Inverse Problems and Learning Machines: stable solutions are predictive (and vice versa for ERM)

Tomaso Poggio
Massachusetts Institute of Technology
Brain and Cognitive Sciences

I will outline recent work on learning theory and inverse problems
(with P. Niyogi, S. Mukherjee and R. Rifkin). Solutions of learning problems by Empirical Risk Minimization (ERM) need to be consistent, so that they may be predictive. They also need to be
well-posed, so that they might be used robustly. We define a statistical form of well-posedness, in terms of CVEEE stability. Our two main results are a) CVEEE stability implies generalization for any general symmetric learning algorithm and b) CVEEE stability of ERM is necessary and sufficient for consistency of ERM. I will conclude describing examples applications of learning algorithms in various domains -- such as visual recognition,
computer graphics and bioinformatics.


Relevant papers can be downloaded from
http://www.ai.mit.edu/projects/cbcl/publications/all-year.html)

Presentation (PDF File)

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