We consider the identifiability theory of probabilistic models and establish
sufficient conditions under which the representations learned by a very broad
family of conditional energy-based models are unique in function space, up to a
simple transformation. In our model family, the energy function is the
dot-product between two feature extractors, one for the dependent variable, and
one for the conditioning variable. We show that under mild conditions, the
features are unique up to scaling and permutation. Our results extend recent
developments in nonlinear ICA, and in fact, they lead to an important
generalization of ICA models. In particular, we show that our model can be used
for the estimation of the components in the framework of Independently
Modulated Component Analysis (IMCA), a new generalization of nonlinear ICA that
relaxes the independence assumption. A thorough empirical study shows that
representations learned by our model from real-world image datasets are
identifiable, and improve performance in transfer learning and semi-supervised
learning tasks.

本研究针对概率模型的可辨识性理论，通过一种广泛的条件能量模型建立充分条件，使得学习到的表示在函数空间上是唯一的，从而可以用于在非线性 ICA 框架下的组件估计，同时提高了图像数据集在迁移学习和半监督学习任务中的性能。