proxy support measure in the formulation is a continuous measure, and in the implementation we choose a uniform

We thank the reviewers for their time and their valuable feedback and thoughtful suggestions. Below are our answers to the reviewers' comments, grouped by topic. To the best of our knowledge, all prior works either consider fixed-support (e.g., [ 's concern of lack of conclusion on which method to choose, we have included a discussion We will add recommendation for higher-dimensional situations to accompany the results in Table B.1 and's concern about recovery methods being costly, method (d) in fact comes at almost no cost Even for continuous regularized OT distance [5] this is not well-understood. We agree these are areas for future work. Gaussians, whose low sample complexity favors discretized methods more than other settings.