Research map / Probabilistic and scientific modeling / Variational and generative sampling
On the Sampling Problem for Kernel Quadrature
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Select a tempered sampling distribution using SMC instead of sampling directly from the target | KQ · Gaussian toy integration, f(x)=1+sin(2πx) | MSE: about 8 orders of magnitude | Helped |
| Select a tempered sampling distribution using SMC instead of sampling directly from the target | KQ · ODE inverse problem (Hooke's law) | integration error | Helped |
| Use a heavier-tailed sampling distribution than the target (ablation) | KQ · Gaussian toy integration, f(x)=1+sin(2πx) | RMSE | Helped |
| Learn kernel parameters in addition to adapting the sampling distribution (ablation) | SMC-KQ · Gaussian toy integration, f(x)=1+sin(2πx) | MSE | Helped |
| Vary the Gaussian kernel length scale (ablation) | KQ · Gaussian toy integration | RMSE | Mixed |
| Vary the initial reference distribution Π₀ (ablation) | SMC-KQ · Gaussian toy integration | RMSE | No clear effect |
| Use SMC-KQ on higher-periodicity integrands (ablation) | KQ · Gaussian integration with f(x)=1+sin(4πx) and 1+sin(8πx) | integration error | Helped |
| Increase the integration dimension (ablation) | SMC-KQ · Gaussian integration, d=2 and d=3 | integration error | Helped |
| Replace independent random points with Halton quasi-random points (ablation) | Tempered KQ · Gaussian toy integration | MSE: up to 10 orders of magnitude | Helped |
Closest papers by meaning
- A Quadrature Rule combining Control Variates and Adaptive Importance Sampling (NeurIPS 2022 · similarity 0.88)
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- Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion (NeurIPS 2024 · similarity 0.83)
- Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization (AAAI 2024 · similarity 0.83)
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