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

arXiv: https://arxiv.org/abs/2309.04626 · HTML: https://mlsanity.com/paper/2309.04626/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 54 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 21 of 21)

- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence](https://mlsanity.com/paper/1505.01462/) (2015)
- [Loss minimization and parameter estimation with heavy tails](https://mlsanity.com/paper/1307.1827/) (2013)
- [Learning without Concentration](https://mlsanity.com/paper/1401.0304/) (2014)
- [Your 2 is My 1, Your 3 is My 9: Handling Arbitrary Miscalibrations in Ratings](https://mlsanity.com/paper/1806.05085/) (2018)
- [Statistical consistency and asymptotic normality for high-dimensional robust M-estimators](https://mlsanity.com/paper/1501.00312/) (2015)
- [A Shrinkage Principle for Heavy-Tailed Data: High-Dimensional Robust Low-Rank Matrix Recovery](https://mlsanity.com/paper/1603.08315/) (2016)
- [Exact and Stable Covariance Estimation from Quadratic Sampling via Convex Programming](https://mlsanity.com/paper/1310.0807/) (2013)
- [ROP: Matrix recovery via rank-one projections](https://mlsanity.com/paper/1310.5791/) (2013)
- [Simultaneous Preference and Metric Learning from Paired Comparisons](https://mlsanity.com/paper/2009.02302/) (2020)
- [Learning Low-Dimensional Metrics](https://mlsanity.com/paper/1709.06171/) (2017)
- [Alternating minimization for generalized rank one matrix sensing: Sharp predictions from a random initialization](https://mlsanity.com/paper/2207.09660/) (2022)
- [Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices](https://mlsanity.com/paper/1306.1154/) (2013)
- [Active Ordinal Querying for Tuplewise Similarity Learning](https://mlsanity.com/paper/1910.04115/) (2019)
- [As you like it: Localization via paired comparisons](https://mlsanity.com/paper/1802.10489/) (2018)
- [One for All: Simultaneous Metric and Preference Learning over Multiple Users](https://mlsanity.com/paper/2207.03609/) (2022)
- [Guaranteed Classification via Regularized Similarity Learning](https://mlsanity.com/paper/1306.3108/) (2013)
- [Methods for Ordinal Peer Grading](https://mlsanity.com/paper/1404.3656/) (2014)

## Built on by (most cited first, 3 of 3)

- [Metric Learning in an RKHS](https://mlsanity.com/paper/2508.04476/) (2025)
- [Ranking Items from Discrete Ratings: The Cost of Unknown User Thresholds](https://mlsanity.com/paper/2510.01871/) (2025)
- [Toward individual-level calibration in affect recognition with perceptual adjustment queries](https://mlsanity.com/paper/2609.21073/) (2026)

## Abstract (arXiv)

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.