Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
This work addresses computational bottlenecks in uncertainty quantification for machine learning practitioners, though it represents an incremental improvement over existing Monte Carlo dropout methods.
The paper tackles the computational inefficiency of Monte Carlo dropout for uncertainty quantification by developing a multilevel Monte Carlo framework that reuses dropout masks across fidelity levels. This approach reduces sampling variance while maintaining unbiased estimates, achieving efficiency gains over standard single-level methods in numerical experiments on PINNs-Uzawa benchmarks.
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.