# Comparing Apples to Oranges: Learning Similarity Functions for Data Produced by Different Distributions

arXiv: https://arxiv.org/abs/2208.12731 · HTML: https://mlsanity.com/paper/2208.12731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 26 Aug 2022.

## Builds on (most cited first, 10 of 10)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Operationalizing Individual Fairness with Pairwise Fair Representations](https://mlsanity.com/paper/1907.01439/) (2019)
- [A Survey on Metric Learning for Feature Vectors and Structured Data](https://mlsanity.com/paper/1306.6709/) (2013)
- [Fairness Through Computationally-Bounded Awareness](https://mlsanity.com/paper/1803.03239/) (2018)
- [Two Simple Ways to Learn Individual Fairness Metrics from Data](https://mlsanity.com/paper/2006.11439/) (2020)
- [Metric Learning for Individual Fairness](https://mlsanity.com/paper/1906.00250/) (2019)
- [Probably Approximately Metric-Fair Learning](https://mlsanity.com/paper/1803.03242/) (2018)
- [A New Notion of Individually Fair Clustering: α-Equitable k-Center](https://mlsanity.com/paper/2106.05423/) (2021)
- [Cost-Effective HITs for Relative Similarity Comparisons](https://mlsanity.com/paper/1404.3291/) (2014)
- [An Empirical Study on Learning Fairness Metrics for COMPAS Data with Human Supervision](https://mlsanity.com/paper/1910.10255/) (2019)

## Abstract (arXiv)

Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems. However, access to an accurate similarity function should not always be considered guaranteed, and this point was even raised by Dwork et al. For instance, it is reasonable to assume that when the elements to be compared are produced by different distributions, or in other words belong to different ``demographic'' groups, knowledge of their true similarity might be very difficult to obtain. In this work, we present an efficient sampling framework that learns these across-groups similarity functions, using only a limited amount of experts' feedback. We show analytical results with rigorous theoretical bounds, and empirically validate our algorithms via a large suite of experiments.