Research map / Probabilistic and scientific modeling / Causal discovery
Identifiable Latent Polynomial Causal Models through the Lens of Change
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Extends identifiability of latent causal models via changing causal influences from linear Gaussian to polynomial causal models with two-parameter exponential family noise, and proposes a variational estimation method that learns polynomial causal representations.
Problem
Identifiability of latent causal variables and causal graph in causal representation learning, where prior results via changing causal influences only covered linear Gaussian models and required many environments.
Approach
Narrow the latent solution space from the perspective of latent noise variables (using nonlinear ICA identifiability on exponential-family noise) and then exploit polynomial composition plus changing causal coefficients to reduce polynomial transformations to permutation/scaling, needing only 2l+1 environments; also show that unchanged coefficients cause non-identifiability and give partial identi
Key results
- Proposed method achieves higher MPC than VAE, beta-VAE and iVAE across linear Beta, linear Gamma and polynomial Gaussian settings on synthetic data.
- Changing only part of the coefficients yields identifiability only for nodes whose coefficients change, consistent with the partial identifiability corollary.
- On the image dataset, interventions on the learned latents recover the ground-truth chain z1->z2->z3, and the method beats baselines on MPC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed polynomial causal representation method instead of the compared baselines | Synthetic data · Synthetic linear Beta, linear Gamma, and polynomial Gaussian models | MPC | Helped |
| Use the proposed method instead of the compared baselines | Chemistry image data · Image dataset | MPC | Helped |
| Use polynomial models with Gaussian noise instead of the other tested model assumptions | Proposed method · fMRI hippocampus data | MPC | Helped |
| Use linear models with Gaussian noise instead of polynomial models with Gaussian noise | Proposed method · fMRI hippocampus data | MPC | Hurt |
| Keep a causal coefficient unchanged across environments (ablation) | Proposed method · Synthetic linear models with Beta noise | MPC | Hurt |
Surprising findings
- Unchanged coefficients in a node's polynomial make that node unidentifiable without extra assumptions, so changes in all coefficients appear necessary in general.
Limitations
- Non-Gaussian noise gradients are high variance; inverse Gaussian and inverse Gamma were unstable so only Gamma and Beta are reported.
- The factorized prior for non-Gaussian noise ignores dependence between causal mechanisms and may not hold in general.
- Learning causal graphs in latent space remains challenging even with identifiability guarantees.
Experimental setup
Datasets: synthetic latent polynomial/linear causal data chemistry image dataset (Lippe et al. modified) fMRI hippocampus dataset
Benchmarks: synthetic latent causal data chemistry image dataset fMRI hippocampus dataset
Metrics: mean Pearson correlation coefficient (MPC) structural Hamming distance (SHD)
Baselines: VAE beta-VAE iVAE
Builds on: iVAE linear Gaussian varying causal models (Liu et al. 2022) nonlinear ICA identifiability implicit reparameterization gradients
Closest papers by meaning
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- Causal Representation Learning Made Identifiable by Grouping of Observational Variables (ICML 2024 · similarity 0.91)
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- Differentiable Causal Discovery for Latent Hierarchical Causal Models (ICLR 2025 · similarity 0.91)
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