In this paper we investigate the efficacy of the score-based martingale posteriors (SMP) (Cui & Walker, 2025; Fong et al., 2023) in the context of modern and large-scale machine learning problems and its potential for meaningful uncertainty quantification. SMPs work with a stochastic gradient ascent-type recursion on the parameter space of stochastic models and construct a martingale on the parameter space. Under simple mathematical assumptions, the recursion can be built so that the parameters form a martingale sequence which possesses a limiting, in time, random variable, the latter of which can be simulated very quickly, in contrast to Monte Carlo-based methods such as Markov chain Monte Carlo. In this expository paper we explore the SMP for inferring the parameters of deep neural networks (DNNs) and, where feasible, compare our results to the state-of-the-art Monte Carlo methods aimed at inferring conventional Bayesian posteriors.

翻译：本文研究了基于分数的鞅后验分布（SMP）（Cui & Walker, 2025；Fong 等, 2023）在现代化大规模机器学习问题中的有效性及其在不确定性量化方面的潜在能力。SMP方法在随机模型的参数空间上采用随机梯度上升型递归，并在参数空间上构造一个鞅。在简单的数学假设下，可以构建该递归使得参数形成一个鞅序列，该序列存在一个随时间变化的极限随机变量，后者相较于马尔可夫链蒙特卡洛等基于蒙特卡洛的方法，能够被极快地模拟。在这篇论述性论文中，我们探讨了SMP在推断深度神经网络（DNN）参数中的应用，并在可行的情况下，将我们的结果与旨在推断传统贝叶斯后验分布的最先进的蒙特卡洛方法进行了比较。