# Elastic-Net Multiple Kernel Learning: Combining Multiple Data Sources for Prediction

arXiv: https://arxiv.org/abs/2512.11547 · HTML: https://mlsanity.com/paper/2512.11547/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 20 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 1 of 1)

- [Supervised Multiple Kernel Learning approaches for multi-omics data integration](https://mlsanity.com/paper/2403.18355/) (2024)

## Abstract (arXiv)

Multiple Kernel Learning (MKL) models combine several kernels in supervised and unsupervised settings to integrate multiple data representations or sources, each represented by a different kernel. MKL seeks an optimal linear combination of base kernels that maximizes a generalized performance measure under a regularization constraint. Various norms have been used to regularize the kernel weights, including l1, l2 and lp, as well as the "elastic-net" penalty, which combines l1- and l2-norm to promote both sparsity and the selection of correlated kernels. This property makes elastic-net regularized MKL (ENMKL) especially valuable when model interpretability is critical and kernels capture correlated information, such as in neuroimaging. Previous ENMKL methods have followed a two-stage procedure: fix kernel weights, train a support vector machine (SVM) with the weighted kernel, and then update the weights via gradient descent, cutting-plane methods, or surrogate functions. Here, we introduce an alternative ENMKL formulation that yields a simple analytical update for the kernel weights. We derive explicit algorithms for both SVM and kernel ridge regression (KRR) under this framework, and implement them in the open-source Pattern Recognition for Neuroimaging Toolbox (PRoNTo). We evaluate these ENMKL algorithms against l1-norm MKL and against SVM (or KRR) trained on the unweighted sum of kernels across three neuroimaging applications. Our results show that ENMKL matches or outperforms l1-norm MKL in all tasks and only underperforms standard SVM in one scenario. Crucially, ENMKL produces sparser, more interpretable models by selectively weighting correlated kernels.