A vector-contraction inequality for Rademacher complexities
This work provides a theoretical tool for analyzing generalization bounds in machine learning, particularly for vector-valued problems, but it is incremental as it builds on existing contraction inequalities.
The paper extends the contraction inequality for Rademacher averages to Lipschitz functions with vector-valued domains and generalizes the bounding expression to arbitrary iid symmetric and sub-gaussian variables, with applications in multi-category learning, K-means clustering, and learning-to-learn.
The contraction inequality for Rademacher averages is extended to Lipschitz functions with vector-valued domains, and it is also shown that in the bounding expression the Rademacher variables can be replaced by arbitrary iid symmetric and sub-gaussian variables. Example applications are given for multi-category learning, K-means clustering and learning-to-learn.