# DAGs with No Curl: An Efficient DAG Structure Learning Approach

@article{Yu2021DAGsWN, title={DAGs with No Curl: An Efficient DAG Structure Learning Approach}, author={Yue Yu and Tian Gao and Naiyu Yin and Qiang Ji}, journal={ArXiv}, year={2021}, volume={abs/2106.07197} }

Recently directed acyclic graph (DAG) structure learning is formulated as a constrained continuous optimization problem with continuous acyclicity constraints and was solved iteratively through subproblem optimization. To further improve efficiency, we propose a novel learning framework to model and learn the weighted adjacency matrices in the DAG space directly. Specifically, we first show that the set of weighted adjacency matrices of DAGs are equivalent to the set of weighted gradients of…

## 25 Citations

### On the Convergence of Continuous Constrained Optimization for Structure Learning

- 2022

Computer Science

AISTATS

This work reviews the standard convergence result of the ALM and shows that the required conditions are not satisfied in the recent continuous constrained formulation for learning DAGs, and establishes the convergence guarantee of QPM to a DAG solution, under mild conditions, based on a property of the DAG constraint term.

### Truncated Matrix Power Iteration for Differentiable DAG Learning

- 2022

Computer Science

NeurIPS

This work discovers that large coefficients on higher-order terms are beneficial for DAG learning, when the spectral radiuses of the adjacency matrices are small, and that larger coefficients for higher- order terms can approximate the DAG constraints much better than the small counterparts.

### DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization

- 2022

Computer Science

NeurIPS

A new acyclicity characterization based on the log-determinant (log-det) function, which leverages the nilpotency property of DAGs and can reach large speed-ups and smaller structural Hamming distances against state-of-the-art methods.

### Differentiable and Transportable Structure Learning

- 2022

Computer Science

ArXiv

D-Struct is introduced which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable, and can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS.

### Convergence of Feedback Arc Set-Based Heuristics for Linear Structural Equation Models

- 2022

Computer Science

PGM

This work builds upon previous contributions on such heuristics by first establishing mathematical convergence analysis, previously lacking, and showing empirically how one can significantly speed-up convergence in practice using simple warmstarting strategies.

### Learning Discrete Directed Acyclic Graphs via Backpropagation

- 2022

Computer Science, Mathematics

ArXiv

DAG-DB is proposed, a framework for learning DAGs by Discrete Backpropagation, based on the architecture of Implicit Maximum Likelihood Estimation, and adopts a probabilistic approach to the problem, sampling binary adjacency matrices from an implicit probability distribution.

### Learning DAGs from Data with Few Root Causes

- 2023

Computer Science

A novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM) is presented and it is proved that the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes.

### Differentiable DAG Sampling

- 2022

Computer Science

ICLR

VI-DP-DAG is guaranteed to output a valid DAG at any time during training and does not require any complex augmented Lagrangian optimization scheme in contrast to existing differentiable DAG learning approaches.

### FedDAG: Federated DAG Structure Learning

- 2023

Computer Science

Trans. Mach. Learn. Res.

This paper takes the first step in developing a gradient-based learning framework named FedDAG, which can learn the DAG structure without directly touching the local data and also can naturally handle the data heterogeneity.

### Structure Learning with Continuous Optimization: A Sober Look and Beyond

- 2023

Computer Science

Investigating in which cases continuous optimization for directed acyclic graph (DAG) structure learning can and cannot perform well and why this happens, and suggesting possible directions to make the search procedure more reliable, suggests that future works should take into account the non-equal noise variances formulation to handle more general settings.

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