On Leave-One-Out Conditional Mutual Information For Generalization
This provides a practical tool for understanding generalization in machine learning, though it is incremental as it builds on existing CMI bounds.
The paper tackles the problem of deriving information-theoretic generalization bounds for supervised learning by introducing a new measure called leave-one-out conditional mutual information (loo-CMI), which is easy to compute and interpret, and empirically validates it as non-vacuous on large-scale image-classification tasks.
We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). Contrary to other CMI bounds, which are black-box bounds that do not exploit the structure of the problem and may be hard to evaluate in practice, our loo-CMI bounds can be computed easily 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 large-scale image-classification tasks.