A strongly quasiconvex PAC-Bayesian bound
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A strongly quasiconvex PAC-Bayesian bound. / Thiemann, Niklas; Igel, Christian; Wintenberger, Olivier; Seldin, Yevgeny.
Proceedings of International Conference on Algorithmic Learning Theory, 15-17 October 2017, Kyoto University, Kyoto, Japan . red. / Steve Hanneke; Lev Reyzin. Proceedings of Machine Learning Research, 2017. s. 466-492 (Proceedings of Machine Learning Research, Bind 76).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - A strongly quasiconvex PAC-Bayesian bound
AU - Thiemann, Niklas
AU - Igel, Christian
AU - Wintenberger, Olivier
AU - Seldin, Yevgeny
PY - 2017
Y1 - 2017
N2 - We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution and its complexity. The complexity is measured by the Kullback-Leibler divergence to a prior. We derive an alternating procedure for minimizing the bound. We show that the bound can be rewritten as a one-dimensional function of the trade-off parameter and provide sufficient conditions under which the function has a single global minimum. When the conditions are satisfied the alternating minimization is guaranteed to converge to the global minimum of the bound. We provide experimental results demonstrating that rigorous minimization of the bound is competitive with cross-validation in tuning the trade-off between complexity and empirical performance. In all our experiments the trade-off turned to be quasiconvex even when the sufficient conditions were violated.
AB - We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution and its complexity. The complexity is measured by the Kullback-Leibler divergence to a prior. We derive an alternating procedure for minimizing the bound. We show that the bound can be rewritten as a one-dimensional function of the trade-off parameter and provide sufficient conditions under which the function has a single global minimum. When the conditions are satisfied the alternating minimization is guaranteed to converge to the global minimum of the bound. We provide experimental results demonstrating that rigorous minimization of the bound is competitive with cross-validation in tuning the trade-off between complexity and empirical performance. In all our experiments the trade-off turned to be quasiconvex even when the sufficient conditions were violated.
M3 - Article in proceedings
T3 - Proceedings of Machine Learning Research
SP - 466
EP - 492
BT - Proceedings of International Conference on Algorithmic Learning Theory, 15-17 October 2017, Kyoto University, Kyoto, Japan
A2 - Hanneke, Steve
A2 - Reyzin, Lev
PB - Proceedings of Machine Learning Research
T2 - The 28th International Conference on Algorithmic Learning Theory (ALT)
Y2 - 15 October 2017 through 17 October 2017
ER -
ID: 197764786