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About this paper
Francois-Xavier Briol, Chris J. Oates, Jon Cockayne, Wilson Ye Chen, Mark Girolami
Researchers developed Sequential Monte Carlo Kernel Quadrature (SMC-KQ), an automatic method for selecting optimal sampling distributions in Kernel Quadrature, which historically suffered from sensitive performance to sampling choices. The method reduced integration error by up to 8 orders of magnitude (4 orders of magnitude in RMSE) compared to default Kernel Quadrature, demonstrating robustness to kernel misspecification and effectiveness in complex Bayesian computation problems.
Key insights
- The optimal sampling distribution for Kernel Quadrature is often not the target distribution itself, and its choice can drastically influence integration accuracy.
- Approximating the optimal sampling distribution via a tempered sequence, where the inverse temperature parameter (t) controls the balance between a reference and target distribution, can effectively guide sample placement.
- An empirical proxy for the RMSE, derived from theoretical error bounds and monitored via a linear smoother, provides a reliable and automatic termination criterion for the adaptive search process.
Summary by alphaXiv.
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