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Extracting Rare Dependence Patterns via Adaptive Sample Reweighting
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Proposes RHSIC/RKCIT, kernel (conditional) independence tests that learn adaptive sample importance weights to amplify rare dependence, and integrates them into the PC algorithm (RD-PC) for causal discovery.
Problem
Existing independence and conditional independence tests miss dependence that is significant only within small regions of the data distribution ("rare dependence"), causing false negatives that propagate errors in causal discovery.
Approach
Learn a non-negative sample reweighting function (in an RKHS, with normalization and regularization) by maximizing a reweighted HSIC/conditional HSIC on a training split, then test independence on the held-out split with the reweighted statistic and a permutation test, and plug the test into PC.
Key results
- On the Sachs (PKA, PJINK) pair, HSIC gives p=0.601 while RHSIC detects dependence with p=0.004.
- On the JPY/USD and federal funds data, HSIC gives p=0.2174 while RHSIC gives p=0.0005, with learned weights highlighting 2001 and 2008.
- In simulations the method controls Type I error near 0.05 and achieves higher power than baselines; in CI tests it achieves about 50% better power than KCIT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply adaptive sample importance reweighting instead of using the original HSIC test | HSIC independence testing · Sachs dataset (PKA, PJINK) | p-value: 0.601 -> 0.004 | Helped |
| Apply adaptive sample importance reweighting using the federal funds rate as reference | HSIC independence testing · Monthly JPY/USD exchange rates and U.S. federal funds rates (1990–2010) | p-value: 0.2174 -> 0.0005 | Helped |
| Use adaptive sample importance reweighting to detect rare dependence | Independence tests · Synthetic Data Generation I and II | power | Helped |
| Use adaptive sample importance reweighting for conditional independence testing | KCIT · Synthetic conditional independence tests | power: 50% better | Helped |
Surprising findings
- Standard HSIC on the whole sample fails to reject independence in Example 1.1 (p=0.1359) even though the dependence is highly significant (p=6.8e-11) within a small subregion.
Limitations
- Requires a known reference variable C for the reweighting and for the RD-PC correction step.
- Assumes no latent confounders and relies on Markov and faithfulness assumptions for RD-PC soundness.
- Permutation-based calibration and kernel ridge regression for conditional tests add computational cost (not quantified).
Experimental setup
Datasets: Sachs flow cytometry dataset FRED JPY/USD exchange rate and federal funds rate data synthetic data (DG I, DG II, CI generators)
Benchmarks: Synthetic DG I and DG II independence tests Synthetic CI tests Sachs dataset FRED exchange rate and federal funds dataset
Metrics: Type I error rate power p-value
Baselines: HSIC RDC FHSIC FisherScan LFHSIC KCIT RCIT CCIT
Builds on: HSIC KCIT PC algorithm RCIT
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