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Disentangled Representation Learning in Non-Markovian Causal Systems
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Proposes graphical criteria and an algorithm (CRID) that determine which latent causal variables can be disentangled from non-Markovian, multi-domain, arbitrary-intervention data, producing a causal disentanglement map.
Problem
Causal disentangled representation learning when latent causal variables are generated by a non-Markovian (confounded) system and data come from heterogeneous domains and arbitrary interventions, where full disentanglement is often impossible.
Approach
Introduces latent selection diagrams and graphical criteria (∆Q sets, invariant factors) that determine disentangleability of target variables from entangled ones without requiring Markovianity or one intervention per node, plus an algorithm (CRID) that outputs a causal disentanglement map.
Key results
- On simulations with chain, collider, and non-Markovian latent graphs, learned representations' MCC matches the disentanglement predicted by CRID (e.g., V3 disentangled from V1 in the chain, V3 disentangled from {V1,V2,V4} in the non-Markovian graph).
- The paper claims to be the first disentangled representation learning work relaxing Markovianity, allowing arbitrary interventions and multi-domain data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use observational and two intervention distributions targeting V3 | Causal representation learning on the chain graph · Synthetic chain graph | MCC | Helped |
| Use observational distributions from two domains | Causal representation learning on the chain graph · Synthetic chain graph | MCC | Helped |
| Use observational distributions from four domains with changes on V1 and V3 | Causal representation learning on the collider graph · Synthetic collider graph | MCC | Helped |
| Use two interventions targeting V3 | Causal representation learning on the non-Markovian graph · Synthetic non-Markovian graph | MCC | Helped |
Surprising findings
- Full disentanglement of the root variable V1 is achieved without intervening on V1 in the chain graph.
Limitations
- Assumes soft interventions do not alter the causal graph structure and no structural changes across domains.
- Assumes known intervention targets and known latent causal graph; structure learning is treated separately.
- Sufficient-change (genericity) assumptions required; the paper notes these can be violated when densities are fine-tuned.
Experimental setup
Datasets: synthetic data from latent selection diagrams MNIST
Benchmarks: synthetic latent selection diagram simulations (chain, collider, non-Markovian graphs) MNIST image editing
Metrics: mean correlation coefficient (MCC)
Baselines: Lachapelle et al. 2023 (sparsity-based functional dependency) Jiang & Aragam 2023 Yao et al. 2022
Builds on: nonlinear ICA selection diagrams causal representation learning identifiability
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