# Recurrent Neural Goodness-of-Fit Test for Time Series

arXiv: https://arxiv.org/abs/2410.13986 · HTML: https://mlsanity.com/paper/2410.13986/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 61 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Fast Two-Sample Testing with Analytic Representations of Probability Measures](https://mlsanity.com/paper/1506.04725/) (2015)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [FinDiff: Diffusion Models for Financial Tabular Data Generation](https://mlsanity.com/paper/2309.01472/) (2023)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Two-sample Testing Using Deep Learning](https://mlsanity.com/paper/1910.06239/) (2019)
- [AutoDiff: combining Auto-encoder and Diffusion model for tabular data synthesizing](https://mlsanity.com/paper/2310.15479/) (2023)
- [Counterfactual Generative Models for Time-Varying Treatments](https://mlsanity.com/paper/2305.15742/) (2023)
- [Neural Spectral Marked Point Processes](https://mlsanity.com/paper/2106.10773/) (2021)
- [Sequential Adversarial Anomaly Detection for One-Class Event Data](https://mlsanity.com/paper/1910.09161/) (2019)
- [A kernel Stein test of goodness of fit for sequential models](https://mlsanity.com/paper/2210.10741/) (2022)
- [Conditional Generative Modeling for High-dimensional Marked Temporal Point Processes](https://mlsanity.com/paper/2305.12569/) (2023)

## Built on by (most cited first, 2 of 2)

- [Global-Decision-Focused Neural ODEs for Proactive Grid Resilience Management](https://mlsanity.com/paper/2502.18321/) (2025)
- [Learning to Test: Latent Representation Learning for Dynamic Instability Detection](https://mlsanity.com/paper/2604.10967/) (2026)

## Abstract (arXiv)

Time series data are crucial across diverse domains such as finance and healthcare, where accurate forecasting and decision-making rely on advanced modeling techniques. While generative models have shown great promise in capturing the intricate dynamics inherent in time series, evaluating their performance remains a major challenge. Traditional evaluation metrics fall short due to the temporal dependencies and potential high dimensionality of the features. In this paper, we propose the REcurrent NeurAL (RENAL) Goodness-of-Fit test, a novel and statistically rigorous framework for evaluating generative time series models. By leveraging recurrent neural networks, we transform the time series into conditionally independent data pairs, enabling the application of a chi-square-based goodness-of-fit test to the temporal dependencies within the data. This approach offers a robust, theoretically grounded solution for assessing the quality of generative models, particularly in settings with limited time sequences. We demonstrate the efficacy of our method across both synthetic and real-world datasets, outperforming existing methods in terms of reliability and accuracy. Our method fills a critical gap in the evaluation of time series generative models, offering a tool that is both practical and adaptable to high-stakes applications.