Learning Bidirectional Causal Interactions with Heteroscedastic Neural Networks

2026-07-27 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

SEM-DNN, a novel heteroscedastic neural simultaneous-equation estimator, is introduced for learning contemporaneous bidirectional causal interactions from observational data without external instruments. This method identifies structural effects by exploiting conditional covariance diagonalization: only the true interaction coefficients diagonalize the conditional residual covariance when structural shock variances vary nonproportionally across the feature space. SEM-DNN jointly approximates nonlinear structural mean functions and feature-dependent variances using a diagonal Gaussian quasi-likelihood. Monte Carlo experiments, using sample sizes up to n=20000 and true interaction parameters (γ1, γ2)=(0.5, 0.4), demonstrate its superior reliability in recovering structural effects compared to parametric, kernel-based, and separate-equation neural alternatives, despite higher computational costs. An application to ready-to-eat cereal scanner data showcases its utility in analyzing price–sales feedback and evaluating identification strength.

Key takeaway

For research scientists or ML engineers analyzing systems with contemporaneous bidirectional feedback where credible external instruments are unavailable, you should consider SEM-DNN. This method offers a robust approach to estimate direct causal interactions by leveraging conditional heteroscedasticity and neural network flexibility. Be sure to utilize the provided diagnostics to evaluate identification strength and variance calibration, as empirical uncertainty can be substantial, guiding your interpretation of the results.

Key insights

Bidirectional causal interactions can be identified from observational data by exploiting nonproportional conditional variance heteroscedasticity.

Principles

• Nonproportional conditional variances identify bidirectional causal effects.
• Neural networks approximate nonlinear mean and variance functions.
• Stabilized training is crucial for joint mean-variance-interaction learning.

Method

SEM-DNN jointly approximates nonlinear structural mean and feature-dependent variance functions using neural networks, maximizing a diagonal Gaussian quasi-likelihood with a simultaneous-system Jacobian to diagonalize conditional residual covariance.

In practice

• Apply SEM-DNN to two-outcome feedback systems lacking instruments.
• Use diagnostics to assess heteroscedastic identification strength.
• Evaluate variance calibration and optimization sensitivity.

Topics

• Causal Learning
• Simultaneous Equation Models
• Heteroscedastic Neural Networks
• Conditional Covariance Diagonalization
• Observational Data Analysis
• Econometrics

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.