Estimating optimal PAC-Bayes bounds with Hamiltonian Monte Carlo

Autor:	Ujváry, Szilvia, Flamich, Gergely, Fortuin, Vincent, Lobato, José Miguel Hernández
Rok vydání:	2023
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning G.3
Druh dokumentu:	Working Paper
Popis:	An important yet underexplored question in the PAC-Bayes literature is how much tightness we lose by restricting the posterior family to factorized Gaussian distributions when optimizing a PAC-Bayes bound. We investigate this issue by estimating data-independent PAC-Bayes bounds using the optimal posteriors, comparing them to bounds obtained using MFVI. Concretely, we (1) sample from the optimal Gibbs posterior using Hamiltonian Monte Carlo, (2) estimate its KL divergence from the prior with thermodynamic integration, and (3) propose three methods to obtain high-probability bounds under different assumptions. Our experiments on the MNIST dataset reveal significant tightness gaps, as much as 5-6\% in some cases. Comment: Mathematics of Modern Machine Learning Workshop at NeurIPS 2023
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.20053 Zobrazit plný text záznamu View this record from Arxiv