ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA
Provides theoretical foundations for identifiable representation learning, addressing a fundamental problem in unsupervised/self-supervised learning.
The paper establishes conditions under which representations learned by conditional energy-based models are uniquely identifiable up to simple transformations, extending nonlinear ICA theory. Empirical results show these identifiable representations improve performance in transfer learning and semi-supervised learning tasks on real-world image datasets.
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.