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On Leave-One-Out Conditional Mutual Information For Generalization
Mohamad Rida Rammal · Alessandro Achille · Aditya Golatkar · Suhas Diggavi · Stefano Soatto


We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). In contrast to other CMI bounds, which may be hard to evaluate in practice, our loo-CMI bounds are easier to compute and can be interpreted in connection to other notions such as classical leave-one-out cross-validation, stability of the optimization algorithm, and the geometry of the loss-landscape. It applies both to the output of training algorithms as well as their predictions. We empirically validate the quality of the bound by evaluating its predicted generalization gap in scenarios for deep learning. In particular, our bounds are non-vacuous on image-classification tasks.

Author Information

Mohamad Rida Rammal (University of California, Los Angeles)
Alessandro Achille (AWS)
Aditya Golatkar (University of California, Los Angeles)
Suhas Diggavi (UCLA)
Stefano Soatto (UCLA)

Stefano Soatto received his Ph.D. in Control and Dynamical Systems from the California Institute of Technology in 1996; he joined UCLA in 2000 after being Assistant and then Associate Professor of Electrical Engineering and Biomedical Engineering at Washington University, and Research Associate in Applied Sciences at Harvard University. Between 1995 and 1998 he was also Ricercatore in the Department of Mathematics and Computer Science at the University of Udine - Italy. He received his D.Ing. degree (highest honors) from the University of Padova- Italy in 1992. His general research interests are in Computer Vision and Nonlinear Estimation and Control Theory. In particular, he is interested in ways for computers to use sensory information to interact with humans and the environment. Dr. Soatto is the recipient of the David Marr Prize for work on Euclidean reconstruction and reprojection up to subgroups. He also received the Siemens Prize with the Outstanding Paper Award from the IEEE Computer Society for his work on optimal structure from motion. He received the National Science Foundation Career Award and the Okawa Foundation Grant. He is a Member of the Editorial Board of the International Journal of Computer Vision (IJCV) and Foundations and Trends in Computer Graphics and Vision. He is the founder and director of the UCLA Vision Lab; more information is available at http://vision.ucla.edu

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