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Fast Approximation of the Generalized Sliced-Wasserstein Distance

Citation Author(s):
Dung Le, Huy Nguyen, Khai Nguyen, Trang Nguyen, Nhat Ho
Submitted by:
Huy Nguyen
Last updated:
30 March 2024 - 1:02pm
Document Type:
Document Year:
Huy Nguyen
Paper Code:

Generalized sliced-Wasserstein distance is a variant of sliced-Wasserstein distance that exploits the power of non-linear projection through a given defining function to better capture the complex structures of probability distributions. Similar to the sliced-Wasserstein distance, generalized sliced-Wasserstein is defined as an expectation over random projections which can be approximated by the Monte Carlo method. However, the complexity of that approximation can be expensive in high-dimensional settings. To that end, we propose to form deterministic and fast approximations of the generalized sliced-Wasserstein distance by using the concentration of random projections when the defining functions are polynomial function and neural network type function. Our approximations hinge upon an important result that one-dimensional projections of a high-dimensional random vector are approximately Gaussian.

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