Composite Graphical Causal Models for Inference on Heterogeneous-Indexed Data

Arne De Temmerman, Mathias Verbeke
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:887-910, 2026.

Abstract

Complex real-world systems typically consist of multiple interdependent subsystems, where each subsystem can operate under different sampling references. Consequently, the data collected across these subsystems vary in indexing (e.g., time-, distance-, event-indexed), sampling frequency, or faces index misalignment. To approximately model such kind of systems, surrogate models can be used to serve as a computationally-inexpensive replacement during optimization, sensitivity analysis, uncertainty quantification, or interpretation. Conventional modeling approaches require these datasets to be unified into a single, uniformly-indexed table via preprocessing steps such as aggregation and merging. In this work, we introduce a novel approach, Composite Graphical Causal Models (CGCMs), that preserves the original indexing of each data table during both training and inference. By embedding resampling and aggregation operations directly within a GCM, our method eliminates the need for data homogenization as a preprocessing step. Specifically, a set of GCMs is employed each tailored to a distinct indexing, and connected using aggregation functions to model cross-index dependencies. As validated on synthetic datasets, this design enables a more representative modeling of heterogeneous-indexed processes, improving predictive performance and interpretability.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-de-temmerman26a, title = {Composite Graphical Causal Models for Inference on Heterogeneous-Indexed Data}, author = {De Temmerman, Arne and Verbeke, Mathias}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {887--910}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/de-temmerman26a/de-temmerman26a.pdf}, url = {https://proceedings.mlr.press/v323/de-temmerman26a.html}, abstract = {Complex real-world systems typically consist of multiple interdependent subsystems, where each subsystem can operate under different sampling references. Consequently, the data collected across these subsystems vary in indexing (e.g., time-, distance-, event-indexed), sampling frequency, or faces index misalignment. To approximately model such kind of systems, surrogate models can be used to serve as a computationally-inexpensive replacement during optimization, sensitivity analysis, uncertainty quantification, or interpretation. Conventional modeling approaches require these datasets to be unified into a single, uniformly-indexed table via preprocessing steps such as aggregation and merging. In this work, we introduce a novel approach, Composite Graphical Causal Models (CGCMs), that preserves the original indexing of each data table during both training and inference. By embedding resampling and aggregation operations directly within a GCM, our method eliminates the need for data homogenization as a preprocessing step. Specifically, a set of GCMs is employed each tailored to a distinct indexing, and connected using aggregation functions to model cross-index dependencies. As validated on synthetic datasets, this design enables a more representative modeling of heterogeneous-indexed processes, improving predictive performance and interpretability.} }
Endnote
%0 Conference Paper %T Composite Graphical Causal Models for Inference on Heterogeneous-Indexed Data %A Arne De Temmerman %A Mathias Verbeke %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-de-temmerman26a %I PMLR %P 887--910 %U https://proceedings.mlr.press/v323/de-temmerman26a.html %V 323 %X Complex real-world systems typically consist of multiple interdependent subsystems, where each subsystem can operate under different sampling references. Consequently, the data collected across these subsystems vary in indexing (e.g., time-, distance-, event-indexed), sampling frequency, or faces index misalignment. To approximately model such kind of systems, surrogate models can be used to serve as a computationally-inexpensive replacement during optimization, sensitivity analysis, uncertainty quantification, or interpretation. Conventional modeling approaches require these datasets to be unified into a single, uniformly-indexed table via preprocessing steps such as aggregation and merging. In this work, we introduce a novel approach, Composite Graphical Causal Models (CGCMs), that preserves the original indexing of each data table during both training and inference. By embedding resampling and aggregation operations directly within a GCM, our method eliminates the need for data homogenization as a preprocessing step. Specifically, a set of GCMs is employed each tailored to a distinct indexing, and connected using aggregation functions to model cross-index dependencies. As validated on synthetic datasets, this design enables a more representative modeling of heterogeneous-indexed processes, improving predictive performance and interpretability.
APA
De Temmerman, A. & Verbeke, M.. (2026). Composite Graphical Causal Models for Inference on Heterogeneous-Indexed Data. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:887-910 Available from https://proceedings.mlr.press/v323/de-temmerman26a.html.

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