# One for All: Simultaneous Metric and Preference Learning over Multiple Users

arXiv: https://arxiv.org/abs/2207.03609 · HTML: https://mlsanity.com/paper/2207.03609/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 7 Jul 2022.

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

- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Improved Confidence Bounds for the Linear Logistic Model and Applications to Linear Bandits](https://mlsanity.com/paper/2011.11222/) (2020)
- [Finite Sample Prediction and Recovery Bounds for Ordinal Embedding](https://mlsanity.com/paper/1606.07081/) (2016)
- [Active embedding search via noisy paired comparisons](https://mlsanity.com/paper/1905.04363/) (2019)
- [Simultaneous Preference and Metric Learning from Paired Comparisons](https://mlsanity.com/paper/2009.02302/) (2020)
- [Learning Low-Dimensional Metrics](https://mlsanity.com/paper/1709.06171/) (2017)
- [Active Ordinal Querying for Tuplewise Similarity Learning](https://mlsanity.com/paper/1910.04115/) (2019)
- [As you like it: Localization via paired comparisons](https://mlsanity.com/paper/1802.10489/) (2018)
- [Learning Nearest Neighbor Graphs from Noisy Distance Samples](https://mlsanity.com/paper/1905.13267/) (2019)

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

- [PAL: Pluralistic Alignment Framework for Learning from Heterogeneous Preferences](https://mlsanity.com/paper/2406.08469/) (2024)
- [Initializing Services in Interactive ML Systems for Diverse Users](https://mlsanity.com/paper/2312.11846/) (2023)
- [Perceptual adjustment queries and an inverted measurement paradigm for low-rank metric learning](https://mlsanity.com/paper/2309.04626/) (2023)
- [Metric Learning from Limited Pairwise Preference Comparisons](https://mlsanity.com/paper/2403.19629/) (2024)
- [Representer Theorems for Metric and Preference Learning: Geometric Insights and Algorithms](https://mlsanity.com/paper/2304.03720/) (2023)
- [Metric Learning in an RKHS](https://mlsanity.com/paper/2508.04476/) (2025)

## Abstract (arXiv)

This paper investigates simultaneous preference and metric learning from a crowd of respondents. A set of items represented by d-dimensional feature vectors and paired comparisons of the form ``item i is preferable to item j'' made by each user is given. Our model jointly learns a distance metric that characterizes the crowd's general measure of item similarities along with a latent ideal point for each user reflecting their individual preferences. This model has the flexibility to capture individual preferences, while enjoying a metric learning sample cost that is amortized over the crowd. We first study this problem in a noiseless, continuous response setting (i.e., responses equal to differences of item distances) to understand the fundamental limits of learning. Next, we establish prediction error guarantees for noisy, binary measurements such as may be collected from human respondents, and show how the sample complexity improves when the underlying metric is low-rank. Finally, we establish recovery guarantees under assumptions on the response distribution. We demonstrate the performance of our model on both simulated data and on a dataset of color preference judgements across a large number of users.