DeepAI AI Chat
Log In Sign Up

Wasserstein is all you need

by   Sidak Pal Singh, et al.

We propose a unified framework for building unsupervised representations of individual objects or entities (and their compositions), by associating with each object both a distributional as well as a point estimate (vector embedding). This is made possible by the use of optimal transport, which allows us to build these associated estimates while harnessing the underlying geometry of the ground space. Our method gives a novel perspective for building rich and powerful feature representations that simultaneously capture uncertainty (via a distributional estimate) and interpretability (with the optimal transport map). As a guiding example, we formulate unsupervised representations for text, in particular for sentence representation and entailment detection. Empirical results show strong advantages gained through the proposed framework. This approach can be used for any unsupervised or supervised problem (on text or other modalities) with a co-occurrence structure, such as any sequence data. The key tools underlying the framework are Wasserstein distances and Wasserstein barycenters (and, hence the title!).


Optimal transport and Wasserstein distances for causal models

In this paper we introduce a variant of optimal transport adapted to the...

CO-Optimal Transport

Optimal transport (OT) is a powerful geometric and probabilistic tool fo...

Gaussian-Smooth Optimal Transport: Metric Structure and Statistical Efficiency

Optimal transport (OT), and in particular the Wasserstein distance, has ...

Statistical data analysis in the Wasserstein space

This paper is concerned by statistical inference problems from a data se...

Unifying Distributionally Robust Optimization via Optimal Transport Theory

In the past few years, there has been considerable interest in two promi...

PSF field learning based on Optimal Transport Distances

Context: in astronomy, observing large fractions of the sky within a rea...

Unbalanced Optimal Transport: A Unified Framework for Object Detection

During training, supervised object detection tries to correctly match th...