Adversarial orthogonal regression: Two non-linear regressions for causal inference.

Area of Science:

• Machine Learning
• Causal Inference
• Statistical Modeling

Background:

• Traditional regression methods often assume specific noise distributions, limiting their applicability in complex causal inference scenarios.
• Accurate causal structure learning and model estimation are crucial for understanding real-world phenomena.

Purpose of the Study:

• To develop novel nonlinear regression methods, Adversarial Orthogonal Regression (AdOR) and Adversarial Orthogonal Structural Equation Model (AdOSE), for causal discovery.
• To enable robust causal structure learning and model estimation without restrictive assumptions on noise distributions.

Main Methods:

• Adversarial Orthogonal Regression (AdOR) for additive noise models and Adversarial Orthogonal Structural Equation Model (AdOSE) for general structural equation models.
• Simultaneous training of two adversarial networks: a regression network for predictions and a loss network for estimating mutual information (AdOR) or KL-divergence (AdOSE).
• Formulation as a minimax two-player game to achieve equilibrium, enabling estimation of conditional probability distributions or deterministic maps.

Main Results:

• AdOR estimates mutual information between residuals and inputs, while AdOSE estimates the conditional probability distribution of outputs given inputs.
• The proposed methods effectively make regression residuals independent from regressors.
• Demonstrated remarkable performance on both synthetic and real-world datasets compared to existing solutions.

Conclusions:

• AdOR and AdOSE offer powerful, assumption-free nonlinear regression tools for causal inference.
• These methods significantly advance the capabilities of causal direction determination and causal structure learning.
• The proposed techniques provide a robust framework for causal model estimation in diverse applications.