# Conditional Independence Testing via Latent Representation Learning

arXiv: https://arxiv.org/abs/2209.01547 · HTML: https://mlsanity.com/paper/2209.01547/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 55 references that are in the map.
- First posted on arXiv 4 Sep 2022.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [CCMI : Classifier based Conditional Mutual Information Estimation](https://mlsanity.com/paper/1906.01824/) (2019)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Wasserstein Conditional Independence Testing](https://mlsanity.com/paper/2107.14184/) (2021)
- [A New Measure of Conditional Dependence](https://mlsanity.com/paper/1704.00607/) (2017)

## Built on by (most cited first, 9 of 9)

- [Diffeomorphic Information Neural Estimation](https://mlsanity.com/paper/2211.10856/) (2022)
- [Heteroscedastic Causal Structure Learning](https://mlsanity.com/paper/2307.07973/) (2023)
- [Efficient Distribution Matching of Representations via Noise-Injected Deep InfoMax](https://mlsanity.com/paper/2410.06993/) (2024)
- [FMMI: Flow Matching Mutual Information Estimation](https://mlsanity.com/paper/2511.08552/) (2025)
- [Deep Nonparametric Conditional Independence Tests for Images](https://mlsanity.com/paper/2411.06140/) (2024)
- [Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flows](https://mlsanity.com/paper/2407.04980/) (2024)
- [Amortized Conditional Independence Testing](https://mlsanity.com/paper/2502.20925/) (2025)
- [Curse of Slicing: Why Sliced Mutual Information is a Deceptive Measure of Statistical Dependence](https://mlsanity.com/paper/2506.04053/) (2025)
- [Discrete Bridges for Mutual Information Estimation](https://mlsanity.com/paper/2602.08894/) (2026)

## Abstract (arXiv)

Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditional Independence Test)-a novel non-parametric method for conditional independence testing based on representation learning. Our main contribution involves proposing a generative framework in which to test for the independence between X and Y given Z, we first learn to infer the latent representations of target variables X and Y that contain no information about the conditioning variable Z. The latent variables are then investigated for any significant remaining dependencies, which can be performed using the conventional partial correlation test. The empirical evaluations show that LCIT outperforms several state-of-the-art baselines consistently under different evaluation metrics, and is able to adapt really well to both non-linear and high-dimensional settings on a diverse collection of synthetic and real data sets.