Research map / Probabilistic and scientific modeling / Causal discovery
Identifying General Mechanism Shifts in Linear Causal Representations
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Shows that shifted latent nodes in linear causal representations can be identified from few environments with very general interventions, via ICA plus a psi-based sorting and a test statistic, and demonstrates it on synthetic data and a Big Five psychometric dataset.
Problem
Identifying which latent factors undergo causal mechanism shifts across environments in linear causal representation learning, when there are fewer than d environments and interventions are coarse (can change the whole latent graph), without recovering the full SCM or mixing matrix.
Approach
Reduces shifted-node detection to ICA: after ICA on each environment's observations, noise components are ordered by a test function psi so they align across environments, and a node is non-shifted iff its row of the unmixing matrix matches (up to sign) across environments; this is checked with an L1-based statistic against a threshold.
Key results
- On synthetic data with n=10^6 and p=2d, shifted-node detection achieves F1 of 1.000 for d=5 and d=10 on ER2 and reaches 0.6-0.9 at d=30-40.
- In the fully observed case (G=I), the method's F1 exceeds DCI in most settings, e.g. 1.00 vs 0.79 for SF2 with d=10.
- On the Big Five data, male-female comparison flags Neuroticism (0.638) and Extraversion (0.633) as shifted, matching psychology literature; US-UK comparison flags no shifts.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the element-wise absolute-difference formulation of the shift statistic L_i instead of the original row-vector comparison (ablation) | iLCS · Synthetic shift detection | shift detection performance | Helped |
| Use iLCS instead of DCI | Fully observed linear SEMs (G=I) · ER2, d=5 | F1: 0.60 -> 0.80 | Helped |
| Use iLCS instead of DCI | Fully observed linear SEMs (G=I) · ER2, d=10 | F1: 0.92 -> 1.00 | Helped |
| Use iLCS instead of DCI | Fully observed linear SEMs (G=I) · ER2, d=15 | F1: 0.84 -> 0.78 | Hurt |
| Use iLCS instead of DCI | Fully observed linear SEMs (G=I) · ER4, d=10 and d=15 | F1: d=10: 0.89 -> 1.00; d=15: 0.81 -> 0.73 | Mixed |
| Use iLCS instead of DCI | Fully observed linear SEMs (G=I) · SF2 | F1: d=5: 0.73 -> 1.00; d=10: 0.79 -> 1.00; d=15: 0.78 -> 0.78 | Mixed |
| Use iLCS instead of DCI | Fully observed linear SEMs (G=I) · SF4 | F1: d=5: 0.60 -> 0.80; d=10: 0.85 -> 1.00; d=15: 0.68 -> 0.79 | Helped |
| Compare male and female environments with iLCS | iLCS on Big Five personality data · Gender | L_i shift statistic: {0.074, 0.0497, 0.078, 0.638, 0.633} | Mixed |
| Compare US and UK environments with iLCS | iLCS on Big Five personality data · US vs UK | L_i shift statistic: {0.302, 0.258, 0.109, 0.189, 0.088} | No clear effect |
Surprising findings
- Under the US-UK comparison, no latent node is flagged as shifted, consistent with prior claims of cross-cultural personality stability.
- The method's F1 degrades to around 0.6 at d=40 on some graphs, indicating scalability limits.
Limitations
- Relies on a test function psi that differentiates noise components; the alternative distribution-matching approach is computationally expensive.
- Restricted to linear mixing and linear SCMs; nonlinear extension left to future work.
- Detection accuracy degrades for larger latent dimensions (F1 around 0.6 at d=40 for some graphs).
Experimental setup
Datasets: synthetic linear SCM data (ER/SF graphs) Big Five personality test responses (OpenPsychometrics, 19,710 observations after filtering)
Benchmarks: synthetic ER2/ER4/SF2/SF4 graphs Big Five psychometric dataset (gender and US vs UK)
Metrics: precision recall F1 score runtime (s)
Baselines: DCI
Builds on: linear ICA linear causal representation learning under perfect interventions DCI
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