When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by exploiting their inherent statistical nature. We propose algorithms that exploit the redundancy of data relative to a model by subsampling data-cases for every update and reasoning about the uncertainty created in this process. In the context of learning we propose to test for the probability that a stochastically estimated gradient points more than 180 degrees in the wrong direction. In the context of MCMC sampling we use stochastic gradients to improve the efficiency of MCMC updates, and hypothesis tests based on adaptive mini-batches to decide whether to accept or reject a proposed parameter update. Finally, we argue that in the context of likelihood free MCMC one needs to store all the information revealed by all simulations, for instance in a Gaussian process. We conclude that Bayesian methods will remain to play a crucial role in the era of big data and big simulations, but only if we overcome a number of computational challenges.

该研究论文探讨了在面对包含海量数据集和需要超级计算机执行的模拟时，如何利用数据与模型之间的固有统计学特性来提高学习和推理的效率，并提出了相应的基于随机梯度的算法来检测概率、提高MCMC的更新效率和决定参数更新的接受或拒绝，同时探讨了在大数据和大模拟时代中Bayesian方法所面临的一些计算方面的挑战。

利用学习和推理的统计数据