Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models
Uncovering latent variables and their causal relations from observed data is a fundamental yet challenging problem. Existing methods often rely on restrictive assumptions, such as linear relations or invertible mixing functions. To better address this problem under general nonlinear mixing procedures, we propose a condition called the cross-Hessian Rank Constraint (HRC), which serves as a primitive rank-based tool for nonlinear latent causal discovery. In particular, we show that a rank-based property arises from the cross-Hessian of the observed-data log-density in the nonlinear case, revealing information about the latent variables, and reduces to the Tetrad constraints in the linear Ga...
| Authors | Zijian Li, Ruichu Cai, Feng Xie et al. |
|---|---|
| Primary category | cs.LG |
| Published | 21 September 2026 |
| Last updated at source | 21 September 2026 |
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