| Autor: |
Franzese, Giulio, Milios, Dimitrios, Filippone, Maurizio, Michiardi, Pietro |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We revisit the theoretical properties of Hamiltonian stochastic differential equations (SDES) for Bayesian posterior sampling, and we study the two types of errors that arise from numerical SDE simulation: the discretization error and the error due to noisy gradient estimates in the context of data subsampling. Our main result is a novel analysis for the effect of mini-batches through the lens of differential operator splitting, revising previous literature results. The stochastic component of a Hamiltonian SDE is decoupled from the gradient noise, for which we make no normality assumptions. This leads to the identification of a convergence bottleneck: when considering mini-batches, the best achievable error rate is $\mathcal{O}(\eta^2)$, with $\eta$ being the integrator step size. Our theoretical results are supported by an empirical study on a variety of regression and classification tasks for Bayesian neural networks. |
| Databáze: |
arXiv |
| Externí odkaz: |
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