# Knothe-Rosenblatt transport for Unsupervised Domain Adaptation

arXiv: https://arxiv.org/abs/2110.02716 · HTML: https://mlsanity.com/paper/2110.02716/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Semi-supervised Domain Adaptation via Minimax Entropy](https://mlsanity.com/paper/1904.06487/) (2019)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [A DIRT-T Approach to Unsupervised Domain Adaptation](https://mlsanity.com/paper/1802.08735/) (2018)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [RNADE: The real-valued neural autoregressive density-estimator](https://mlsanity.com/paper/1306.0186/) (2013)
- [Parameterized Machine Learning for High-Energy Physics](https://mlsanity.com/paper/1601.07913/) (2016)
- [Subspace Detours: Building Transport Plans that are Optimal on Subspace Projections](https://mlsanity.com/paper/1905.10099/) (2019)
- [Model-based micro-data reinforcement learning: what are the crucial model properties and which model to choose?](https://mlsanity.com/paper/2107.11587/) (2021)
- [Evolution of transfer learning in natural language processing](https://mlsanity.com/paper/1910.07370/) (2019)
- [Artificial Intelligence for 5G Wireless Systems: Opportunities, Challenges, and Future Research Directions](https://mlsanity.com/paper/2009.04943/) (2020)

## Abstract (arXiv)

Unsupervised domain adaptation (UDA) aims at exploiting related but different data sources to tackle a common task in a target domain. UDA remains a central yet challenging problem in machine learning. In this paper, we present an approach tailored to moderate-dimensional tabular problems which are hugely important in industrial applications and less well-served by the plethora of methods designed for image and language data. Knothe-Rosenblatt Domain Adaptation (KRDA) is based on the Knothe-Rosenblatt transport: we exploit autoregressive density estimation algorithms to accurately model the different sources by an autoregressive model using a mixture of Gaussians. KRDA then takes advantage of the triangularity of the autoregressive models to build an explicit mapping of the source samples into the target domain. We show that the transfer map built by KRDA preserves each component quantiles of the observations, hence aligning the representations of the different data sets in the same target domain. Finally, we show that KRDA has state-of-the-art performance on both synthetic and real world UDA problems.