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[2602.21357] Conditional neural control variates for variance reduction in Bayesian inverse problems
Summary
This paper presents a novel approach using conditional neural control variates to reduce variance in Bayesian inverse problems, enhancing Monte Carlo estimation efficiency.
Why It Matters
The study addresses a significant challenge in Bayesian inference for inverse problems, particularly in high-dimensional scenarios where traditional Monte Carlo methods can be inefficient. By introducing a modular method that leverages neural networks, this research has the potential to improve computational efficiency in various applications, including physics-based modeling.
Key Takeaways
- Introduces conditional neural control variates for variance reduction in Bayesian inference.
- Utilizes Stein's identity for scalable high-dimensional problem-solving.
- Demonstrates substantial variance reduction in Darcy flow inverse problems.
Statistics > Machine Learning arXiv:2602.21357 (stat) [Submitted on 24 Feb 2026] Title:Conditional neural control variates for variance reduction in Bayesian inverse problems Authors:Ali Siahkoohi, Hyunwoo Oh View a PDF of the paper titled Conditional neural control variates for variance reduction in Bayesian inverse problems, by Ali Siahkoohi and Hyunwoo Oh View PDF HTML (experimental) Abstract:Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest varies significantly under the posterior, accurate estimates demand many samples -- a cost often prohibitive for partial differential equation-constrained problems. To address this challenge, we introduce conditional neural control variates, a modular method that learns amortized control variates from joint model-data samples to reduce the variance of MC estimators. To scale to high-dimensional problems, we leverage Stein's identity to design an architecture based on an ensemble of hierarchical coupling layers with tractable Jacobian trace computation. Training requires: (i) samples from the joint distribution of unknown parameters and observed data; and (ii) the posterior score function, which can be computed from physics-based likelihood evaluations, neural operator surrogates, or learned generative models such as conditional normalizing flows....
