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Structural Causal Bottleneck Models

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation · 0 citations (OpenAlex)

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Introduces structural causal bottleneck models, where effects between high-dimensional variables pass through low-dimensional bottleneck summaries, with identifiability results and synthetic identifiability, misspecification, and transfer-learning experiments.

Problem

Causal effect estimation and modeling among high-dimensional variables suffers from the curse of dimensionality, and existing dimension reduction (PCA, sufficient dimension reduction, causal representation learning, causal abstraction) either discards target-relevant information or requires heavy as

Approach

Assume each causal mechanism between high-dimensional vectors depends only on a low-dimensional, target-specific bottleneck of each parent (factored or intrinsic), define the induced SCM and equivalence classes, show bottlenecks are identifiable up to invertible maps under injectivity and additive noise, and estimate them via regression with bottleneck-dimension constraints.</�core_idea>

Key results

• In linear SCBMs, bottleneck recovery R^2 saturates around n=10000 and stays strong as node count grows.
• For misspecified bottleneck dimension, identifiability metric increases until the assumed dimension equals the ground truth and does not degrade with overestimation.
• In low-sample transfer learning, using estimated bottleneck variables as conditioning sets reduces MAE of effect estimation relative to conditioning on the observed high-dimensional confounder.

Surprising findings

• Randomly initialized MLP bottleneck spaces collapse numerically to near one-dimensional subspaces for products of as few as three random factors.

Limitations

• Experiments are limited to synthetic data and small graphs; no real-world application.
• Nonlinear experiments show lower identifiability and error propagation grows with graph size.
• Assumes the causal graph is known; graph discovery is left to future work.

Experimental setup

Datasets: synthetic data from randomly sampled SCBMs

Benchmarks: synthetic SCBMs

Metrics: R^2 of bidirectional regression between true and estimated b mean absolute error of causal effect estimate

Baselines: PCA

Builds on: structural causal models information bottleneck sufficient dimension reduction causal representation learning

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