We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is exceptionally challenging even with small datasets but simulation is straightforward. We use data from model simulations as input and train deep neural networks to learn statistical parameters. Our neural-network-based method provides a competitive alternative to current approaches, as demonstrated by considerable accuracy and computational time improvements. It serves as a proof of concept for deep learning in statistical parameter estimation and can be extended to other estimation problems.

翻译：我们提议在无法计算标准概率估算方法时,利用深层次的学习来估计统计模型的参数。我们展示了如何从最高稳定过程估算参数,在这种过程中,即使使用小数据集,推论也极具挑战性,但模拟是直截了当的。我们使用模型模拟数据作为输入,并训练深层神经网络学习统计参数。我们基于神经网络的方法为当前方法提供了一个有竞争力的替代方法,以相当的准确性和计算时间的改进为证明。它可以作为在统计参数估算中深层学习的概念的证明,并可以扩展到其他估算问题。