  Wasserstein distance is a principle measure of data divergence from a
distributional standpoint. However, its application becomes challenging in the
context of data privacy, where sharing raw data is restricted. Prior attempts
have employed techniques like Differential Privacy or Federated optimization to
approximate Wasserstein distance. Nevertheless, these approaches often lack
accuracy and robustness against potential attack. In this study, we investigate
the underlying triangular properties within the Wasserstein space, leading to a
straightforward solution named TriangleWad. This approach enables the
computation of Wasserstein distance between datasets stored across different
entities. Notably, TriangleWad is 20 times faster, making raw data information
truly invisible, enhancing resilience against attacks, and without sacrificing
estimation accuracy. Through comprehensive experimentation across various tasks
involving both image and text data, we demonstrate its superior performance and
generalizations.
