# Cooperative learning for multiview analysis

arXiv: https://arxiv.org/abs/2112.12337 · HTML: https://mlsanity.com/paper/2112.12337/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 61 references that are in the map.
- First posted on arXiv 23 Dec 2021.

## Builds on (most cited first, 8 of 8)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [A Survey on Contrastive Self-supervised Learning](https://mlsanity.com/paper/2011.00362/) (2020)
- [Pathomic Fusion: An Integrated Framework for Fusing Histopathology and Genomic Features for Cancer Diagnosis and Prognosis](https://mlsanity.com/paper/1912.08937/) (2019)
- [Dykstra's Algorithm, ADMM, and Coordinate Descent: Connections, Insights, and Extensions](https://mlsanity.com/paper/1705.04768/) (2017)
- [Collaborative Regression](https://mlsanity.com/paper/1401.5823/) (2014)
- [Sparse Linear Discriminant Analysis for Multi-view Structured Data](https://mlsanity.com/paper/1911.05643/) (2019)

## Built on by (most cited first, 19 of 19)

- [Trusted Multi-View Classification with Dynamic Evidential Fusion](https://mlsanity.com/paper/2204.11423/) (2022)
- [Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework](https://mlsanity.com/paper/2302.12247/) (2023)
- [Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications](https://mlsanity.com/paper/2306.04539/) (2023)
- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [Partial Information Decomposition via Normalizing Flows in Latent Gaussian Distributions](https://mlsanity.com/paper/2510.04417/) (2025)
- [Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data](https://mlsanity.com/paper/2211.16403/) (2022)
- [Multimodal Learning for Multi-Omics: A Survey](https://mlsanity.com/paper/2211.16509/) (2022)
- [Morphological Profiling for Drug Discovery in the Era of Deep Learning](https://mlsanity.com/paper/2312.07899/) (2023)
- [Bayesian Transfer Learning](https://mlsanity.com/paper/2312.13484/) (2023)
- [Relative Sparsity for Medical Decision Problems](https://mlsanity.com/paper/2211.16566/) (2022)
- [Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning](https://mlsanity.com/paper/2602.04872/) (2026)
- [Foundations of Multisensory Artificial Intelligence](https://mlsanity.com/paper/2404.18976/) (2024)
- [Data Science Principles for Interpretable and Explainable AI](https://mlsanity.com/paper/2405.10552/) (2024)
- [Meta Fusion: A Unified Framework For Multimodality Fusion with Mutual Learning](https://mlsanity.com/paper/2507.20089/) (2025)
- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [Coupled Training with Privileged Information and Unlabeled Data](https://mlsanity.com/paper/2605.23268/) (2026)
- [Optimizing Prognostic Biomarker Discovery in Pancreatic Cancer Through Hybrid Ensemble Feature Selection and Multi-Omics Data](https://mlsanity.com/paper/2509.02648/) (2025)
- [PliableBVS: A flexible Bayesian variable selection method for modeling interactions with mandatory modifying variables](https://mlsanity.com/paper/2606.02017/) (2026)
- [DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing](https://mlsanity.com/paper/2608.02769/) (2026)

## Abstract (arXiv)

We propose a new method for supervised learning with multiple sets of features ("views"). The multiview problem is especially important in biology and medicine, where "-omics" data such as genomics, proteomics and radiomics are measured on a common set of samples. Cooperative learning combines the usual squared error loss of predictions with an "agreement" penalty to encourage the predictions from different data views to agree. By varying the weight of the agreement penalty, we get a continuum of solutions that include the well-known early and late fusion approaches. Cooperative learning chooses the degree of agreement (or fusion) in an adaptive manner, using a validation set or cross-validation to estimate test set prediction error. One version of our fitting procedure is modular, where one can choose different fitting mechanisms (e.g. lasso, random forests, boosting, neural networks) appropriate for different data views. In the setting of cooperative regularized linear regression, the method combines the lasso penalty with the agreement penalty, yielding feature sparsity. The method can be especially powerful when the different data views share some underlying relationship in their signals that can be exploited to boost the signals. We show that cooperative learning achieves higher predictive accuracy on simulated data and a real multiomics example of labor onset prediction. Leveraging aligned signals and allowing flexible fitting mechanisms for different modalities, cooperative learning offers a powerful approach to multiomics data fusion.