# Leveraging Pre-Images to Discover Nonlinear Relationships in Multivariate Environments

arXiv: https://arxiv.org/abs/2106.00842 · HTML: https://mlsanity.com/paper/2106.00842/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Large-scale nonlinear Granger causality: A data-driven, multivariate approach to recovering directed networks from short time-series data](https://mlsanity.com/paper/2009.04681/) (2020)
- [A Perspective on Gaussian Processes for Earth Observation](https://mlsanity.com/paper/2007.01238/) (2020)
- [Ultrasound Elasticity Imaging Using Physics-based Models And Learning-based Plug-And-Play Priors](https://mlsanity.com/paper/2103.14096/) (2021)
- [Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing](https://mlsanity.com/paper/1902.06828/) (2019)
- [Large-Scale Extended Granger Causality for Classification of Marijuana Users From Functional MRI](https://mlsanity.com/paper/2101.01832/) (2021)
- [Machine Common Sense](https://mlsanity.com/paper/2006.08409/) (2020)
- [A statistical framework for model-based inverse problems in ultrasound elastography](https://mlsanity.com/paper/2010.10729/) (2020)
- [Finite Element Reconstruction Of Stiffness Images In MR Elastography Using Statistical Physical Forward Modeling And Proximal Optimization Methods](https://mlsanity.com/paper/2103.14632/) (2021)
- [MR elasticity reconstruction using statistical physical modeling and explicit data-driven denoising regularizer](https://mlsanity.com/paper/2105.12922/) (2021)

## Built on by (most cited first, 3 of 3)

- [Re-defining Radiology Quality Assurance (QA) -- Artificial Intelligence (AI)-Based QA by Restricted Investigation of Unequal Scores (AQUARIUS)](https://mlsanity.com/paper/2205.00629/) (2022)
- [Cross Modal Global Local Representation Learning from Radiology Reports and X-Ray Chest Images](https://mlsanity.com/paper/2301.10951/) (2023)
- [Enhancing Graph Attention Neural Network Performance for Marijuana Consumption Classification through Large-scale Augmented Granger Causality (lsAGC) Analysis of Functional MR Images](https://mlsanity.com/paper/2410.18506/) (2024)

## Abstract (arXiv)

Causal discovery, beyond the inference of a network as a collection of connected dots, offers a crucial functionality in scientific discovery using artificial intelligence. The questions that arise in multiple domains, such as physics, physiology, the strategic decision in uncertain environments with multiple agents, climatology, among many others, have roots in causality and reasoning. It became apparent that many real-world temporal observations are nonlinearly related to each other. While the number of observations can be as high as millions of points, the number of temporal samples can be minimal due to ethical or practical reasons, leading to the curse-of-dimensionality in large-scale systems. This paper proposes a novel method using kernel principal component analysis and pre-images to obtain nonlinear dependencies of multivariate time-series data. We show that our method outperforms state-of-the-art causal discovery methods when the observations are restricted by time and are nonlinearly related. Extensive simulations on both real-world and synthetic datasets with various topologies are provided to evaluate our proposed methods.