ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA

TL;DR

This paper introduces ICE-BeeM, a class of conditional energy-based models with provable identifiability, extending nonlinear ICA to a more general framework and demonstrating improved transfer and semi-supervised learning performance.

Contribution

It establishes identifiability conditions for a broad family of conditional energy-based models and generalizes nonlinear ICA through IMCA, relaxing independence assumptions.

Findings

Representations learned are identifiable from real-world images.

Model improves transfer learning performance.

Model enhances semi-supervised learning results.

Abstract

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.