# Learning relationships between data obtained independently

arXiv: https://arxiv.org/abs/1601.00504 · HTML: https://mlsanity.com/paper/1601.00504/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2016.

## Built on by (most cited first, 6 of 6)

- [Weakly Supervised Regression with Interval Targets](https://mlsanity.com/paper/2306.10458/) (2023)
- [Permuted and Unlinked Monotone Regression in ℝd: an approach based on mixture modeling and optimal transport](https://mlsanity.com/paper/2201.03528/) (2022)
- [Shuffled linear regression through graduated convex relaxation](https://mlsanity.com/paper/2209.15608/) (2022)
- [Regularization for Shuffled Data Problems via Exponential Family Priors on the Permutation Group](https://mlsanity.com/paper/2111.01767/) (2021)
- [Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives](https://mlsanity.com/paper/2506.19025/) (2025)
- [Bridged Clustering: Semi-Supervised Sparse Bridging](https://mlsanity.com/paper/2510.07182/) (2025)

## Abstract (arXiv)

The aim of this paper is to provide a new method for learning the relationships between data that have been obtained independently. Unlike existing methods like matching, the proposed technique does not require any contextual information, provided that the dependency between the variables of interest is monotone. It can therefore be easily combined with matching in order to exploit the advantages of both methods. This technique can be described as a mix between quantile matching, and deconvolution. We provide for it a theoretical and an empirical validation.