Algorithmic and dynamical stability #
This entrypoint collects the stability chapter. We keep three pieces together because they are often used in the same arguments, while still leaving each piece in its own source file:
Stability.Coredefines datasets, replace-one/remove-one perturbations, learning maps, losses, population error, empirical error, and standard algorithmic-stability notions.Stability.Dynamicsgives the discrete-time dynamical-system vocabulary used by recurrent models, samplers, and stability diagnostics.Stability.RidgeRegression1Dis the worked theorem development: a concrete, fully proved stability analysis for bounded one-dimensional ridge regression.
References:
- Bousquet and Elisseeff, "Stability and Generalization", JMLR 2002.
- Shalev-Shwartz et al., "Learnability, Stability and Uniform Convergence", JMLR 2010.
- Hardt, Recht, and Singer, "Train faster, generalize better: Stability of stochastic gradient descent", ICML 2016.