Research map / Probabilistic and scientific modeling / Causal discovery
Out-of-Variable Generalisation for Discriminative Models
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.
Studies out-of-variable (OOV) generalization, showing marginal consistency alone cannot identify target predictors, and proposes MomentLearn, which uses third residual moments in a source environment to estimate partial derivatives and predict Y in a target environment where Y is unobserved.
Problem
Predicting a target variable in an environment whose variables were never jointly observed with it in any source environment, where only overlapping marginal information is available.
Approach
After fitting a source regression, the third central moment of the residuals reveals the partial derivative of the true generating function with respect to the unobserved cause (under additive noise and independent covariates), which is used to build a target predictor without observing Y in the target environment.
Key results
- On polynomial function class (linear+interaction+square terms), MomentLearn achieved MSE 0.32 vs Oracle 0.31 and Marginal 0.52 on the linear-terms class.
- On GP-sampled functions with X3^2 terms, MomentLearn MSE 0.67 vs Marginal 1.46 and Mean Imputed 1.31, though Oracle reached 0.18.
- MomentLearn beats the joint-observation predictor only for roughly the first 100 joint target samples in the few-sample experiment.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MomentLearn instead of the marginal predictor | OOV prediction · Linear additive | MSE: 0.52 $\pm$ 0.45 -> 0.32 $\pm$ 0.15 | Helped |
| Use MomentLearn instead of the mean-imputed predictor | OOV prediction · Linear additive | MSE: 0.45 $\pm$ 0.21 -> 0.32 $\pm$ 0.15 | Helped |
| Use MomentLearn instead of the marginal predictor | OOV prediction · Linear interactions | MSE: 0.80 $\pm$ 0.75 -> 0.31 $\pm$ 0.48 | Helped |
| Use MomentLearn instead of the mean-imputed predictor | OOV prediction · Linear interactions | MSE: 0.48 $\pm$ 0.45 -> 0.31 $\pm$ 0.48 | Helped |
| Use MomentLearn instead of the marginal predictor | OOV prediction · Interactions and squares | MSE: 1.75 $\pm$ 1.27 -> 0.71 $\pm$ 0.37 | Helped |
| Use MomentLearn instead of the mean-imputed predictor | OOV prediction · Interactions and squares | MSE: 1.50 $\pm$ 1.03 -> 0.71 $\pm$ 0.37 | Helped |
| Use MomentLearn instead of the marginal predictor | OOV prediction · GP1(X1, X2) + α3X3 | MSE: 0.33 $\pm$ 0.14 -> 0.06 $\pm$ 0.04 | Helped |
| Use MomentLearn instead of the mean-imputed predictor | OOV prediction · GP1(X1, X2) + α3X3 | MSE: 0.37$\pm$ 0.26 -> 0.06 $\pm$ 0.04 | Helped |
| Use MomentLearn instead of the marginal predictor | OOV prediction · GP1 + GP2·X3 | MSE: 0.41 $\pm$ 0.37 -> 0.10 $\pm$ 0.06 | Helped |
| Use MomentLearn instead of the mean-imputed predictor | OOV prediction · GP1 + GP2·X3 | MSE: 0.32 $\pm$ 0.25 -> 0.10 $\pm$ 0.06 | Helped |
| Use MomentLearn instead of the marginal predictor | OOV prediction · GP1 + GP2·X3 + GP3·X3² | MSE: 1.46 $\pm$ 1.21 -> 0.67 $\pm$ 0.59 | Helped |
| Use MomentLearn instead of the mean-imputed predictor | OOV prediction · GP1 + GP2·X3 + GP3·X3² | MSE: 1.31 $\pm$ 0.95 -> 0.67 $\pm$ 0.59 | Helped |
Surprising findings
- Marginal consistency alone cannot identify the target predictor in common OOV scenarios, even though optimal source and target predictors satisfy it.
- Residual third moment reveals the partial derivative w.r.t. the unobserved cause, so the target predictor can be learned without ever observing Y in the target environment.
Limitations
- Theory relies on additive noise, independent covariates, smooth functions, and first-order Taylor approximation.
- Only a proof-of-concept evaluated on synthetic data; no real-world experiments.
- Exact identification guaranteed only for a restricted class of generating functions; performance degrades on X3^2 terms.
Experimental setup
Datasets: synthetic data (polynomial, nonlinear, GP-sampled functions)
Benchmarks: synthetic OOV regression tasks
Metrics: MSE relative log loss vs oracle
Baselines: Oracle Marginal predictor Mean Imputed predictor
Builds on: Independent Causal Mechanisms marginal consistency mean imputation
Closest papers by meaning
- On the Out-of-Distribution Generalization of Self-Supervised Learning (ICML 2025 · similarity 0.86)
- Discrepancies are Virtue: Weak-to-Strong Generalization through Lens of Intrinsic Dimension (ICML 2025 · similarity 0.86)
- Relating Misfit to Gain in Weak-to-Strong Generalization Beyond the Squared Loss (ICML 2025 · similarity 0.85)
- Domain Generalisation via Imprecise Learning (ICML 2024 · similarity 0.85)
- Do causal predictors generalize better to new domains? (NeurIPS 2024 · similarity 0.85)
- Out-of-Domain Generalization in Dynamical Systems Reconstruction (ICML 2024 · similarity 0.85)
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.