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CORR
2010
Springer

On the Stability of Empirical Risk Minimization in the Presence of Multiple Risk Minimizers

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On the Stability of Empirical Risk Minimization in the Presence of Multiple Risk Minimizers
Abstract--Recently Kutin and Niyogi investigated several notions of algorithmic stability--a property of a learning map conceptually similar to continuity--showing that training-stability is sufficient for consistency of Empirical Risk Minimization while distribution-free CV-stability is necessary and sufficient for having finite VC-dimension. This paper concerns a phase transition in the training stability of ERM, conjectured by the same authors. Kutin and Niyogi proved that ERM on finite hypothesis spaces containing a unique risk minimizer has training stability that scales exponentially with sample size, and conjectured that the existence of multiple risk minimizers prevents even super-quadratic convergence. We prove this result for the strictly weaker notion of CV-stability, positively resolving the conjecture.
Benjamin I. P. Rubinstein, Aleksandr Simma
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Benjamin I. P. Rubinstein, Aleksandr Simma
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