Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification

• URL: http://arxiv.org/abs/2601.13272v1
• Date: Mon, 19 Jan 2026 18:17:25 GMT
• Title: Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
• Authors: Aaron Pim, Tristan Pryer,
• Abstract summary: We develop multilevel Monte Carlo (MLMC) framework for uncertainty quantification.<n>Treat dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of forward passes used to estimate predictive moments.<n>We derive explicit bias, variance and effective cost expressions, together with sample-allocation rules across levels.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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