use of kernels in labeled graphs.