A is a True Distance

Proposition 4.1 is a direct extension of the following well-known bound for the 2-Wasserstein distance Then, for our setting, we have: Proposition 4.1 . In the notation of Section 3, Lemma B.1 implies that for every feature-label pairs Clearly, Gelbrich's bound holds with equality when We next analyze step (i) individually for the two OTDD versions. Information about all the datasets used, including references, are provided in Table 1 .