不追求唯一解，而是挖掘潜在变量间的可靠关系。
Identifying Metric Structures of Deep Latent Variable Models
- 通过理论证明，在弱条件下可识别变量间距离、角度等关系
- 无需额外标注数据，实验验证了潜在空间距离更可靠
- 适合需要可信解释的模型使用者，如医疗或金融领域
深度隐变量模型学习数据的紧凑表示，理想情况下反映现象内在机制。然而，这些潜在表示在统计上不可识别，无法唯一确定。因此，领域专家在解释时需格外谨慎。现有方法通过添加约束（如要求标注数据或限制模型表达能力）来缓解不可识别性。本文转换目标：不追求识别潜在变量本身，而是识别它们之间的关系，如有意义的距离、夹角和体积。我们在非常宽松的模型条件下证明这一目标是可行的，且无需额外标注数据。实验表明，该理论能带来更可靠的潜在距离，为从深度隐变量模型中提取可信结论提供了原则性路径。
原文摘要 · Abstract (English)
Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be uniquely determined. Domain experts, therefore, need to tread carefully when interpreting these. Current solutions limit the lack of identifiability through additional constraints on the latent variable model, e.g. by requiring labeled training data, or by restricting the expressivity of the model. We change the goal: instead of identifying the latent variables, we identify relationships between them such as meaningful distances, angles, and volumes. We prove this is feasible under very mild model conditions and without additional labeled data. We empirically demonstrate that our theory results in more reliable latent distances, offering a principled path forward in extracting trustworthy conclusions from deep latent variable models.
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