Nonnegative DAG Learning via Concomitant Estimation

2026-09-28

AI Summary

This study addresses the problem of learning directed acyclic graphs (DAGs) with non-negative edge weights from observational data. To this end, it proposes the NoCo estimator, which jointly recovers the weighted graph structure and noise variances. By exploiting the non-negativity of edge weights, the method simplifies the optimization landscape. Furthermore, it introduces a smoothed companion Lasso criterion coupled with a log-determinant constraint to circumvent KKT degeneracy. An efficient solver is developed based on the method of multipliers, block sequential convex approximation, and proximal gradient descent. The proposed approach significantly improves both DAG structure recovery and edge weight estimation accuracy across diverse scenarios, offering a novel framework for non-negative causal discovery that combines rigorous theoretical guarantees with computational efficiency.

Abstract

We study the problem of learning directed acyclic graphs (DAGs) with nonnegative edge weights from observational data. We propose the Nonnegative and Concomitant (NoCo) DAG estimator, which jointly recovers the weighted graph structure and the exogenous noise variances in the linear structural equation model for the observations. Different from prior art, this noise-adaptive formulation blends a smoothed concomitant lasso criterion with a simpler log-determinant acyclicity constraint that exploits nonnegativity and yields a more benign optimization landscape. Specifically, nonnegative weights allow us to impose acyclicity directly on the adjacency matrix without elementwise squaring of its entries, thus avoiding the well-documented degeneracy of the Karush-Kuhn-Tucker conditions. Computationally, we develop a method of multipliers' algorithm that accommodates both homoscedastic and heteroscedastic noise profiles. Within each iteration, we use block successive convex approximation to minimize the augmented Lagrangian, alternating between proximal gradient steps for the adjacency matrix and closed-form updates for the noise scales. Simulated experiments demonstrate NoCo's improved structural and edge-weight recovery relative to competing methods in a variety of settings, highlighting the benefits of exploiting nonnegativity along with noise adaptivity.

Problem

• Directed Acyclic Graph
• Nonnegative Edge Weights
• Observational Data
• Structure Learning
• Linear Structural Equation Model

Innovation

• Directed Acyclic Graph
• Concomitant Estimation
• Nonnegative Weights
• Log-determinant Acyclicity Constraint
• Block Successive Convex Approximation