One for All: Simultaneous Metric and Preference Learning over Multiple Users
One for All: Simultaneous Metric and Preference Learning over Multiple Users
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DOI：
10.48550/arxiv.2207.03609
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Gregory H. Canal;Blake Mason;Ramya Korlakai Vinayak;R. Nowak
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文献类型：
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作者：
Gregory H. Canal;Blake Mason;Ramya Korlakai Vinayak;R. Nowak
本文从一组被调查者中调查了同时偏好和度量学习。给出了由$d$维特征向量表示的项的集合以及由每个用户进行的形式为``项$i$‘比项’$j$‘’的配对比较。我们的模型联合学习了一个距离度量，该度量描述了人群对项目相似性的一般衡量标准，以及每个用户反映其个人偏好的潜在理想点。该模型具有获取个人偏好的灵活性，同时享受在人群中摊销的指标学习样本成本。我们首先在无声、连续的反应环境中研究这个问题(即反应等于项目距离的差异)，以了解学习的基本限度。接下来，我们为可能从人类受访者那里收集的噪声、二进制测量建立预测误差保证，并展示当潜在的度量是低阶时，样本复杂性如何改善。最后，我们在响应分布的假设下建立了恢复保证。我们在模拟数据和大量用户的颜色偏好判断数据集上演示了我们的模型的性能。
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.