Gaussian-Smoothed Sliced Divergences: Theoretical Properties and Applications in Privacy-Preserving Domain Adaptation

This work investigates the theoretical properties of Gaussian-smoothed sliced divergences, including their topological and statistical properties. It establishes that under mild conditions, the smoothing and slicing operations preserve the metric property. The paper also focuses on the sample complexity of such divergences, particularly the Gaussian-smoothed sliced Wasserstein distance, and proves that it converges at a rate of O(n^(-1/2)). Additionally, the authors derive continuity properties of the divergences with respect to the smoothing parameter, which is crucial for the privacy-utility trade-off.