Bayesian Rips Active Learning: Topology-Aware Acquisition for Rare Lineages

Rare cellular lineages form disconnected or weakly-connected components in gene-expression space, yet standard active learning (AL) acquisitions concentrate queries in dense regions and fail to sample across them. We propose Bayesian Rips Active Learning (BRAL), which augments Gaussian process predictive entropy with a topological signal: each candidate is scored by how much it would change the Vietoris-Rips persistent $H_0$ of the currently labeled set, favoring selections that expand into disconnected regions. On Paul15 hematopoietic data (${\sim}2.5\%$ rare Megakaryocytes), BRAL discovers $42$ of $68$ rare cells at a 5% budget---nearly twice the best baseline. On PBMC~3k, BRAL achieves the highest rare-class F1 ($0.89$) with the lowest variance across seeds.