Conformal novelty detection for multiple metabolic networks

Graphical representations are useful to model complex data in general and biological interactions in particular. Our main motivation is the comparison of metabolic networks in the wider context of developing noninvasive accurate diagnostic tools. However, comparison and classification of graphs is still extremely challenging, although a number of highly efficient methods such as graph neural networks were developed in the recent decade. Important aspects are still lacking in graph classification: interpretability and guarantees on classification quality, i.e., control of the risk level or false discovery rate control.

In our contribution, we introduce a statistically sound approach to control the false discovery rate in a classification task for graphs in a semi-supervised setting. Our procedure identifies novelties in a dataset, where a graph is considered to be a novelty when its topology is significantly different from those in the reference class. It is noteworthy that the procedure is a conformal prediction approach, which does not make any distributional assumptions on the data and that can be seen as a wrapper around traditional machine learning models, so that it takes full advantage of existing methods. The performance of the proposed method is assessed on several standard benchmarks. It is also adapted and applied to the difficult task of classifying metabolic networks, where each graph is a representation of all metabolic reactions of a bacterium and to real task from a cancer data repository.

Our approach efficiently controls - in highly complex data - the false discovery rate, while maximizing the true discovery rate to get the most reasonable predictive performance. This contribution is focused on confident classification of complex data, what can be further used to explore complex human pathologies and their mechanisms.