arXiv Machine Learning By Zijian Li, Ruichu Cai, Feng Xie, Xinshuai Dong, Haoyue Dai, Yuewen Sun, Yujia Zheng, Guangyi Chen, Yingyao Hu, Kun Zhang

Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models

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arXiv AI
3d ago

Differentiable Structure Learning for Cyclic Linear Gaussian Models with Latent Confounders

The paper introduces a method for learning causal structures in linear Gaussian models that may contain directed cycles and an unknown number of latent confounders, bounded by a maximum. It derives the covariance of observed variables, defines marginal quasi-equivalence to identify when different models produce the same observational distributions, and formulates structure learning as a minimization of Gaussian negative log-likelihood with a complexity penalty counting edges and latent variables. Using Bernoulli gates to parameterize edge and latent inclusion, the authors obtain a closed‑form differentiable objective whose expected value shares the same global optimum as the discrete problem, and demonstrate experimentally that this approach yields lower recovery error than prior methods.

By Sadegh Khorasani, Ali Najar, Saber Salehkaleybar, Negar Kiyavash