Research map / Probabilistic and scientific modeling / Causal discovery
Permutation-based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes MPRT, a permutation-based rank test for cross-covariance matrices that stays valid when variables are discretized, and applies it to PC and RLCD causal discovery on mixed and Big Five personality data.
Problem
x
Approach
Estimate the correlation matrix by pseudo-likelihood with polyserial/polychoric terms and a geometric parameterization, then build the null distribution of the CCA likelihood-ratio statistic by permuting the discretized data (permuting only one side, justified by exchangeability of canonical variables beyond the top-k), instead of using the chi-square approximation.
Key results
- On mixed data, MPRT controls Type I error near alpha=0.05 while CCART-D and CCART-DE fail to control it, and MPRT's Type II error decreases with sample size.
- In PC skeleton recovery at N=2000, MPRT reaches F1 0.96 and SHD 0.20 versus Fisher-Z F1 0.78 and SHD 1.40.
- On Big Five data, CCART-D p-values all become very small, requiring alpha around 1e-10 to find structure, whereas MPRT yields interpretable latent variables for openness and neuroticism.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MPRT instead of Fisher-Z in PC | PC algorithm on partially discretized data · PC skeleton, N=500 | F1 score: 0.81 -> 0.84 | Helped |
| Use MPRT instead of Fisher-Z in PC | PC algorithm on partially discretized data · PC skeleton, N=1000 | F1 score: 0.80 -> 0.9 | Helped |
| Use MPRT instead of Fisher-Z in PC | PC algorithm on partially discretized data · PC skeleton, N=2000 | F1 score: 0.78 -> 0.96 | Helped |
| Use MPRT instead of KCI in PC | PC algorithm on partially discretized data · PC skeleton, N=1000 | F1 score: 0.88 -> 0.9 | Helped |
| Use MPRT instead of KCI in PC | PC algorithm on partially discretized data · PC skeleton, N=2000 | SHD: 0.93 -> 0.20 | Helped |
| Use MPRT instead of CCART-D in PC | PC algorithm on partially discretized data · PC skeleton, N=2000 | F1 score: 0.77 -> 0.96 | Helped |
| Use MPRT instead of CCART-DE in PC | PC algorithm on partially discretized data · PC skeleton, N=2000 | SHD: 1.60 -> 0.20 | Helped |
| Use permutation-based null distribution rather than the CCA analytic null distribution | MPRT on continuous data · Continuous data, different sample sizes | Type I error | No clear effect |
| Use MPRT with mixed data rather than CCART-D or CCART-DE | Rank testing with partially discretized data · Mixed data, different sample sizes | Type I error control: 0.05 | Helped |
| Increase sample size | MPRT on mixed data · Mixed data, different sample sizes | Type II error | Helped |
| Use MPRT instead of Fisher-Z in PC | PC algorithm on partially discretized data · PC skeleton, N=2000 | SHD: 1.40 -> 0.20 | Helped |
Surprising findings
- Plugging maximum-likelihood correlation estimates from discretized data into the chi-square CCA rank test yields p-values concentrated near zero, so the test rejects almost everything.
- Naively treating ordinal codes as continuous values can produce a cross-covariance matrix with a completely different rank (e.g., rank 1 vs rank 3), even with infinite samples.
Limitations
- No theoretical power analysis; only Type I error control is established.
- Assumes a linear SCM with a known parametric form for the likelihood; without it consistent threshold and correlation recovery may fail.
- Real-data experiment uses a subset of 13 items from two personality dimensions and lacks ground-truth validation.
Experimental setup
Datasets: Big Five personality dataset (openpsychometrics.org)
Benchmarks: synthetic linear Gaussian rank-test settings synthetic PC skeleton recovery Big Five personality data
Metrics: Type I error Type II error F1 score for skeleton SHD for skeleton
Baselines: CCART-C CCART-D CCART-DE Fisher-Z KCI
Builds on: PC algorithm RLCD CCA rank test (CCART) polychoric correlation polyserial correlation
Closest papers by meaning
- A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables (ICLR 2024 · similarity 0.86)
- Latent Variable Causal Discovery under Selection Bias (ICML 2025 · similarity 0.85)
- Causal Discovery via Conditional Independence Testing with Proxy Variables (ICML 2024 · similarity 0.85)
- Permutation-Free High-Order Interaction Tests (ICML 2025 · similarity 0.85)
- Score-Based Causal Discovery of Latent Variable Causal Models (ICML 2024 · similarity 0.84)
- Learning Discrete Latent Variable Structures with Tensor Rank Conditions (NeurIPS 2024 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.