# Sparse Domain Transfer via Elastic Net Regularization

arXiv: https://arxiv.org/abs/2405.07489 · HTML: https://mlsanity.com/paper/2405.07489/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 43 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [SEAN: Image Synthesis with Semantic Region-Adaptive Normalization](https://mlsanity.com/paper/1911.12861/) (2019)
- [DRIT++: Diverse Image-to-Image Translation via Disentangled Representations](https://mlsanity.com/paper/1905.01270/) (2019)
- [Few-shot Image Generation via Cross-domain Correspondence](https://mlsanity.com/paper/2104.06820/) (2021)
- [U-GAT-IT: Unsupervised Generative Attentional Networks with Adaptive Layer-Instance Normalization for Image-to-Image Translation](https://mlsanity.com/paper/1907.10830/) (2019)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Real-Time User-Guided Image Colorization with Learned Deep Priors](https://mlsanity.com/paper/1705.02999/) (2017)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Patch-Based Image Inpainting with Generative Adversarial Networks](https://mlsanity.com/paper/1803.07422/) (2018)
- [TSIT: A Simple and Versatile Framework for Image-to-Image Translation](https://mlsanity.com/paper/2007.12072/) (2020)
- [Reusing Discriminators for Encoding: Towards Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/2003.00273/) (2020)
- [Unpaired Image-to-Image Translation using Adversarial Consistency Loss](https://mlsanity.com/paper/2003.04858/) (2020)
- [TransGaGa: Geometry-Aware Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1904.09571/) (2019)
- [Towards Instance-level Image-to-Image Translation](https://mlsanity.com/paper/1905.01744/) (2019)
- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [Distance-based Confidence Score for Neural Network Classifiers](https://mlsanity.com/paper/1709.09844/) (2017)
- [Rationalizing Text Matching: Learning Sparse Alignments via Optimal Transport](https://mlsanity.com/paper/2005.13111/) (2020)
- [Reversible GANs for Memory-efficient Image-to-Image Translation](https://mlsanity.com/paper/1902.02729/) (2019)
- [Domain Re-Modulation for Few-Shot Generative Domain Adaptation](https://mlsanity.com/paper/2302.02550/) (2023)

## Abstract (arXiv)

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 L1-norm and L2-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.