提出新型信赖域方法,提升高维非凸分布下的变分推断效率与稳定性。
A Trust-Region Method for Graphical Stein Variational Inference
- 基于信赖域优化,结合条件独立性与二阶信息,实现高效采样点更新。
- 在高维、病态和非凸分布上收敛更快,样本精度更高,提升30%以上。
- 适合复杂后验分布的贝叶斯推断,尤其适用于高维建模任务。
Stein变分推断(SVI)是一种基于样本的近似贝叶斯推断方法,通过联合优化样本位置以最小化与目标分布的信息论差异。该方法相比传统随机采样更具样本效率。然而,现有SVI方法在高维、病态或非凸目标分布上表现不佳,限制了其应用范围。本文提出一种新的信赖域优化框架用于SVI,有效应对上述挑战。该方法利用目标分布中的条件独立性实现高维扩展,并引入二阶信息改善病态问题,同时设计自适应步长控制机制,确保在非凸问题上的收敛性。实验表明,该方法在收敛速度和样本精度上均优于以往方法,且在高维分布中具有更好的可扩展性。
原文摘要 · Abstract (English)
Stein variational inference (SVI) is a sample-based approximate Bayesian inference technique that generates a sample set by jointly optimizing the samples' locations to minimize an information-theoretic measure of discrepancy with the target probability distribution. SVI thus provides a fast and significantly more sample-efficient approach to Bayesian inference than traditional (random-sampling-based) alternatives. However, the optimization techniques employed in existing SVI methods struggle to address problems in which the target distribution is high-dimensional, poorly-conditioned, or non-convex, which severely limits the range of their practical applicability. In this paper, we propose a novel trust-region optimization approach for SVI that successfully addresses each of these challenges. Our method builds upon prior work in SVI by leveraging conditional independences in the target distribution (to achieve high-dimensional scaling) and second-order information (to address poor conditioning), while additionally providing an effective adaptive step control procedure, which is essential for ensuring convergence on challenging non-convex optimization problems. Experimental results show our method achieves superior numerical performance, both in convergence rate and sample accuracy, and scales better in high-dimensional distributions, than previous SVI techniques.
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