Graph Normalizing Flows to Pre-image Free Machine Learning for Regression

Clément Glédel, Benoit Gaüzère, Paul Honeine

Abstract: In Machine Learning, data embedding is a fundamental aspect of creating nonlinear models. However, they often lack interpretability due to the limited access to the embedding space, also called latent space. As a result, it is highly desirable to represent, in the input space, elements from the embedding space. Nevertheless, obtaining the inverse embedding is a challenging task, and it involves solving the hard pre-image problem. This task becomes even more challenging when dealing with structured data like graphs, which are complex and discrete by nature. This article presents a novel approach for graph regression using Normalizing Flows (NFs), in order to avoid the pre-image problem. By creating a latent representation space using a NF, the method overcomes the difficulty of finding an inverse transformation. The approach aims at supervising the space generation process in order to create a space suitable for the specific regression task. Furthermore, any result obtained in the generated space can be translated into the input space through the application of the inverse transformation learned by the model. The effectiveness of our approach is demonstrated by using a NF model on different regression problems. We validate the ability of the method to efficiently handle both the pre-image generation and the regression task.