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

TL;DR

This paper introduces perceptual adjustment queries (PAQ), a new feedback mechanism for low-rank metric learning that combines advantages of cardinal and ordinal queries, and proposes a specialized estimator with theoretical guarantees.

Contribution

The paper proposes PAQ as a novel, efficient human feedback method for metric learning and develops a two-stage estimator with sample complexity guarantees for high-dimensional low-rank matrix recovery.

Findings

Numerical simulations show the estimator's effectiveness.

PAQ combines benefits of cardinal and ordinal queries.

The estimator has provable sample complexity bounds.

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.