The packagemultiview is a new method for supervisedlearning with multiple sets of features calledviews. Themulti-view problem is especially important in biology and medicine,where “-omics” data such as genomics, proteomics and radiomics aremeasured on a common set of samples. Cooperative learning combines theusual squared error loss of predictions with an “agreement” penalty toencourage the predictions from different data views to agree. By varyingthe weight of the agreement penalty, we get a continuum of solutionsthat include the well-known early and late fusion approaches.Cooperative learning chooses the degree of agreement (or fusion) in anadaptive manner, using a validation set or cross-validation to estimatetest set prediction error.
In the setting of cooperative regularized linear regression, themethod combines the lasso penalty with the agreement penalty, yieldingfeature sparsity. The method can be especially powerful when thedifferent data views share some underlying relationship in their signalsthat can be exploited to boost the signals.
As shown in Ding et al. (2021),cooperative learning achieves higher predictive accuracy on simulateddata and real multiomics examples of labor onset prediction and breastductal carcinoma in situ and invasive breast cancer classification.Leveraging aligned signals and allowing flexible fitting mechanisms fordifferent modalities, cooperative learning offers a powerful approach tomultiomics data fusion.