Conditional Bayesian Quadrature
This work addresses a computational bottleneck for researchers and practitioners in fields like Bayesian analysis and finance where expensive evaluations are common, offering an incremental improvement over existing probabilistic numerical methods.
The paper tackles the problem of estimating conditional expectations when sampling or evaluating integrands is expensive, proposing a Bayesian quadrature approach that incorporates prior smoothness information about the integrands and conditional expectations. The result is a method that quantifies uncertainty and achieves fast convergence rates, validated theoretically and empirically on tasks in Bayesian sensitivity analysis, computational finance, and decision-making under uncertainty.
We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian quadrature), our novel approach allows to incorporates prior information about the integrands especially the prior smoothness knowledge about the integrands and the conditional expectation. As a result, our approach provides a way of quantifying uncertainty and leads to a fast convergence rate, which is confirmed both theoretically and empirically on challenging tasks in Bayesian sensitivity analysis, computational finance and decision making under uncertainty.