# MixCIT: A Kernel Based Local-Polynomial Debiased Test for Conditional Independence on Mixed-Type Data

arXiv: https://arxiv.org/abs/2607.12830 · HTML: https://mlsanity.com/paper/2607.12830/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 88 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [Sparse-Push: Communication- & Energy-Efficient Decentralized Distributed Learning over Directed & Time-Varying Graphs with non-IID Datasets](https://mlsanity.com/paper/2102.05715/) (2021)
- [Bias correction for Chatterjee's graph-based correlation coefficient](https://mlsanity.com/paper/2508.09040/) (2025)
- [Limit theorems of Azadkia-Chatterjee's conditional graph correlation](https://mlsanity.com/paper/2606.15433/) (2026)

## Abstract (arXiv)

Conditional independence testing (CIT) is fundamental to modern statistical inference in areas related to causal discovery and variable selection. While marginal independence is relatively well-understood, despite multiple advances, no existing non-parametric CIT provides a unified, efficient, and statistically guaranteed solution across heterogeneous data. We introduce a graph-based test statistic comparing kernel similarities of the response within composite neighborhoods that use exact matching on discrete components and kn-nearest-neighbor matching on continuous ones. The raw statistic, related to prior constructions, suffices under fully discrete conditioning. However, when at least one conditioning variable is continuous, we instead use a local-polynomial debiased variant that cancels the local smoothing bias. We rigorously establish its asymptotic null distribution across all data-type combinations. We further prove a dimension-free n-1/4 detection threshold under local alternatives, eliminating the phase transition that affects geometric estimators in high dimensions. Finally, we develop efficient algorithms with near-quadratic complexity and analytic graph-based calibration, bypassing the cubic bottlenecks of global kernel methods.