Research map / Probabilistic and scientific modeling / Causal discovery
Regularizing towards Causal Invariance: Linear Models with Proxies
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add proxy-based anchor regularization using temperature | OLS on pollution prediction · Pollution, 9 scenarios with λ > 0 | Mean MSE: 0.537 -> 0.531 | Helped |
| Target the loss to held-out-season temperature statistics | OLS on pollution prediction · Pollution, 9 scenarios with λ > 0 | Mean MSE: 0.537 -> 0.525 | Helped |
| Use two noisy proxies instead of one | Proxy Anchor Regression on pollution prediction · Pollution, 9 scenarios with λ > 0 | Mean MSE: 0.531 -> 0.531 | No clear effect |
| Use two noisy proxies instead of one | Proxy Targeted Anchor Regression on pollution prediction · Pollution, 9 scenarios with λ > 0 | Mean MSE: 0.529 -> 0.526 | Helped |
| Use training temperature and estimated test mean temperature as a bias correction | OLS on pollution prediction · Pollution, 9 scenarios with λ > 0 | Mean MSE: 0.537 -> 0.569 | Hurt |
| Use two noisy proxies to estimate the cross-proxy regularizer | Proxy Anchor Regression under synthetic interventions · Synthetic data, intervention MSPE | MSPE | Helped |
| Increase proxy noise when using a single proxy | Proxy Anchor Regression under synthetic interventions · Synthetic data, intervention MSPE | MSPE | Hurt |
| Target the loss to the anticipated intervention mean and covariance | Targeted Anchor Regression · Synthetic targeted shift | MSPE under intervention | Helped |
| Target the loss to a specific intervention | Targeted Anchor Regression · Synthetic training distribution | MSPE | Hurt |
| Use two proxies rather than one to account for measurement noise | Proxy Anchor Regression with causal and anti-causal predictors · Synthetic causal/anti-causal predictors | Weight on causal predictors | Helped |
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