# Toward Scalable and Valid Conditional Independence Testing with Spectral Representations

arXiv: https://arxiv.org/abs/2512.19510 · HTML: https://mlsanity.com/paper/2512.19510/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 75 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 29 of 29)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [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)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Local permutation tests for conditional independence](https://mlsanity.com/paper/2112.11666/) (2021)
- [Nonparametric independence testing via mutual information](https://mlsanity.com/paper/1711.06642/) (2017)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [Efficient Conditionally Invariant Representation Learning](https://mlsanity.com/paper/2212.08645/) (2022)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [Neural Conditional Probability for Uncertainty Quantification](https://mlsanity.com/paper/2407.01171/) (2024)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [Spectral Representation Learning for Conditional Moment Models](https://mlsanity.com/paper/2210.16525/) (2022)
- [Spectral Representation for Causal Estimation with Hidden Confounders](https://mlsanity.com/paper/2407.10448/) (2024)
- [Domain-specific optimization and diverse evaluation of self-supervised models for histopathology](https://mlsanity.com/paper/2310.13259/) (2023)
- [Conditional Diffusion Models Based Conditional Independence Testing](https://mlsanity.com/paper/2412.11744/) (2024)
- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2505.18671/) (2025)
- [On the Hardness of Conditional Independence Testing In Practice](https://mlsanity.com/paper/2512.14000/) (2025)
- [Position: Causal Machine Learning Requires Rigorous Synthetic Experiments for Broader Adoption](https://mlsanity.com/paper/2508.08883/) (2025)
- [On the power of conditional independence testing under model-X](https://mlsanity.com/paper/2005.05506/) (2020)
- [Primal-Dual Spectral Representation for Off-policy Evaluation](https://mlsanity.com/paper/2410.17538/) (2024)
- [Demystifying Spectral Feature Learning for Instrumental Variable Regression](https://mlsanity.com/paper/2506.10899/) (2025)
- [Representation Learning for Equivariant Inference with Guarantees](https://mlsanity.com/paper/2505.19809/) (2025)
- [Outcome-Aware Spectral Feature Learning for Instrumental Variable Regression](https://mlsanity.com/paper/2512.00919/) (2025)

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

- [Learning Conditional Expectation Operators via Functional Newton Updates](https://mlsanity.com/paper/2609.35598/) (2026)

## Abstract (arXiv)

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity. Kernel methods using partial covariance operators offer a more principled approach but suffer from limited adaptivity and scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of partial covariance operators and use them to construct a simple test statistic. We also introduce a bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Experiments on real and synthetic data suggest that this approach offers a principled and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.