Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Non-negative Weighted DAG Structure Learning

Samuel Rey, Seyed Saman Saboksayr, Gonzalo Mateos

TL;DR

The paper tackles learning DAG structure from nodal observations under a linear SEM, proposing a convex acyclicity approach that requires non-negative edge weights. It introduces the log-determinant based acyclicity $h_{ldet}(W)$ and casts DAG learning as an abstract convex optimization problem solved via a method of multipliers, guaranteeing a global minimum. Theoretical results show recoverability of the true DAG in the infinite-sample limit, and extensive synthetic experiments demonstrate superior performance over state-of-the-art non-convex methods, particularly on Erdős–Rényi graphs. This work offers a reliable, convex alternative for causal structure discovery with practical implications for scalable DAG learning and causal inference.

Abstract

We address the problem of learning the topology of directed acyclic graphs (DAGs) from nodal observations, which adhere to a linear structural equation model. Recent advances framed the combinatorial DAG structure learning task as a continuous optimization problem, yet existing methods must contend with the complexities of non-convex optimization. To overcome this limitation, we assume that the latent DAG contains only non-negative edge weights. Leveraging this additional structure, we argue that cycles can be effectively characterized (and prevented) using a convex acyclicity function based on the log-determinant of the adjacency matrix. This convexity allows us to relax the task of learning the non-negative weighted DAG as an abstract convex optimization problem. We propose a DAG recovery algorithm based on the method of multipliers, that is guaranteed to return a global minimizer. Furthermore, we prove that in the infinite sample size regime, the convexity of our approach ensures the recovery of the true DAG structure. We empirically validate the performance of our algorithm in several reproducible synthetic-data test cases, showing that it outperforms state-of-the-art alternatives.

Non-negative Weighted DAG Structure Learning

TL;DR

The paper tackles learning DAG structure from nodal observations under a linear SEM, proposing a convex acyclicity approach that requires non-negative edge weights. It introduces the log-determinant based acyclicity and casts DAG learning as an abstract convex optimization problem solved via a method of multipliers, guaranteeing a global minimum. Theoretical results show recoverability of the true DAG in the infinite-sample limit, and extensive synthetic experiments demonstrate superior performance over state-of-the-art non-convex methods, particularly on Erdős–Rényi graphs. This work offers a reliable, convex alternative for causal structure discovery with practical implications for scalable DAG learning and causal inference.

Abstract

We address the problem of learning the topology of directed acyclic graphs (DAGs) from nodal observations, which adhere to a linear structural equation model. Recent advances framed the combinatorial DAG structure learning task as a continuous optimization problem, yet existing methods must contend with the complexities of non-convex optimization. To overcome this limitation, we assume that the latent DAG contains only non-negative edge weights. Leveraging this additional structure, we argue that cycles can be effectively characterized (and prevented) using a convex acyclicity function based on the log-determinant of the adjacency matrix. This convexity allows us to relax the task of learning the non-negative weighted DAG as an abstract convex optimization problem. We propose a DAG recovery algorithm based on the method of multipliers, that is guaranteed to return a global minimizer. Furthermore, we prove that in the infinite sample size regime, the convexity of our approach ensures the recovery of the true DAG structure. We empirically validate the performance of our algorithm in several reproducible synthetic-data test cases, showing that it outperforms state-of-the-art alternatives.
Paper Structure (7 sections, 18 equations, 1 figure)

This paper contains 7 sections, 18 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Fundamentals of DAG structure learning
  3. Non-negative DAG structure learning
  4. Convex acyclicity functions via non-negative matrices
  5. DAG structure learning via method of multipliers
  6. Numerical experiments
  7. Conclusion

Figures (1)

  • Figure 1: Evaluation of the proposed DAG structure learning method across different scenarios. a) reports the error of ${\hat{\mathbf W} }$ as the number of samples increases. b) presents the normalized SHD between ${\hat{\mathbf W} }$ and the true DAG structure as the number of nodes increases. c) illustrates the error of ${\hat{\mathbf W} }$ for different values of the variance of the exogenous input ${\mathbf Z}$.

Theorems & Definitions (2)

  • proof
  • proof