DOSA-MO: Dual-stage Optimizer for Systematic overestimation Adjustment in Multi-Objective problems improves biomarker discovery

The challenge in biomarker discovery and validation using machine learning from omics data lies in the abundance of molecular features but scarcity of samples. Most machine learning-based feature selection methods necessitate of hyperparameter tuning, typically performed by evaluating numerous alternatives on a validation set. Every evaluation has a performance estimation error and when the selection takes place between many models the best ones are almost certainly overestimated. Biomarker identification is a typical multi-objective problem with trade-offs between the predictive ability and the parsimony in the number of molecular features. Genetic algorithms are a popular tool for multi-objective optimization but they evolve numerous solutions and are prone to overestimation. Methods have been proposed to reduce the overestimation after a model has already been selected in single-objective problems, but to the best of our knowledge no algorithm existed that was capable of reducing the overestimation during the optimization, leading to a better model selection, or that had been applied in the more general domain of multi-objective problems. We propose DOSA-MO, a novel multi-objective optimization wrapper algorithm that learns how the original estimation, its variance, and the feature set size of the solutions predict the overestimation, and adjusts the expectation of the performance during the optimization, improving the composition of the solution set. We verify that DOSA-MO improves the performance of a state-of-the-art genetic algorithm on left-out or external sample sets, when predicting cancer subtypes and/or patient overall survival, using three transcriptomics datasets for kidney and breast cancer.