The generative adversarial networks (GANs) have recently been applied to estimating the distribution of independent and identically distributed data, and have attracted a lot of research attention. In this paper, we use the blocking technique to demonstrate the effectiveness of GANs for estimating the distribution of stationary time series. Theoretically, we derive a non-asymptotic error bound for the Deep Neural Network (DNN)-based GANs estimator for the stationary distribution of the time series. Based on our theoretical analysis, we propose an algorithm for estimating the change point in time series distribution. The two main results are verified by two Monte Carlo experiments respectively, one is to estimate the joint stationary distribution of $5$-tuple samples of a 20 dimensional AR(3) model, the other is about estimating the change point at the combination of two different stationary time series. A real world empirical application to the human activity recognition dataset highlights the potential of the proposed methods.
翻译:最近,基因对抗网络(GANs)被用于估算独立和相同分布数据的分布,并吸引了大量的研究关注。在本文中,我们使用封隔技术来显示GANs在估计固定时间序列分布方面的有效性。理论上,我们为时间序列的固定分布得出一个非静态误差,该误差系基于深神经网络(DNN)的GANs测算器。根据我们的理论分析,我们提出一个算法,用于估算时间序列分布的变化点。两个主要结果分别由蒙特卡洛的两个实验加以验证,一个是估计20维AR(3)模型的5美元数字样本的联合固定分布,另一个是估计两个不同固定时间序列的组合。人类活动识别数据集的实际世界经验应用强调了拟议方法的潜力。