Deep Gaussian Processes on Directed Acyclic Graphs

• URL: http://arxiv.org/abs/2607.09645v1
• Date: Fri, 10 Jul 2026 17:41:11 GMT
• Title: Deep Gaussian Processes on Directed Acyclic Graphs
• Abstract summary: Many real-world processes can be represented as compositions of functions along a directed acyclic graph (DAG)<n>These functions are partially observed across the DAG, with noisy and heterogeneously sampled measurements.<n>We theoretically study their prior-collapse behaviour, and the effect of graph topology and intermediate observations on information preservation.<n>We offer a structured variational approximation that retains graph dependencies, preserves compositional uncertainty, and captures the explaining-away behaviour of colliders.
• Score: 11.74273181198187
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many real-world processes can be represented as compositions of functions along a directed acyclic graph (DAG). In causal modelling, these correspond to the underlying mechanisms; in engineering, to multiple fidelity levels; and in gene-regulatory networks, to transcription factors. These functions are partially observed across the DAG, with noisy and heterogeneously sampled measurements, posing significant challenges for reconstruction, uncertainty propagation, and inference. To tackle these challenges, we place priors over functions and naturally arrive at Deep Gaussian Processes over DAGs. We theoretically study their prior-collapse behaviour, and the effect of graph topology and intermediate observations on the preservation of information. We obtain almost-sure lower bounds on the asymptotic frequency of depths at which the distinction between inputs is preserved, identify broad kernel classes for which these hold, and prove an observation by \cite{dunlop2018} on the role of input connections. We offer a structured variational approximation that retains graph dependencies, preserves compositional uncertainty, and captures the explaining-away behaviour of colliders. Finally, we empirically validate our theoretical results and our methodology, and model a latent-collider DAG, a protein signalling network, and a multi-fidelity heavy-ion collision emulation task, attaining state-of-the-art performance while recovering low-fidelity contributions and yielding interpretability of the simulator hierarchy.

Related papers

• SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery [0.0]
  SVI-DAG is a structured variational inference approach to causal discovery.<n>It supports expressive and multimodal posterior learning over DAGs.<n>We evaluate SVI-DAG against 5 state-of-the-art Bayesian DAG learning methods.
  arXiv  Detail & Related papers  (2026-08-05T14:56:14Z)
• Towards Fast GNN Surrogates for CO2 Migration in Complex Geological Formations [58.079925240809644]
  We propose an end-to-end graph neural surrogate tailored to CO$$ibility plume migration forecasting in geological storage.<n>The method is evaluated on the SPE11A benchmark, a well-known industry test case designed to assess CO$$ storage scenarios.<n>The proposed model produces competitive forecasts of gas saturation and liquid-phase density, with cumulative errors that remain moderate over extended forecasting horizons.
  arXiv  Detail & Related papers  (2026-06-15T18:19:17Z)
• Concomitant DAG Learning: On the Roles of Noise Adaptivity, Sparsity, and Non-negativity [14.977112037008224]
  Directed acyclic graphs (DAGs) enable principled reasoning about cause-effect interactions in complex systems.<n>Most classical structure identification approaches face two key obstacles: the challenge of enforcing acyclicity, and identifiability challenges arising from latent or heterogeneous noise.<n>This tutorial offers an overview of recent signal processing and advances that address these issues by recasting DAG structure learning as a continuous, score-based estimation problem.
  arXiv  Detail & Related papers  (2026-05-22T12:00:00Z)
• Reinforcement Learning for Microcanonical Graph Ensemble with Assortativity Constraints [1.0896567381206717]
  How network structure determines function is a fundamental question, and it can be investigated by graph ensembles with precisely controlled structural properties.<n>Here we introduce the Deep Microcanonical Graph Generator (DMGG), a reinforcement learning framework that transforms any given graph through degree-preserving rewirings.
  arXiv  Detail & Related papers  (2026-05-22T06:57:41Z)
• RAwR: Role-Aware Rewiring via Approximate Equitable Partition [1.5445058818973285]
  We introduce RAwR, a computationally efficient rewiring framework.<n> RAwR augments the input graph with a quotient graph derived from equitable partitions.<n> Empirical evaluations across a diverse suite of benchmarks demonstrate RAwR achieves state-of-the-art results.
  arXiv  Detail & Related papers  (2026-05-10T10:15:40Z)
• SIGMA: Scalable Spectral Insights for LLM Collapse [51.863164847253366]
  We introduce SIGMA (Spectral Inequalities for Gram Matrix Analysis), a unified framework for model collapse.<n>By utilizing benchmarks that deriving and deterministic bounds on the matrix's spectrum, SIGMA provides a mathematically grounded metric to track the contraction of the representation space.<n>We demonstrate that SIGMA effectively captures the transition towards states, offering both theoretical insights into the mechanics of collapse.
  arXiv  Detail & Related papers  (2026-01-06T19:47:11Z)
• Transformers Provably Learn Directed Acyclic Graphs via Kernel-Guided Mutual Information [91.66597637613263]
  transformer-based models leveraging the attention mechanism have demonstrated strong empirical success in capturing complex dependencies within graphs.<n>We introduce a novel information-theoretic metric: the kernel-guided mutual information (KG-MI) based on the $f$-divergence.<n>We prove that, given sequences generated by a $K$-parent DAG, training a single-layer, multi-head transformer via a gradient ascent converges to the global optimum time.
  arXiv  Detail & Related papers  (2025-10-29T14:07:12Z)
• Information-theoretic Quantification of High-order Feature Effects in Classification Problems [0.19791587637442676]
  We present an information-theoretic extension of the High-order interactions for Feature importance (Hi-Fi) method.<n>Our framework decomposes feature contributions into unique, synergistic, and redundant components.<n>Results indicate that the proposed estimator accurately recovers theoretical and expected findings.
  arXiv  Detail & Related papers  (2025-07-06T11:50:30Z)
• Understanding the Effect of GCN Convolutions in Regression Tasks [8.299692647308323]
  Graph Convolutional Networks (GCNs) have become a pivotal method in machine learning for modeling functions over graphs.<n>We consider networks for which the graph structure implies that neighboring nodes exhibit similar signals.<n>We examine how two common convolutions - the original GCN and GraphSAGE convolutions - affect the learning error.
  arXiv  Detail & Related papers  (2024-10-26T04:19:52Z)
• Revealing Decurve Flows for Generalized Graph Propagation [108.80758541147418]
  This study addresses the limitations of the traditional analysis of message-passing, central to graph learning, by defining em textbfgeneralized propagation with directed and weighted graphs. We include a preliminary exploration of learned propagation patterns in datasets, a first in the field.
  arXiv  Detail & Related papers  (2024-02-13T14:13:17Z)
• DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets [81.75973217676986]
  Gene regulatory networks (GRN) describe interactions between genes and their products that control gene expression and cellular function. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over DAGs, but not both. In this paper we leverage the fact that it is possible to estimate the "velocity" of gene expression with RNA velocity techniques to develop an approach that addresses both challenges.
  arXiv  Detail & Related papers  (2023-02-08T16:36:40Z)
• BCDAG: An R package for Bayesian structure and Causal learning of Gaussian DAGs [77.34726150561087]
  We introduce the R package for causal discovery and causal effect estimation from observational data. Our implementation scales efficiently with the number of observations and, whenever the DAGs are sufficiently sparse, the number of variables in the dataset. We then illustrate the main functions and algorithms on both real and simulated datasets.
  arXiv  Detail & Related papers  (2022-01-28T09:30:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.