On the Sparse DAG Structure Learning Based on Adaptive Lasso

Danru Xu; Erdun Gao; Wei Huang; Menghan Wang; Andy Song; Mingming Gong

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arXiv · 2209.02946

On the Sparse DAG Structure Learning Based on Adaptive Lasso

Danru Xu·Erdun Gao·Wei Huang·Menghan Wang·Andy Song·Mingming Gong

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Abstract

Learning the underlying Bayesian Networks (BNs), represented by directed acyclic graphs (DAGs), of the concerned events from purely-observational data is a crucial part of evidential reasoning. This task remains challenging due to the large and discrete search space. A recent flurry of developments followed NOTEARS[1] recast this combinatorial problem into a continuous optimization problem by leveraging an algebraic equality characterization of acyclicity. However, the continuous optimization methods suffer from obtaining non-spare graphs after the numerical optimization, which leads to the inflexibility to rule out the potentially cycle-inducing edges or false discovery edges with small values. To address this issue, in this paper, we develop a completely data-driven DAG structure learning method without a predefined value to post-threshold small values. We name our method NOTEARS with adaptive Lasso (NOTEARS-AL), which is achieved by applying the adaptive penalty method to ensure the sparsity of the estimated DAG. Moreover, we show that NOTEARS-AL also inherits the oracle properties under some specific conditions. Extensive experiments on both synthetic and a real-world dataset demonstrate that our method consistently outperforms NOTEARS.

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Danru Xu, Erdun Gao, Wei Huang, Menghan Wang, Andy Song, Mingming Gong. 2022-09-07. On the Sparse DAG Structure Learning Based on Adaptive Lasso. https://arxiv.org/abs/2209.02946

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