Local Geometric Analysis and Applications to Learning Algorithms.

Local geometric analysis is a method to define a coordinate system in a small neighborhood in the space of distributions and the functional space over a given alphabet. It is a powerful technique since the notions of distance, projection, and inner product defined this way are useful in the optimization problems involving distributions, such as regressions. It has been used in many places in the literature such as correlation analysis, correspondence analysis. In this talk, we will go through some of the basic setups and properties, and discuss a specific problem we called ``universal feature selectionâ , which has close connections to some of the popular learning algorithms such as matrix completion and deep-learning. We will use this problem to motivate definitions of new information metrics for partial information and the relevance to specific queries.Non UBCUnreviewedAuthor affiliation: Massachusetts Institute of TechnologyFacult