Overview

Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization

TLDR

TODO

Summary

Focusing on Convex Potential Flow or CP-Flow: framework to develop probabilistic models with tractable densities

Presenting a new tool to efficiently training them in MLE: a gradient estimator for the log determinant of the Jacobian

1. Motivations

1.1 Introduction

• Flow based models as trainable tools to develop probabilistic models with tractable densities

1.2 Applications

• Density Estimation

• Variational Inference

1.3 Theoretical Guarantees

1.3.1 Trainability

• Convexity –> Invertibility that is required for Training

1.3.2 Universality

• Universal Density Approximators

1.3.3 Optimality

• Optimal in the Optimal Transport sense