An Investigation into Coupling a Stochastic Approximation with a Pseudo-Marginal Sampler

EPSRC: Max Hird: EP/ t517793 /1从概率分布中学习和采样的算法是机器学习、人工智能和自然科学的重要组成部分。在方法论的前沿和日常的科学追求中，人们不需要找太远就能找到这样的算法。Wang-Landau算法就是一个例子。它结合了采样步骤和学习步骤，来学习我们知识有限的概率分布。概率分布可能超过物理状态，所以一个有效运行的算法将允许模拟蛋白质折叠的动力学，例如。学习步骤结合了从抽样步骤中获得的信息，形成了更完整的分布图像。学习步骤的特殊形式是许多神经网络的基础，称为随机逼近。由于我们对分布的了解不完全，我们不能采用标准抽样方法。因此，我们需要使用更奇特的采样器。将外来采样器与随机近似相结合的方法尚未得到充分探索，并且可能富有成果。我们将尝试评估这种耦合的行为，这是文献中尚未存在的评估。

EPSRC : Max Hird : EP/T517793/1Algorithms that learn and sample from probability distributions form an important part of machine learning, AI, and the natural sciences. One needn't look far to find such algorithms at the bleeding edge of methodology, and in everyday scientific pursuit. The Wang-Landau algorithm is an example. It combines a sampling step with a learning step, to learn a probability distribution about which our knowledge is limited. The probability distribution may be over physical states, so an efficiently running algorithm would allow the simulation of the dynamics of protein folding, for instance.The learning step incorporates information gained from the sampling step, forming a more complete picture of the distribution. The particular form of the learning step is foundational in many neural networks and is called stochastic approximation. Due to our incomplete knowledge of the distribution, we cannot apply standard sampling methods. We therefore need to employ a more exotic sampler.Coupling exotic samplers alongside stochastic approximation is underexplored, and potentially fruitful. We will try to assess the behaviour of such a coupling, an assessment not yet existing in the literature.