# Data-Driven Modeling of Noise Time Series with Convolutional Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2207.01110 · HTML: https://mlsanity.com/paper/2207.01110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 107 references that are in the map.
- First posted on arXiv 3 Jul 2022.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis](https://mlsanity.com/paper/1910.06711/) (2019)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [Pros and Cons of GAN Evaluation Measures: New Developments](https://mlsanity.com/paper/2103.09396/) (2021)
- [GANSynth: Adversarial Neural Audio Synthesis](https://mlsanity.com/paper/1902.08710/) (2019)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [Learning to See by Looking at Noise](https://mlsanity.com/paper/2106.05963/) (2021)
- [An empirical study on evaluation metrics of generative adversarial networks](https://mlsanity.com/paper/1806.07755/) (2018)
- [Non-Stationary Texture Synthesis by Adversarial Expansion](https://mlsanity.com/paper/1805.04487/) (2018)
- [Conditional GAN for timeseries generation](https://mlsanity.com/paper/2006.16477/) (2020)
- [Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions](https://mlsanity.com/paper/2101.09113/) (2021)
- [Comparing Representations for Audio Synthesis Using Generative Adversarial Networks](https://mlsanity.com/paper/2006.09266/) (2020)
- [Adversarial Generation of Time-Frequency Features with application in audio synthesis](https://mlsanity.com/paper/1902.04072/) (2019)
- [GAN2GAN: Generative Noise Learning for Blind Denoising with Single Noisy Images](https://mlsanity.com/paper/1905.10488/) (2019)
- [Feasibility of Modeling Orthogonal Frequency-Division Multiplexing Communication Signals with Unsupervised Generative Adversarial Networks](https://mlsanity.com/paper/2109.05107/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning noise-induced transitions by multi-scaling reservoir computing](https://mlsanity.com/paper/2309.05413/) (2023)

## Abstract (arXiv)

Random noise arising from physical processes is an inherent characteristic of measurements and a limiting factor for most signal processing and data analysis tasks. Given the recent interest in generative adversarial networks (GANs) for data-driven modeling, it is important to determine to what extent GANs can faithfully reproduce noise in target data sets. In this paper, we present an empirical investigation that aims to shed light on this issue for time series. Namely, we assess two general-purpose GANs for time series that are based on the popular deep convolutional GAN (DCGAN) architecture, a direct time-series model and an image-based model that uses a short-time Fourier transform (STFT) data representation. The GAN models are trained and quantitatively evaluated using distributions of simulated noise time series with known ground-truth parameters. Target time series distributions include a broad range of noise types commonly encountered in physical measurements, electronics, and communication systems: band-limited thermal noise, power law noise, shot noise, and impulsive noise. We find that GANs are capable of learning many noise types, although they predictably struggle when the GAN architecture is not well suited to some aspects of the noise, e.g., impulsive time-series with extreme outliers. Our findings provide insights into the capabilities and potential limitations of current approaches to time-series GANs and highlight areas for further research. In addition, our battery of tests provides a useful benchmark to aid the development of deep generative models for time series.