A multitask multiple kernel learning formulation for discriminating early- and late-stage cancers

Motivation: Genomic information is increasingly being used in diagnosis, prognosis and treatment of cancer. The severity of the disease is usually measured by the tumor stage. Therefore, identifying pathways playing an important role in progression of the disease stage is of great interest. Given that there are similarities in the underlying mechanisms of different cancers, in addition to the considerable correlation in the genomic data, there is a need for machine learning methods that can take these aspects of genomic data into account. Furthermore, using machine learning for studying multiple cancer cohorts together with a collection of molecular pathways creates an opportunity for knowledge extraction. Results: We studied the problem of discriminating early- and late-stage tumors of several cancers using genomic information while enforcing interpretability on the solutions. To this end, we developed a multitask multiple kernel learning (MTMKL) method with a co-clustering step based on a cutting-plane algorithm to identify the relationships between the input tasks and kernels. We tested our algorithm on 15 cancer cohorts and observed that, in most cases, MTMKL outperforms other algorithms (including random forests, support vector machine and single-task multiple kernel learning) in terms of predictive power. Using the aggregate results from multiple replications, we also derived similarity matrices between cancer cohorts, which are, in many cases, in agreement with available relationships reported in the relevant literature.