AI 中文总结
针对潜在变量依赖噪声导致的可识别性挑战，研究更一般的错误设定结构，提出精确与近似可识别性保证，并开发无监督变分估计器，实验验证其有效性。
AI 中文摘要
依赖于潜在变量的噪声的存在对可识别性构成了根本性挑战。现有结果依赖于在给定潜在变量条件下观测值之间的条件独立性。我们研究一种更一般的“错误设定结构”，其中这种条件分解不成立，并建立了精确和近似可识别性的保证。我们将结构错误设定刻画为一个扰动因子分析问题。对于精确可识别性，我们在谱分离和受控扰动下建立了子空间可识别性，随后在结构稀疏性下建立了分量级可识别性。当精确条件无法保证时，我们推导出一个近似子空间可识别性定理。基于这些结果，我们开发了一种无监督变分估计器来恢复潜在变量。实验证明了所提出框架的有效性。
英文摘要
The presence of noise that depends on the latent variables poses a fundamental challenge to identifiability. Existing results rely on conditional independence among the observations given the latent variables. We study a more general \emph{misspecified structure}, where this conditional factorization does not hold, and establish both precise and approximate identifiability guarantees. We characterize structural misspecification as a perturbed factor analysis problem. For precise identifiability, we establish subspace identifiability under spectral separation and controlled perturbation, followed by component-wise identifiability under structural sparsity. When the precise condition is not guaranteed, we derive an approximate subspace-identifiability theorem. Based on these results, we develop an unsupervised variational estimator for recovering latent variables. Experiments demonstrate the effectiveness of the proposed framework.
