A Distribution Dependent and Independent Complexity Analysis of Manifold Regularization [article]

Alexander Mey, Tom Viering, Marco Loog
2019 arXiv   pre-print
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for models that add a convex data dependent regularization term to a supervised learning process, as is in particular done in Manifold regularization. We then compare the bound for those semi-supervised methods to purely supervised methods, and discuss a setting in
more » ... hich the semi-supervised method can only have a constant improvement, ignoring logarithmic terms. By viewing Manifold regularization as a kernel method we then derive Rademacher bounds which allow for a distribution dependent analysis. Finally we illustrate that these bounds may be useful for choosing an appropriate manifold regularization parameter in situations with very sparsely labeled data.
arXiv:1906.06100v2 fatcat:k644o3i3e5fdtfht25k7ytthou