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Causal Representation Learning Made Identifiable by Grouping of Observational Variables
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Proposes G-CaRL, an unsupervised causal representation learning framework that assumes observed variables form known non-overlapping groups, proves identifiability of group-specific latent causal variables and inter-group causal graphs without temporal structure, interventions or supervision, and validates it on simulations, SERGIO gene regulatory data, and 3DIdent images.
Problem
Causal representation learning is severely ill-posed because it combines representation learning and causal discovery; existing identifiability results rely on temporal structure, supervision, or interventions that are often too restrictive in practice.
Approach
Assume the observed variables partition into known groups, each generated only from its own group of latent causal variables, with pairwise (exponential-family-like) Bayesian network causal relations across and within groups. Identifiability follows from non-factorizability and asymmetry of the causal potential, and a self-supervised contrastive method discriminates real samples from group-wise sh
Key results
- In Simulation 1 (3 groups of 10 latent variables, DAG), G-CaRL recovers latent variables and inter-group causal graphs with much higher performance than all baselines, per the paper's comparison figure.
- G-CaRL remains reasonably good with directed cycles and latent confounders (Simulation 2) and gives the best results among baselines on SERGIO gene regulatory data.
- On high-dimensional 3DIdent image observations, G-CaRL gives reasonably good estimation versus MVCRL and CCL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use G-CaRL instead of the evaluated baselines | CRL methods · Simulation 1: DAG | latent-variable correlation | Helped |
| Use G-CaRL instead of the evaluated baselines | CRL methods · Simulation 1: DAG | causal-graph F1-score | Helped |
| Use G-CaRL instead of the evaluated baselines | CRL methods · Simulation 2: cyclic graphs with latent confounders | CRL performance | Mixed |
| Use G-CaRL instead of the evaluated baselines | CRL methods · Gene regulatory network recovery | causal-graph recovery performance | Helped |
| Increase mixing-model complexity | G-CaRL · Simulation 1: DAG | estimation performance | Hurt |
| Increase the number of latent variables | G-CaRL · Simulation 1: DAG | estimation performance | Hurt |
| Increase the number of groups | G-CaRL · Simulation 1: DAG | estimation performance | Hurt |
| Increase the sample size | G-CaRL · Simulation 1: DAG | estimation performance | Helped |
Surprising findings
- The baseline CCL performs worst in the DAG simulation, which the authors attribute to its mutual-independence assumption among variables.
Limitations
- Identifiability of causal graphs only holds for inter-group connections; intra-group connections remain unidentified.
- Requires a known grouping of observed variables and, for the strong theorems, invertible group-wise mixings with equal latent and observed dimensions.
- Linear Gaussian SEMs are not identifiable under the model, and some graph conditions (co-parent/co-child) require dense inter-group connections.
Experimental setup
Datasets: SERGIO synthetic single-cell gene expression 3DIdent
Benchmarks: SERGIO gene regulatory network 3DIdent
Metrics: correlation F1-score
Baselines: MVCRL CausalVAE CCL MFCVAE VaDE beta-VAE
Builds on: nonlinear ICA causal additive models CCL MVCRL
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