Domain Adaptation with Regularized Optimal Transport

Abstract

We present a new and original method to solve the domain adaptation problem using optimal transport. By searching for the best transportation plan between the probability distribution functions of a source and a target domain, a non-linear and invertible transformation of the learning samples can be estimated. Any standard machine learning method can then be applied on the transformed set, which makes our method very generic. We propose a new optimal transport algorithm that incorporates label information in the optimization: this is achieved by combining an efficient matrix scaling technique together with a majoration of a non-convex regularization term. By using the proposed optimal transport with label regularization, we obtain significant increase in performance compared to the original transport solution. The proposed algorithm is computationally efficient and effective, as illustrated by its evaluation on a toy example and a challenging real life vision dataset, against which it achieves competitive results with respect to state-of-theart methods.

Optimal Mass Transport: Signal processing and machine-learning applications

“…The optimal transport framework has recently attracted ample attention from the machine learning and statistics communities [12, 19, 25, 28, 36]. Some applications of the optimal transport in these arenas include various transport-based learning methods [19, 28, 36, 48], domain adaptation, Bayesian inference [12, 13], and hypothesis testing [15, 42] among others.…”

“…Some applications of the optimal transport in these arenas include various transport-based learning methods [19, 28, 36, 48], domain adaptation, Bayesian inference [12, 13], and hypothesis testing [15, 42] among others. Here we provide a brief overview of the recent developments of transport-based methods in machine learning and statistics.…”

“…These techniques have been used to simplify and augment the accuracy of numerous pattern recognition-related problems. Some examples covered in this tutorial include image retrieval [32, 44], signal and image representation [25, 27, 40, 50], inverse problems [30], cancer detection [4, 39], texture and color modeling [18, 41], shape and image registration [22, 29], and machine learning [12, 17, 19, 28, 36, 42], to name a few. This tutorial is meant to serve as an introductory guide to those wishing to familiarize themselves with these emerging techniques.…”

Optimal transport for data fusion in remote sensing

“…(4). Moreover, one can also use the class information in one of the domain to promote a better transportation for instance by using an appropriate class-based regularization of the coupling matrix [8]. is a critical problem.…”

“…In many situations, we assume a smooth transportation plan between distributions. In these cases, we can enforce some kind of regularization to help obtaining a better transportation by including additional prior in the optimization problem, such as Laplacian [12]), entropy [13], or class-regularization [8] on the transport matrix . When using a regularization, the optimal transport optimization problem can be reformulated as…”