The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schr\"odinger bridge remain an active area of research. We prove an equivalence between the SBP and maximum likelihood estimation enabling direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.

翻译：Schr\'odinger桥问题(SBP)发现,在先前的随机进化中,两种概率分布之间最有可能发生随机变化。除了自然科学的应用之外,这类问题在机器学习中也有重要的应用,如数据集校正和假设测试。虽然这一问题背后的理论相对成熟,但估计Schr\'odinger桥的可缩放数字方法仍然是一个活跃的研究领域。我们证明,SBP和最大概率估计是等同的,能够直接应用成功的机器学习技术。我们提议了一个数字程序,利用高山进程估算SBPs,并展示我们在数字模拟和实验中的实际使用方法。