# Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data

arXiv: https://arxiv.org/abs/2501.18990 · HTML: https://mlsanity.com/paper/2501.18990/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 11 of 11)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Models](https://mlsanity.com/paper/1309.7004/) (2013)
- [High Dimensional Semiparametric Latent Graphical Model for Mixed Data](https://mlsanity.com/paper/1404.7236/) (2014)
- [On the Parameter Identifiability of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2407.16975/) (2024)
- [A Scalable Conditional Independence Test for Nonlinear, Non-Gaussian Data](https://mlsanity.com/paper/1401.5031/) (2014)
- [Permutation Inference for Canonical Correlation Analysis](https://mlsanity.com/paper/2002.10046/) (2020)
- [A Conditional Independence Test in the Presence of Discretization](https://mlsanity.com/paper/2404.17644/) (2024)

## Built on by (most cited first, 5 of 5)

- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [A Sample Efficient Conditional Independence Test in the Presence of Discretization](https://mlsanity.com/paper/2506.08747/) (2025)
- [Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey](https://mlsanity.com/paper/2608.11156/) (2026)
- [DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables](https://mlsanity.com/paper/2610.06086/) (2026)

## Abstract (arXiv)

Recent advances have shown that statistical tests for the rank of cross-covariance matrices play an important role in causal discovery. These rank tests include partial correlation tests as special cases and provide further graphical information about latent variables. Existing rank tests typically assume that all the continuous variables can be perfectly measured, and yet, in practice many variables can only be measured after discretization. For example, in psychometric studies, the continuous level of certain personality dimensions of a person can only be measured after being discretized into order-preserving options such as disagree, neutral, and agree. Motivated by this, we propose Mixed data Permutation-based Rank Test (MPRT), which properly controls the statistical errors even when some or all variables are discretized. Theoretically, we establish the exchangeability and estimate the asymptotic null distribution by permutations; as a consequence, MPRT can effectively control the Type I error in the presence of discretization while previous methods cannot. Empirically, our method is validated by extensive experiments on synthetic data and real-world data to demonstrate its effectiveness as well as applicability in causal discovery.