Perceptual adjustment queries and an inverted measurement paradigm for low-rank metric learning

Austin Xu, Andrew McRae, Jingyan Wang, Mark A. Davenport, Ashwin Pananjady

Keywords: human querying, high dimensional low rank matrix estimation, metric learning

TL;DR: We propose a new human query, apply it to the problem of low-rank metric learning, and prove sample complexity upper bounds in a high-dimensional setting.

Abstract: We introduce a new type of query mechanism for collecting human feedback, called the perceptual adjustment query (PAQ). Being both informative and cognitively lightweight, the PAQ adopts an inverted measurement scheme, and combines advantages from both cardinal and ordinal queries. We showcase the PAQ in the metric learning problem, where we collect PAQ measurements to learn an unknown Mahalanobis distance. This gives rise to a high-dimensional, low-rank matrix estimation problem to which standard matrix estimators cannot be applied. Consequently, we develop a two-stage estimator for metric learning from PAQs, and provide sample complexity guarantees for this estimator. We present numerical simulations demonstrating the performance of the estimator and its notable properties.

Submission Number: 13943