Cross-Cluster Weighted Forests

Abstract

Building trustworthy machine learning algorithms for biological applications requires adapting to data heterogeneity from different sources, batches, distributions, or studies. We propose the 'Cross-Cluster Weighted Forest' (CCWF), an ensembling approach that explicitly leverages heterogeneity in the feature distribution to produce more accurate and more generalizable predictors than the standard Random Forest in cases when data can be naturally clustered. CCWF generalizes the RF architecture to an outer unsupervised layer, supervised subtasks, and ensembling. Specifically it involves unsupervised clustering of the training data, fitting a Random Forest on each cluster, and combining the forests via stacked regression weights that reward cross-cluster generalizability. We provide a theoretical analysis of an analytically tractable forest model showing that cluster-based ensembling is asymptotically more accurate than training a single forest on the full data, with the gain driven by bias reduction. In simulations, we find that CCWF is robust across data-generating regimes and outcome models; furthermore, we explore the influence of data partitioning and ensemble weighting strategies on the benefits of our method. Finally, we apply our approach to cancer molecular profiling and gene expression datasets that are naturally divisible into clusters; in both simulations and real data examples, we illustrate that our approach outperforms classic Random Forest by margins of 30-40%, aligning with our theoretical results. Overall, we show that CCWF provides a statistically grounded prediction algorithm for data spanning multiple domains or sub-populations, a structure common in biological applications.