Interpretable metric learning in comparative metagenomics: The adaptive Haar-like distance

Random forests have emerged as a promising tool in comparative metagenomics because they can predict environmental characteristics based on microbial composition in datasets where beta-diversity metrics fall short of revealing meaningful relationships between samples. Nevertheless, despite this efficacy, they lack biological insight in tandem with their predictions, potentially hindering scientific advancement. To overcome this limitation, we leverage a geometric characterization of random forests to introduce a data-driven phylogenetic beta-diversity metric, the adaptive Haar-like distance. This new metric assigns a weight to each internal node (i.e., split or bifurcation) of a reference phylogeny, indicating the relative importance of that node in discerning environmental samples based on their microbial composition. Alongside this, a weighted nearest-neighbors classifier, constructed using the adaptive metric, can be used as a proxy for the random forest while maintaining accuracy on par with that of the original forest and another state-of-the-art classifier, CoDaCoRe. As shown in datasets from diverse microbial environments, however, the new metric and classifier significantly enhance the biological interpretability and visualization of high-dimensional metagenomic samples. Traditional phylogenetic beta-diversity metrics, particularly weighted and unweighted UniFrac, have had great success in comparing and visualizing high-dimensional metagenomic samples. Nonetheless, these metrics rely upon pre-established biological assumptions that might not capture key microbial players or relationships between some samples. On the contrary, supervised machine learning algorithms, such as random forests, can often capture intricate relationships between microbial samples; however, unveiling these relationships is often challenging due to the intricate inner mechanisms inherent to these algorithms.The adaptive Haar-like distance integrates the merits of beta-diversity metrics and random forests, allowing for precise, intuitive, and visual comparison of metagenomic samples, offering valuable scientific insight into the distinctions and associations among microbial environments.