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构成了机器学习、人工智能和自然科学的重要组成部分。人们不需要花很长时间就能在方法论的前沿和日常的科学追求中找到这样的算法。Wang-Landau算法就是一个例子。它将抽样步骤和学习步骤结合起来，学习我们所知有限的概率分布。例如，概率分布可能是在物理状态上的，因此高效运行的算法将允许模拟蛋白质折叠的动力学。学习步骤结合了从采样步骤获得的信息，形成了更完整的分布图景。学习步骤的特殊形式在许多神经网络中是基本的，称为随机逼近。由于我们对分布的了解不完全，我们不能采用标准的抽样方法。因此，我们需要使用一种更奇特的采样器。将奇特采样器与随机近似相结合还没有得到充分的探索，而且可能是卓有成效的。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.