Copula-ResLogit: A Deep-Copula Framework for Unobserved Confounding Effects

2026-03-11

AI Summary

This study addresses the challenge of non-causal dependencies in travel demand analysis arising from unobserved confounding factors. To this end, it proposes an interpretable joint modeling framework that integrates residual neural networks (ResNets) with copula models. The approach first employs copula functions to characterize the dependence structure among variables, thereby identifying potential confounding effects. It then leverages an embedded ResNet component to flexibly model and adjust for these effects. As the first work to combine ResNets with copulas for confounding control, the framework enhances interpretability without sacrificing model flexibility. Empirical evaluations on two real-world datasets demonstrate that the method substantially attenuates or even eliminates spurious dependencies induced by unobserved confounders, confirming its effectiveness in detecting and correcting for hidden confounding effects.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Causal Learning
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

A key challenge in travel demand analysis is the presence of unobserved factors that may generate non-causal dependencies, obscuring the true causal effects. To address the issue, the study introduces a novel deep learning based fully interpretable joint modelling framework, Copula-ResLogit, which integrates the flexibility of Residual Neural Network (ResNet) architectures with the dependence capturing capabilities of copula models. This hybrid structure enables us to first detect unobserved confounding through traditional copula function based joint modelling and then mitigate these hidden associations by incorporating deep learning components. The study applies this framework to two case studies, including the relationship between stress levels and wait time of pedestrians when crossing mid block in VR and the dependencies between travel mode choice and travel distance in London travel behaviour data. Results show that Copula-ResLogit substantially reduces or eliminates the dependencies, demonstrating the ability of residual layers to account for hidden confounding effects.

Problem

• unobserved confounding
• travel demand analysis
• non-causal dependencies
• causal effects

Innovation

• deep-copula
• unobserved confounding
• ResNet
• copula models
• causal inference