TITLE: Dataset Dynamics via Gradient Flows in Probability Space 

ABSTRACT: Various machine learning tasks, from generative modeling to domain
adaptation, revolve around the concept of dataset transformation and
manipulation. While various methods exist for transforming unlabeled datasets,
principled methods to do so for labeled (e.g., classification) datasets are
missing. In this work, we propose a novel framework for dataset transformation,
which we cast as optimization over data-generating joint probability
distributions. We approach this class of problems through Wasserstein gradient
flows in probability space, and derive practical and efficient particle-based
methods for a flexible but well-behaved class of objective functions. Through
various experiments, we show that this framework can be used to impose
constraints on classification datasets, adapt them for transfer learning, or to
re-purpose fixed or black-box models to classify -- with high accuracy --
previously unseen datasets.
Various machine learning tasks, from generative modeling to domain
adaptation, revolve around the concept of dataset transformation and
manipulation. While various methods exist for transforming unlabeled datasets,
principled methods to do so for labeled (e.g., classification) datasets are
missing. In this work, we propose a novel framework for dataset transformation,
which we cast as optimization over data-generating joint probability
distributions. We approach this class of problems through Wasserstein gradient
flows in probability space, and derive practical and efficient particle-based
methods for a flexible but well-behaved class of objective functions. Through
various experiments, we show that this framework can be used to impose
constraints on classification datasets, adapt them for transfer learning, or to
re-purpose fixed or black-box models to classify -- with high accuracy --
previously unseen datasets.
Dataset Dynamics via Gradient Flows in Probability Space
http://arxiv.org/abs/2010.12760v2