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Deep Gaussian Processes on Directed Acyclic Graphs

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Differentiable and score-based DAG learning · 0 citations (OpenAlex)

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Defines deep Gaussian processes over general DAGs (DAG-DGPs) with nodewise fusion kernels and intermediate observations, proves non-collapse/contraction results, and proposes structured (clique-chordal) and mean-field variational inference.

Problem

Deep GP priors over compositions of functions along a DAG can suffer prior collapse, and existing DGP inference cannot handle heterogeneous partial observations at internal nodes or preserve explaining-away dependencies across branches of a general DAG.

Approach

Places GP priors on each non-root node of a DAG with multi-parent fusion kernels and local observations, proves almost-sure lower bounds on non-collapse frequency via progressive antichains, and uses a chordal-completion precision structure for variational posterior that retains explaining-away couplings.

Key results

• On the synthetic COLLIDER task, DAG-SVI reduces RMSE to 0.055 from 0.114 for DAG-VI and CRPS to 0.060 from 0.075.
• On Sachs extrapolation, DAG-SVI improves RMSE to 0.642 (vs 0.737 for DAG-VI) and CRPS to 0.299 (vs 0.325).
• On the heavy-ion published split, DAG-SVI gives the best RMSE, N-RMSE and CRPS, with L2 contributing most to the high-fidelity prediction.

Surprising findings

• On Sachs interpolation, DAG-VI and DAG-SVI perform almost identically (RMSE 0.646 vs 0.642), with DAG-VI slightly better on CRPS.

Limitations

• Assumes a well-specified DAG; graph misspecification is not handled.
• Scaling to much larger graphs is stated as an open challenge.
• Non-collapse results require a separating-node condition that may be hard to verify in some topologies.

Experimental setup

Datasets: Sachs flow cytometry heavy-ion collision emulation dataset synthetic latent-collider

Benchmarks: Sachs interpolation/extrapolation COLLIDER heavy-ion multi-fidelity split

Metrics: RMSE CRPS N-RMSE NLL

Baselines: DAG-VI GMGP d-GMGP

Builds on: deep Gaussian processes doubly stochastic variational inference input-connected DGP graphical multi-fidelity GP

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