Sparse Domain Transfer via Elastic Net Regularization

TL;DR

This paper introduces ENOT, a novel optimal transport method that enforces sparsity in domain transfer maps using elastic net regularization, improving feature selection in computer vision and language tasks.

Contribution

The paper proposes the ENOT framework combining L1 and L2 regularization for sparse and stable domain transfer, with a dual formulation for efficient computation and feature selection.

Findings

ENOT effectively finds sparse transport maps in synthetic and real data.

ENOT improves feature selection in domain transfer tasks.

Empirical results demonstrate the success of ENOT in various applications.

Abstract

Transportation of samples across different domains is a central task in several machine learning problems. A sensible requirement for domain transfer tasks in computer vision and language domains is the sparsity of the transportation map, i.e., the transfer algorithm aims to modify the least number of input features while transporting samples across the source and target domains. In this work, we propose Elastic Net Optimal Transport (ENOT) to address the sparse distribution transfer problem. The ENOT framework utilizes the $L_1$-norm and $L_2$-norm regularization mechanisms to find a sparse and stable transportation map between the source and target domains. To compute the ENOT transport map, we consider the dual formulation of the ENOT optimization task and prove that the sparsified gradient of the optimal potential function in the ENOT's dual representation provides the ENOT transport map. Furthermore, we demonstrate the application of the ENOT framework to perform feature selection for sparse domain transfer. We present the numerical results of applying ENOT to several domain transfer problems for synthetic Gaussian mixtures and real image and text data. Our empirical results indicate the success of the ENOT framework in identifying a sparse domain transport map.