Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914265148948480 |
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| author | Pim, Aaron Pryer, Tristan |
| author_facet | Pim, Aaron Pryer, Tristan |
| contents | We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward passes used to estimate predictive moments. We construct coupled coarse--fine estimators by reusing dropout masks across fidelities, yielding telescoping MLMC estimators for both predictive means and predictive variances that remain unbiased for the corresponding dropout-induced quantities while reducing sampling variance at fixed evaluation budget. We derive explicit bias, variance and effective cost expressions, together with sample-allocation rules across levels. Numerical experiments on forward and inverse PINNs--Uzawa benchmarks confirm the predicted variance rates and demonstrate efficiency gains over single-level MC-dropout at matched cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13272 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification Pim, Aaron Pryer, Tristan Machine Learning Computation We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward passes used to estimate predictive moments. We construct coupled coarse--fine estimators by reusing dropout masks across fidelities, yielding telescoping MLMC estimators for both predictive means and predictive variances that remain unbiased for the corresponding dropout-induced quantities while reducing sampling variance at fixed evaluation budget. We derive explicit bias, variance and effective cost expressions, together with sample-allocation rules across levels. Numerical experiments on forward and inverse PINNs--Uzawa benchmarks confirm the predicted variance rates and demonstrate efficiency gains over single-level MC-dropout at matched cost. |
| title | Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification |
| topic | Machine Learning Computation |
| url | https://arxiv.org/abs/2601.13272 |