The effect of non-linear signal in classification problems using gene expression

Author summaryIf we could consistently predict biological conditions from mRNA levels, it could help discover biomarkers for disease diagnosis. Deep learning has become widely used for many tasks including biomarker discovery. It is unclear whether the complexity of these models is helpful. We evaluate whether or not more complex non-linear models have an advantage over simpler linear ones for a set of prediction tasks. We find that, at least for tissue prediction and prediction of metadata-derived sex prediction, linear models perform just as well as non-linear ones. However, we also demonstrate the presence of a predictive signal in the data that only the non-linear models can use. Our results suggest that the non-linear signals may be redundant with linear ones or that current deep neural networks are not able to successfully use the signal when linear signals are present. Those building predictive models from transcriptomic data are faced with two conflicting perspectives. The first, based on the inherent high dimensionality of biological systems, supposes that complex non-linear models such as neural networks will better match complex biological systems. The second, imagining that complex systems will still be well predicted by simple dividing lines prefers linear models that are easier to interpret. We compare multi-layer neural networks and logistic regression across multiple prediction tasks on GTEx and Recount3 datasets and find evidence in favor of both possibilities. We verified the presence of non-linear signal when predicting tissue and metadata sex labels from expression data by removing the predictive linear signal with Limma, and showed the removal ablated the performance of linear methods but not non-linear ones. However, we also found that the presence of non-linear signal was not necessarily sufficient for neural networks to outperform logistic regression. Our results demonstrate that while multi-layer neural networks may be useful for making predictions from gene expression data, including a linear baseline model is critical because while biological systems are high-dimensional, effective dividing lines for predictive models may not be.