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

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