淬火系综采样
Quenched Ensemble Sampling
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中文总结 AI 辅助
本文提出淬火系综采样，通过将硬约束推广为排斥势，在相变处高效采样，估计边际似然与配分函数，并应用于贝叶斯神经网络模型比较。
中文摘要 AI 辅助
在从物理系统的能量函数中进行采样时，一些最尖锐的挑战出现在相变处，此时态密度发生突变，许多采样算法停滞不前。嵌套采样是一种粒子方法，在硬能量约束下遍历态密度，已知其对这种相变具有鲁棒性，但其在高维中的应用受到在该约束下采样难度的限制。在这项工作中，我们引入了淬火系综采样，它将硬约束推广为能量边界处的一族排斥势。这保留了能量单调递减的淬火路径，同时使受约束的目标适用于可扩展的基于梯度的核。我们在合成的相变模型上证明，我们的方法能够估计边际似然，并在一个一阶相变中抽取后验样本，而诸如回火之类的流行替代方法在此失败。我们将该程序应用于贝叶斯神经网络中的边际似然估计，使得能够在网络架构之间进行模型比较。最后，在高维连续格点场论中，我们展示了该方法穿越一阶相变并估计配分函数。
英文摘要
Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states changes abruptly and many sampling algorithms stall. Nested sampling is a particle method that traverses the density of states under a hard energy constraint and is known to be robust to such transitions, but its application in high dimension is limited by the difficulty of sampling under that constraint. In this work we introduce Quenched Ensemble Sampling, which generalises the hard constraint to a family of repulsive potentials at the energy boundary. This preserves the quenched path of monotonically decreasing energy while making the constrained target amenable to scalable gradient-based kernels. We demonstrate on synthetic models of phase transitions that our method estimates the marginal likelihood and draws posterior samples across a first-order transition where popular alternatives such as tempering fail. We apply the procedure to marginal likelihood estimation in Bayesian neural networks, enabling model comparison between network architectures. Finally, in a high-dimensional continuous lattice field theory, we show that this method traverses a first-order transition and estimates the partition function.
发表机构
- Kavli Institute for Cosmology Cambridge（剑桥卡夫利宇宙学研究所）
- Institute of Astronomy, University of Cambridge（剑桥大学天文研究所）
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