Tree-Sliced Entropy Partial Transport

Optimal Transport (OT) has emerged as a fundamental tool in machine learning for comparing probability distributions in a geometrically meaningful manner. However, a key limitation of classical OT is its requirement that the source and target distributions have equal total mass, limiting its use in real-world settings involving imbalanced data, noise, outliers, or structural inconsistencies. Partial Transport (PT) addresses this limitation by allowing only a fraction of the mass to be transported, offering greater flexibility and robustness. Nonetheless, similar to OT, PT remains computationally expensive, as it typically involves solving large-scale linear programs--especially in high-dimensional spaces. To alleviate this computational burden, several emerging works have introduced the Tree-Sliced Wasserstein (TSW) distance, which projects distributions onto tree-metric spaces where OT problems admit closed-form solutions.