Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling
This addresses a bottleneck in Bayesian statistics for researchers and practitioners by providing a more efficient debiased inference algorithm, though it is incremental as it builds on existing MLMC techniques.
The paper tackles the computational cost of debiasing estimators for model evidence in Bayesian inference by proposing a multilevel Monte Carlo (MLMC) sampling method, achieving an order-of-magnitude reduction in computational cost compared to previous estimators.
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic objectives because the existing debiasing techniques are computationally costly to apply. To overcome this issue, we apply an MLMC sampling technique to construct low-variance unbiased estimators both for the model evidence and its gradient. In the theoretical analysis, we show that the computational cost required for our proposed MLMC estimator to estimate the model evidence or its gradient with a given accuracy is an order of magnitude smaller than those of the previously known estimators. Our numerical experiments confirm considerable computational savings compared to the conventional estimators. Combining our MLMC estimator with gradient-based stochastic optimization results in a new scalable, efficient, debiased inference algorithm for Bayesian statistical models.