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

TL;DR

This paper presents a unified model for learning both item similarity metrics and individual user preferences simultaneously from crowd-sourced comparison data, with theoretical guarantees and practical validation.

Contribution

It introduces a flexible joint learning framework for metrics and preferences, with theoretical analysis and empirical validation on real and simulated data.

Findings

Prediction error bounds for noisy binary responses

Sample complexity improves with low-rank metrics

Successful application to color preference data

Abstract

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.