Research map / Probabilistic and scientific modeling / Causal discovery
Causal Representation Learning from Multiple Distributions: A General Setting
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Shows that in fully nonparametric causal representation learning from multiple distributions (no hard interventions), sparsity plus sufficient changes recover the moralized causal graph and latent variables up to structured indeterminacies, and proposes a VAE-based change encoding network validated on simulations.
Problem
Recovering latent causal variables and their causal graph from observed nonlinear mixtures when the data come from multiple distributions (heterogeneous or nonstationary), without parametric assumptions or hard interventions.
Approach
Under sparsity on the recovered Markov network and sufficient changes in causal mechanisms, the latent Markov network is identifiable up to isomorphism and each latent is recovered as a function of itself and its intimate neighbors; the Markov network equals the moralized DAG under relaxed faithfulness (SAF and SUCF), which are shown to be necessary and sufficient.
Key results
- Simulations on 4-variable Y-structure and chain graphs show a strong one-to-one correspondence between estimated and true latent components in most cases.
- The sparsity-regularized model recovers the Y-structure adjacency (nonzero entries A13, A23, A34) consistent with the true graph.
- Theory shows the recovered latent Markov network is isomorphic to the true one under minimal-edge sparsity and sufficient changes.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add sparsity regularization to the estimated causal adjacency matrix | Change Encoding Network · Simulated Y-structure | causal structure recovery | Helped |
Surprising findings
- Nonlinear ICA-style independent components as functions of X generally do not exist across domains when the true latent DAG is not empty.
Limitations
- Sparsity regularization in the practical model is an l1 approximation of the Markov-network edge-count constraint.
- Experiments are limited to small simulated graphs with 4 variables.
- Assumes all causal mechanisms change; the case where only a subset changes is left for future work.
Experimental setup
Datasets: simulated latent SEM data (Y-structure and chain, 4 variables)
Benchmarks: simulated Y-structure and chain graphs
Metrics: correlation between estimated and true latents recovered adjacency matrix
Baselines: VAE iVAE
Builds on: iVAE nonlinear ICA with auxiliary variables faithfulness assumption
Closest papers by meaning
- Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity (NeurIPS 2024 · similarity 0.91)
- A Sparsity Principle for Partially Observable Causal Representation Learning (ICML 2024 · similarity 0.90)
- Identifiable Latent Polynomial Causal Models through the Lens of Change (ICLR 2024 · similarity 0.89)
- Causal Representation Learning via Counterfactual Intervention (AAAI 2024 · similarity 0.89)
- Disentangled Representation Learning in Non-Markovian Causal Systems (NeurIPS 2024 · similarity 0.89)
- Causal Representation Learning Made Identifiable by Grouping of Observational Variables (ICML 2024 · similarity 0.89)
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