# Distribution estimation and change-point estimation for time series via DNN-based GANs

arXiv: https://arxiv.org/abs/2211.14577 · HTML: https://mlsanity.com/paper/2211.14577/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 26 Nov 2022.

## Builds on (most cited first, 19 of 19)

- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [On the Discrimination-Generalization Tradeoff in GANs](https://mlsanity.com/paper/1711.02771/) (2017)
- [An error analysis of generative adversarial networks for learning distributions](https://mlsanity.com/paper/2105.13010/) (2021)
- [Kernel Change-point Detection with Auxiliary Deep Generative Models](https://mlsanity.com/paper/1901.06077/) (2019)
- [2-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANs](https://mlsanity.com/paper/1902.07197/) (2019)
- [Approximability of Discriminators Implies Diversity in GANs](https://mlsanity.com/paper/1806.10586/) (2018)
- [Multiple-change-point detection for high dimensional time series via sparsified binary segmentation](https://mlsanity.com/paper/1611.08639/) (2016)
- [Approximation bounds for norm constrained neural networks with applications to regression and GANs](https://mlsanity.com/paper/2201.09418/) (2022)
- [Generative adversarial networks in time series: A survey and taxonomy](https://mlsanity.com/paper/2107.11098/) (2021)
- [On the capacity of deep generative networks for approximating distributions](https://mlsanity.com/paper/2101.12353/) (2021)
- [Deconstructing Generative Adversarial Networks](https://mlsanity.com/paper/1901.09465/) (2019)
- [A likelihood approach to nonparametric estimation of a singular distribution using deep generative models](https://mlsanity.com/paper/2105.04046/) (2021)
- [Time-series Transformer Generative Adversarial Networks](https://mlsanity.com/paper/2205.11164/) (2022)
- [JointGAN: Multi-Domain Joint Distribution Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1806.02978/) (2018)
- [InDiD: Instant Disorder Detection via Representation Learning](https://mlsanity.com/paper/2106.02602/) (2021)
- [Non-Asymptotic Error Bounds for Bidirectional GANs](https://mlsanity.com/paper/2110.12319/) (2021)

## Abstract (arXiv)

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.