4 accepted papers
This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesic curves in the space of probability measures that best capture the modes of variation of the underlying dataset. We fir…
The canonical approach in generative modeling is to split model fitting into two blocks: define first how to sample noise (e.g. Gaussian) and choose next what to do with it (e.g. using a single map or flows). We explore in this work an alternative route that ties sampling and mapping. We find inspir…
In 1991, Brenier proved a theorem that generalizes the polar decomposition for square matrices -- factored as PSD $\times$ unitary -- to any vector field $F:\mathbb{R}^d\rightarrow \mathbb{R}^d$. The theorem, known as the polar factorization theorem, states that any field $F$ can be recovered as the…
The theoretical analysis of deep neural networks (DNN) is arguably among the most challenging research directions in machine learning (ML) right now, as it requires from scientists to lay novel statistical learning foundations to explain their behaviour in practice. While some success has been achie…