Reproduce “Stein Points” on OpenResearch
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About this paper
Wilson Ye Chen, Lester Mackey, Jackson Gorham, François-Xavier Briol, Chris J. Oates
Researchers introduce Stein Points, a deterministic method for approximating un-normalised probability distributions, like Bayesian posteriors, using a small set of representative points. This approach iteratively minimizes the Kernel Stein Discrepancy, generating more uniformly spread point sets compared to MCMC for modest numbers of points and demonstrating convergence rates of O(√(log(n)/n)).
Key insights
- The Kernel Stein Discrepancy (KSD) can effectively serve as an objective function for deterministic point set construction, enabling accurate approximation of un-normalised target distributions.
- Stein Point methods, particularly the greedy variant, produce more spread-out and representative point sets compared to MCMC, mitigating the issue of sample clustering for small 'n'.
- Theoretical analysis confirms that KSDs constructed with the new inverse log and IMQ score kernels control weak convergence, formally linking KSD minimization to improved distributional approximation.
Summary by alphaXiv.
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