Gradient-based Causal Structure Learning with Normalizing Flow

TL;DR

This paper introduces DAG-NF, a score-based normalizing flow approach for causal structure learning that leverages Jacobian matrices and extends existing methods like NOTEARS to improve efficiency and applicability.

Contribution

It proposes DAG-NF, a novel method combining normalizing flows with causal discovery, extending NOTEARS and enabling application to flow-based neural networks.

Findings

Reduces computational complexity of causal graph search.

Applicable to various flow-based neural networks.

Demonstrates effective causal structure learning.

Abstract

In this paper, we propose a score-based normalizing flow method called DAG-NF to learn dependencies of input observation data. Inspired by Grad-CAM in computer vision, we use jacobian matrix of output on input as causal relationships and this method can be generalized to any neural networks especially for flow-based generative neural networks such as Masked Autoregressive Flow(MAF) and Continuous Normalizing Flow(CNF) which compute the log likelihood loss and divergence of distribution of input data and target distribution. This method extends NOTEARS which enforces a important acylicity constraint on continuous adjacency matrix of graph nodes and significantly reduce the computational complexity of search space of graph.