Effect of kernel bandwidth h on statistical and computational error

Quantify how the kernel bandwidth h influences statistical estimation error and computational error in training locally defined transport maps with Sinkhorn-approximated Wasserstein losses, including trade-offs arising from neighborhood size and bandwidth scaling in higher dimensions.

Background

The framework relies on kernel weights based on W2 distances, with bandwidth h selected via a nearest-neighbor heuristic. Bandwidth governs the locality of the estimator and affects both accuracy and stability, especially in higher-dimensional settings where performance was observed to degrade without careful tuning.

The authors explicitly state that understanding the impact of bandwidth h on statistical and computational error is an unresolved issue to be addressed in future work, highlighting a key practical and theoretical aspect of the method.