arXiv：cs.LG（机器学习，全量分类）· Sadegh Khorasani, Ali Najar, Saber Salehkaleybar, Negar Kiyavash·· 5 小时前AI 评分35
面向含隐混杂因子的循环线性高斯模型的可微结构学习
Differentiable Structure Learning for Cyclic Linear Gaussian Models with Latent Confounders
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研究提出一种面向含循环与未知数量外生隐混杂因子的线性高斯结构因果模型的可微结构学习方法，通过 Bernoulli 门参数化有向边与候选隐变量，对惩罚负对数似然取期望后得到闭式可微复杂度惩罚，并证明其与离散结构学习目标具有相同全局下确界。在代数忠实性、结构最小性与模型重叠假设下，该方法对全局得分最小解具备至边际准等价的一致性，实验显示其恢复误差低于此前方法。
正文
Abstract:We study causal structure learning from observational data in linear Gaussian structural causal models in the presence of directed cycles and an unknown number of exogenous latent confounders, bounded by a given maximum. We derive the covariance of the observed variables and introduce marginal quasi-equivalence, which characterizes when different causal models share a full-dimensional subset of the observational distributions they can generate. We formulate structure learning as minimization of the Gaussian negative log-likelihood with a logarithmically scaled complexity penalty that counts directed edges and latent variables. For a fixed number of observed variables and a fixed upper bound on latent variables, we establish consistency of global score minimizers up to marginal quasi-equivalence under algebraic faithfulness, structural minimality, and model-overlap assumptions. We parameterize the inclusion of directed edges and candidate latent variables using Bernoulli gates, whose continuous probabilities are optimized jointly with the structural coefficients. Averaging the penalized negative log-likelihood over these gates yields an objective with a closed-form differentiable complexity penalty. We prove that this expected objective has the same global infimum as the corresponding discrete structure-learning objective. Experimental results show that our approach achieves lower recovery error than previous methods in several experimental settings.
| Comments: | 42 pages, including appendices |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2609.38618 [cs.LG] |
| (or arXiv:2609.38618v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.38618 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Sadegh Khorasani [view email]
[v1]
Tue, 29 Sep 2026 22:22:21 UTC (422 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org