Adversarial Orthogonal Regression: Two non-Linear Regressions for Causal Inference

TL;DR

This paper introduces two adversarial nonlinear regression methods, AdOR and AdOSE, for causal inference that do not assume noise distribution and effectively learn causal structures through minimax training.

Contribution

The paper presents novel adversarial regression techniques, AdOR and AdOSE, capable of causal inference without noise assumptions, advancing causal structure learning methods.

Findings

Both methods outperform previous solutions in synthetic experiments.

AdOR accurately estimates mutual information between residuals and inputs.

AdOSE effectively models conditional distributions in causal models.

Abstract

We propose two nonlinear regression methods, named Adversarial Orthogonal Regression (AdOR) for additive noise models and Adversarial Orthogonal Structural Equation Model (AdOSE) for the general case of structural equation models. Both methods try to make the residual of regression independent from regressors while putting no assumption on noise distribution. In both methods, two adversarial networks are trained simultaneously where a regression network outputs predictions and a loss network that estimates mutual information (in AdOR) and KL-divergence (in AdOSE). These methods can be formulated as a minimax two-player game; at equilibrium, AdOR finds a deterministic map between inputs and output and estimates mutual information between residual and inputs, while AdOSE estimates a conditional probability distribution of output given inputs. The proposed methods can be used as subroutines to address several learning problems in causality, such as causal direction determination (or more generally, causal structure learning) and causal model estimation. Synthetic and real-world experiments demonstrate that the proposed methods have a remarkable performance with respect to previous solutions.