# Discovering Nonlinear Relations with Minimum Predictive Information Regularization

arXiv: https://arxiv.org/abs/2001.01885 · HTML: https://mlsanity.com/paper/2001.01885/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2020.

## Built on by (most cited first, 16 of 16)

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- [CausalMMM: Learning Causal Structure for Marketing Mix Modeling](https://mlsanity.com/paper/2406.16728/) (2024)
- [Double Machine Learning Based Structure Identification from Temporal Data](https://mlsanity.com/paper/2311.06012/) (2023)
- [Towards Intercultural Affect Recognition: Audio-Visual Affect Recognition in the Wild Across Six Cultures](https://mlsanity.com/paper/2208.00344/) (2022)
- [Learning domain-specific causal discovery from time series](https://mlsanity.com/paper/2209.05598/) (2022)
- [A Graph Dynamics Prior for Relational Inference](https://mlsanity.com/paper/2306.06041/) (2023)
- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representations](https://mlsanity.com/paper/2311.00923/) (2023)
- [Discovering group dynamics in coordinated time series via hierarchical recurrent switching-state models](https://mlsanity.com/paper/2401.14973/) (2024)
- [Bayesian Vector AutoRegression with Factorised Granger-Causal Graphs](https://mlsanity.com/paper/2402.03614/) (2024)
- [An Interpretable Neural Network for Parameter Inference](https://mlsanity.com/paper/2106.05536/) (2021)
- [A VAE-based Framework for Learning Multi-Level Neural Granger-Causal Connectivity](https://mlsanity.com/paper/2402.16131/) (2024)

## Abstract (arXiv)

Identifying the underlying directional relations from observational time series with nonlinear interactions and complex relational structures is key to a wide range of applications, yet remains a hard problem. In this work, we introduce a novel minimum predictive information regularization method to infer directional relations from time series, allowing deep learning models to discover nonlinear relations. Our method substantially outperforms other methods for learning nonlinear relations in synthetic datasets, and discovers the directional relations in a video game environment and a heart-rate vs. breath-rate dataset.