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One for All: Simultaneous Metric and Preference Learning over Multiple Users
Gregory Canal · Blake Mason · Ramya Korlakai Vinayak · Robert Nowak

Wed Nov 30 09:00 AM -- 11:00 AM (PST) @ Hall J #731
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.

Author Information

Gregory Canal (University of Wisconsin, Madison)
Gregory Canal

Greg Canal joined the University of Wisconsin-Madison in 2021 as a postdoctoral research associate, working with Rob Nowak at the Wisconsin Institute for Discovery. He completed his PhD at Georgia Tech in Electrical and Computer Engineering. For his thesis, he developed and analyzed new active machine learning algorithms inspired by feedback coding theory. During his first year as a postdoc he developed a new approach for multi-user recommender systems, and he is currently exploring new active learning algorithms for deep neural networks. For his next career phase, he plans on pursuing a position as an industry research scientist.

Blake Mason (Amazon)

Blake Mason is Doctoral Student at the University of Wisconsin-Madison studying Electrical and Computer Engineering under the advisement of Professor Robert Nowak. Prior to his graduate studies, he completed his bachelors in electrical engineering at the University of Southern California.

Ramya Korlakai Vinayak (University of Wisconsin-Madison)
Robert Nowak (University of Wisconsion-Madison)

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