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Conditional Diffusion Models Based Conditional Independence Testing
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Proposes CDCIT, a conditional independence test that uses score-based conditional diffusion models to sample from X|Z inside a conditional randomization test, with a classifier-based CMI statistic.
Problem
Conditional independence testing requires the conditional distribution X|Z, which is typically unknown; existing approximations (GANs, kNN, smoothing) suffer from instability, poor diversity, or curse of dimensionality, inflating type I error in high-dimensional and mixed-type conditioning sets.
Approach
Replace GAN or kNN conditional samplers in the conditional randomization test with a conditional score-based diffusion model to generate null samples of X given Z, and pair it with a classifier-based conditional mutual information estimator as the test statistic; theory bounds the TV distance of generated samples and the excess type I error.
Key results
- On synthetic post-nonlinear and mixed models, CDCIT controls type I error near 0.05 while achieving high power as d_z grows from 10 to 100, while GCIT, CCIT and KCIT show inflated type I error in most scenarios.
- On the Flow-Cytometry CI benchmark, CDCIT achieves recall 0.98 and F-score 0.83, the best among compared tests (GCIT F-score 0.77).
- In the conditional-sampler comparison, the diffusion sampler yields the lowest quantile MSE on Models M1 and M3 versus WGANs, Sinkhorn GANs and k-NN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use conditional diffusion sampling instead of WGANs, Sinkhorn GANs, or k-NN | Conditional distribution estimation for CRT · Models M1 and M3 | quantile MSE | Helped |
| Use conditional diffusion sampling instead of the alternatives | Conditional distribution estimation for CRT · Model M2 | quantile MSE | Mixed |
| Use CDCIT rather than the competing methods | Conditional-independence testing on breast cancer data · Breast cancer dataset | average prediction MSE: 0.706 -> 0.696 | Helped |
| Use CDCIT rather than GCIT | Conditional-independence testing · Flow-Cytometry | recall: 0.80 -> 0.98 | Helped |
| Use CDCIT rather than GCIT | Conditional-independence testing · Flow-Cytometry | F-score: 0.77 -> 0.83 | Helped |
| Increase the test sample size n | CDCIT · Post-nonlinear and mixed synthetic models | power | Helped |
| Increase the test sample size n | CDCIT · Post-nonlinear and mixed synthetic models | type I error | No clear effect |
| Use a smaller conditional-sampler training sample size N | CDCIT · Post-nonlinear and mixed synthetic models | type I error | Hurt |
| Vary the number of repetitions B | CDCIT · Post-nonlinear and mixed synthetic models | type I error and power | No clear effect |
Surprising findings
- The diffusion sampler is not uniformly best: on Model M2 it is not always the top performer, and k-NN wins some quantiles.
- Smaller N (conditional sampler training size) inflates type I error, attributed to difficulty training the diffusion model.
Limitations
- Theoretical type I error control holds only asymptotically and requires sample size N growing faster than n^(1/(Gamma_1 - delta)), with strong smoothness and sub-Gaussian assumptions.
- Performance depends on the number of samples used to train the conditional sampler; small N inflates type I error.
- Real-data evaluation lacks ground truth and relies on a proxy prediction-MSE metric.
Experimental setup
Datasets: synthetic post-nonlinear and mixed-type models METABRIC breast cancer genomic dataset Flow-Cytometry dataset
Benchmarks: synthetic post-nonlinear model synthetic mixed-type model METABRIC breast cancer Flow-Cytometry
Metrics: type I error power mean squared error of quantiles precision recall F-score prediction MSE
Baselines: GCIT NNSCIT CCIT KCIT LPCIT DGCIT NNLSCIT WGANs Sinkhorn GANs k-NN
Builds on: conditional randomization test classifier-based CMI estimator score-based diffusion models GCIT NNSCIT
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