Permutation invariant networks to learn Wasserstein metrics

10/12/2020
by   Arijit Sehanobish, et al.
21

Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine learning community especially for its principled way of comparing distributions. In this work, we use a permutation invariant network to map samples from probability measures into a low-dimensional space such that the Euclidean distance between the encoded samples reflects the Wasserstein distance between probability measures. We show that our network can generalize to correctly compute distances between unseen densities. We also show that these networks can learn the first and the second moments of probability distributions.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/19/2018

Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions

Embedding complex objects as vectors in low dimensional spaces is a long...
research
10/20/2017

Learning Wasserstein Embeddings

The Wasserstein distance received a lot of attention recently in the com...
research
08/25/2022

A deep learning framework for geodesics under spherical Wasserstein-Fisher-Rao metric and its application for weighted sample generation

Wasserstein-Fisher-Rao (WFR) distance is a family of metrics to gauge th...
research
05/16/2016

Probing the Geometry of Data with Diffusion Fréchet Functions

Many complex ecosystems, such as those formed by multiple microbial taxa...
research
05/30/2017

The Cramer Distance as a Solution to Biased Wasserstein Gradients

The Wasserstein probability metric has received much attention from the ...
research
02/14/2023

Linearized Wasserstein dimensionality reduction with approximation guarantees

We introduce LOT Wassmap, a computationally feasible algorithm to uncove...
research
06/17/2015

Learning with a Wasserstein Loss

Learning to predict multi-label outputs is challenging, but in many prob...

Please sign up or login with your details

Forgot password? Click here to reset