Distribution estimation and change-point estimation for time series via DNN-based GANs
This work addresses distribution and change-point estimation in time series for applications like activity recognition, representing an incremental advancement by applying GANs to stationary time series with theoretical backing.
The paper tackles distribution estimation for stationary time series using DNN-based GANs, deriving a non-asymptotic error bound and proposing a change-point estimation algorithm, with verification through Monte Carlo experiments on a 20-dimensional AR(3) model and a real-world human activity recognition dataset.
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.