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Unifying Causal Representation Learning with the Invariance Principle

ICLR 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Causal representation identifiability · 1 citations (OpenAlex)

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Proposes a unified invariance-based framework showing that many causal representation learning identifiability results follow from aligning representations with known data invariances, and validates it on ISTAnt treatment-effect estimation and a synthetic nintervention ablation.

Problem

Causal representation learning methods rely on carefully crafted, fragmented problem settings tied to Pearl's causal hierarchy, which limits their applicability to real-world high-dimensional data where settings do not fit neatly.

Approach

Makes the invariance principle explicit: identifiability of latent causal variables follows from enforcing known invariance properties (sufficient for the invariant partition) across observables sharing an equivalence relation, which need not be causal. This unifies multiview, interventional, temporal, multi-task CRL and domain generalization, and allows mixing several invariances in one method.

Key results

• On ISTAnt, with invariance regularization lambda_INV=100 the TERB drops to about 20% from 100% under ERM (experiment subsampling).
• In the synthetic nintervention ablation, the marginal-invariant nodes z1 and z3 are block-identified with R^2 of 0.863 and 0.872, while the intervened z2 gets R^2 0.065.
• The paper argues that 30 existing identification results are special cases of its invariance framework.

Measured effects reported in the paper

Surprising findings

• Non-causal 'nintervention' (cutting all edges of a node and changing its marginal) still yields block identifiability of the invariant nodes, showing interventional CRL methods rely on distributional invariance rather than causal interventions.
• Causal assumptions are needed for graph identification but not for latent variable identification.

Limitations

• Excludes discrete variables and finite-sample guarantees.
• Variant (non-invariant) latents are not identifiable in general without independence conditions.
• Experiments are limited to one real-world dataset (ISTAnt) and a small synthetic ablation.

Experimental setup

Datasets: ISTAnt

Benchmarks: ISTAnt

Metrics: balanced accuracy Treatment Effect Relative Bias (TERB) R^2 (kernel ridge regression for block identifiability)

Baselines: ERM V-REx

Builds on: V-REx multiview CRL interventional CRL temporal CRL block identifiability

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