# Robust low-rank estimation with multiple binary responses using pairwise AUC loss

arXiv: https://arxiv.org/abs/2601.08618 · HTML: https://mlsanity.com/paper/2601.08618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [A reduced-rank approach to predicting multiple binary responses through machine learning](https://mlsanity.com/paper/2306.05829/) (2023)
- [High-dimensional sparse classification using exponential weighting with empirical hinge loss](https://mlsanity.com/paper/2312.12952/) (2023)
- [Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix](https://mlsanity.com/paper/2406.14269/) (2024)
- [From bilinear regression to inductive matrix completion: a quasi-Bayesian analysis](https://mlsanity.com/paper/2210.15290/) (2022)
- [Concentration properties of fractional posterior in 1-bit matrix completion](https://mlsanity.com/paper/2404.08969/) (2024)
- [Misclassification bounds for PAC-Bayesian sparse deep learning](https://mlsanity.com/paper/2405.01304/) (2024)
- [A sparse PAC-Bayesian approach for high-dimensional quantile prediction](https://mlsanity.com/paper/2409.01687/) (2024)
- [PAC-Bayesian AUC classification and scoring](https://mlsanity.com/paper/1410.1771/) (2014)
- [Optimal sparse phase retrieval via a quasi-Bayesian approach](https://mlsanity.com/paper/2504.09509/) (2025)
- [Bayesian Pliable Lasso with Horseshoe Prior for Interaction Effects in GLMs with Missing Responses](https://mlsanity.com/paper/2509.07501/) (2025)

## Abstract (arXiv)

Multiple binary responses arise in many modern data-analytic problems. Although fitting separate logistic regressions for each response is computationally attractive, it ignores shared structure and can be statistically inefficient, especially in high-dimensional and class-imbalanced regimes. Low-rank models offer a natural way to encode latent dependence across tasks, but existing methods for binary data are largely likelihood-based and focus on pointwise classification rather than ranking performance. In this work, we propose a unified framework for learning with multiple binary responses that directly targets discrimination by minimizing a surrogate loss for the area under the ROC curve (AUC). The method aggregates pairwise AUC surrogate losses across responses while imposing a low-rank constraint on the coefficient matrix to exploit shared structure. We develop a scalable projected gradient descent algorithm based on truncated singular value decomposition. Exploiting the fact that the pairwise loss depends only on differences of linear predictors, we simplify computation and analysis. We establish non-asymptotic convergence guarantees, showing that under suitable regularity conditions, leading to linear convergence up to the minimax-optimal statistical precision. Extensive simulation studies demonstrate that the proposed method is robust in challenging settings such as label switching and data contamination and consistently outperforms likelihood-based approaches.