# Parallel integrative learning for large-scale multi-response regression with incomplete outcomes

arXiv: https://arxiv.org/abs/2104.05076 · HTML: https://mlsanity.com/paper/2104.05076/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 11 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Tuning parameter selection in high dimensional penalized likelihood](https://mlsanity.com/paper/1605.03321/) (2016)
- [Generalized High-Dimensional Trace Regression via Nuclear Norm Regularization](https://mlsanity.com/paper/1710.08083/) (2017)
- [SOFAR: large-scale association network learning](https://mlsanity.com/paper/1704.08349/) (2017)
- [Low Rank Matrix Completion with Exponential Family Noise](https://mlsanity.com/paper/1502.06919/) (2015)
- [Scalable Interpretable Multi-Response Regression via SEED](https://mlsanity.com/paper/1608.03686/) (2016)
- [Asymptotic equivalence of regularization methods in thresholded parameter space](https://mlsanity.com/paper/1605.03310/) (2016)
- [Multivariate Functional Regression via Nested Reduced-Rank Regularization](https://mlsanity.com/paper/2003.04786/) (2020)

## Built on by (most cited first, 1 of 1)

- [Simultaneous Heterogeneity and Reduced-rank Learning for Multivariate Response Regression](https://mlsanity.com/paper/2512.06514/) (2025)

## Abstract (arXiv)

Multi-task learning is increasingly used to investigate the association structure between multiple responses and a single set of predictor variables in many applications. In the era of big data, the coexistence of incomplete outcomes, large number of responses, and high dimensionality in predictors poses unprecedented challenges in estimation, prediction, and computation. In this paper, we propose a scalable and computationally efficient procedure, called PEER, for large-scale multi-response regression with incomplete outcomes, where both the numbers of responses and predictors can be high-dimensional. Motivated by sparse factor regression, we convert the multi-response regression into a set of univariate-response regressions, which can be efficiently implemented in parallel. Under some mild regularity conditions, we show that PEER enjoys nice sampling properties including consistency in estimation, prediction, and variable selection. Extensive simulation studies show that our proposal compares favorably with several existing methods in estimation accuracy, variable selection, and computation efficiency.