  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.
