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Identifying Causal Direction via Variational Bayesian Compression

ICML 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation

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Proposes COMIC, a bivariate causal discovery method that scores each direction by the variational Bayesian codelength of a Bayesian neural network conditional model, and shows non-separable-compatibility for identifiability.

Problem

Distinguishing cause from effect between two variables from purely observational data using algorithmic Markov condition / MDL codelengths, where previous conditional models (simple basis functions or Gaussian processes) trade off fitness against computational cost.

Approach

Model conditionals with one-hidden-layer Bayesian neural networks (mean-field Gaussian variational posteriors) and use the variational Bayesian codelength (bits-back / ELBO-based) as the complexity-aware codelength for each causal direction, comparing the two direction scores.

Key results

• COMIC perfectly determines causal direction on AN, AN-s, LS, LS-s and MN-U synthetic benchmarks.
• COMIC achieves second-best overall performance, behind GPLVM, across all benchmarks, with lower variance than most baselines.
• On the real-world Tubingen benchmark, COMIC performs comparably to other complexity-based methods (GPLVM, SLOPPY-AIC, SLOPE, QCCD) and outperforms LOCI and CAM.

Measured effects reported in the paper

Surprising findings

• GPLVM, which requires the most GPU compute, attains the best overall results, while COMIC is second-best.
• IGCI with the uniform reference measure, despite targeting low-noise settings, shows the lowest accuracy on SIM-ln.

Limitations

• Non-convexity of the learning objective may affect convergence and consistency.
• Standard Gaussian marginal codelength for the cause introduces a bias toward more Gaussian causes.
• Restricted to the bivariate setting under causal sufficiency.

Experimental setup

Datasets: AN AN-s LS LS-s MN-U SIM SIM-c SIM-G SIM-ln CE-Multi CE-Net CE-Cha

Benchmarks: AN AN-s LS LS-s MN-U SIM SIM-c SIM-G SIM-ln CE-Multi CE-Net CE-Cha

Metrics: accuracy bidirectional AUROC

Baselines: SLOPPY (AIC) SLOPPY (BIC) SLOPER SLOPE QCCD IGCI GPLVM LOCI CAM

Builds on: SLOPE SLOPPY QCCD LOCI CAM GPLVM-based causal discovery

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