Minimax lower bounds for partial optimal transport estimation

Establish minimax lower bounds for direct estimation of conditional mean persistence measures in partial optimal transport.

Background

The paper develops upper convergence bounds for estimating conditional weighted persistence measures directly in partial optimal transport, allowing the target measure to have atoms or lower-dimensional support. Unlike the supremum-norm intensity result, the paper does not establish a matching minimax lower bound for this measure-level loss. Such a lower bound would determine whether the reported partial-transport rates are statistically optimal.

References

Several directions for future work therefore arise naturally. On the theoretical side, it remains to establish minimax lower bounds for direct estimation in partial optimal transport and to determine whether the logarithmic factor at $q=1$ in \Cref{thm:pot-rate} is intrinsic.

— Weighted persistence intensity regression  (2609.01387 - Pegoraro et al., 1 Sep 2026) in Section Discussion