Metric Learning from Limited Pairwise Preference Comparisons
<|reference_start|>Metric Learning from Limited Pairwise Preference Comparisons: We study metric learning from preference comparisons under the ideal point model, in which a user prefers an item over another if it is closer to their latent ideal item. These items are embedded into $\mathbb{R}^d$ equipped with an unknown Mahalanobis distance shared across users. While recent work shows that it is possible to simultaneously recover the metric and ideal items given $\mathcal{O}(d)$ pairwise comparisons per user, in practice we often have a limited budget of $o(d)$ comparisons. We study whether the metric can still be recovered, even though it is known that learning individual ideal items is now no longer possible. We show that in general, $o(d)$ comparisons reveal no information about the metric, even with infinitely many users. However, when comparisons are made over items that exhibit low-dimensional structure, each user can contribute to learning the metric restricted to a low-dimensional subspace so that the metric can be jointly identified. We present a divide-and-conquer approach that achieves this, and provide theoretical recovery guarantees and empirical validation.<|reference_end|>
@article{wang2024metric,
    title={Metric Learning from Limited Pairwise Preference Comparisons},
    author={Zhi Wang, Geelon So, Ramya Korlakai Vinayak},
    journal={arXiv preprint arXiv:2403.19629},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19629},
    primaryClass={cs.LG stat.ML}
}