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Fall 2013 GRASP Seminar: Aleix Martinez, Ohio State University, "My Adventures With Bayes: Searching For Bayes Optimal Solutions In Machine Learning, Statistics, Computer Vision, Neuroscience And Beyond"
Presenter: Aleix Martinez (Homepage)
Friday September 20, 2013 from 11:00am to 12:00pm
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 vision and others. We will first derive Bayes optimal solutions in Discriminant Analysis. We will then extend the notion of homoscedasticity (meaning of the same variance) to spherical-homoscedasticity (meaning of the same variance up to a rotation) and show how this allows us to generalize the Bayes criterion beyond previously defined domains. This will lead to a new concept of kernel mappings with applications in classification (machine learning), shape analysis (statistics), and structure from motion (computer vision). We will conclude with an outline of ongoing research for nonparametric kernel learning.
Aleix M. Martinez is an associate professor in the Department of Electrical and Computer Engineering at The Ohio State University (OSU), where he is the founder and director of the Computational Biology and Cognitive Science Lab. He is also affiliated with the Department of Biomedical Engineering and to the Center for Brain and Cognitive Science where he is a member of the executive committee. Aleix has served as an associate editor of IEEE Transactions on Pattern Analysis and Machine Intelligence, Image and Vision Computing, and Computer Vision and Image Understanding of which he currently serves as the editor-in-chief. He has been an area chair for many top conferences and is currently a Program co-Chair for CVPR 2014.