Learning Bidirectional Causal Interactions with Heteroscedastic Neural Networks

2026-07-24 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

SEM-DNN, a novel heteroscedastic neural simultaneous-equation estimator, is proposed for learning contemporaneous bidirectional causal interactions from observational data without external instruments. This method identifies reciprocal structural interactions by exploiting conditional covariance diagonalization, assuming structural shocks have zero conditional means, are conditionally uncorrelated given predetermined covariates, and exhibit nonproportional conditional variances. SEM-DNN jointly approximates nonlinear structural mean functions and feature-dependent variances using a diagonal Gaussian quasi-likelihood. The approach establishes unique identification and positive-definite local curvature of its profiled population criterion. Monte Carlo experiments demonstrate that SEM-DNN more reliably recovers structural effects compared to parametric, kernel-based, and separate-equation neural alternatives, despite incurring greater computational cost. Its practical application is illustrated with ready-to-eat cereal scanner data, analyzing price-sales feedback.

Key takeaway

For research scientists or ML engineers modeling complex systems with endogenous variables, SEM-DNN offers a robust approach to identify bidirectional causal interactions without external instruments. You should consider its reliance on nonproportional conditional variances and the increased computational cost compared to simpler alternatives. Evaluate its suitability when your data exhibits heteroscedasticity and you need precise structural effect recovery.

Key insights

Bidirectional causal interactions can be identified from observational data using heteroscedastic neural networks and conditional covariance diagonalization.

Principles

• Conditional covariance diagonalization enables identification.
• Nonproportional conditional variances are key for identification.
• Causal interpretation relies on invariant mechanisms.

Method

SEM-DNN jointly approximates nonlinear structural mean functions and feature-dependent variances using a diagonal Gaussian quasi-likelihood incorporating the simultaneous-system Jacobian.

In practice

• Analyze contemporaneous price-sales feedback.
• Assess identification strength and variance calibration.
• Apply to scanner data for market dynamics.

Topics

• Bidirectional Causality
• Heteroscedastic Neural Networks
• Causal Inference
• Simultaneous Equation Models
• Conditional Covariance
• Observational Data

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

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.