Sliced Wasserstein Kernels for Probability Distributions

By Soheil Kolouri, Yang Zou, Gustavo Kunde Rohde. 2015

182 citations recorded by the source corpus.

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as powerful discrepancy measures for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutions to the problem and have revamped their practical applications in machine learning. In this paper, we exploit the widely used kernel methods and provide a family of provably positive definite kernels based on the Sliced Wasserstein distance and demonstrate the benefits of these kernels in a variety of learning tasks. Our work provides a new perspective on the application of optimal transport flavored distances through kernel methods in machine learning tasks.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Computational Optimal Transport (2018, methodology): “This result can be used to define a positive definite kernel [Kolouri et al., 2016].”
Optimal Mass Transport: Signal processing and machine-learning applications (2017, methodology): “[28] utilized the sliced-Wasserstein metric and provided a family of positive definite kernels, denoted sliced-Wasserstein kernels, and showed the advantages of learning with such kernels.”
“GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models” (2018, unknown): “As proven in Kolouri et al. 2016, this Wasserstein distance based kernel is a positive deﬁnite (p.d.) kernel.”
Subspace Robust Wasserstein distances (2019, methodology): “This approach can be used to deﬁne kernels (Kolouri et al., 2016 We consider two discrete measures (red and blue dots) on the plane.”
Generalized Sliced Wasserstein Distances (2019, background): “Therefore, it has recently attracted ample attention and successfully been applied to a variety of practical tasks (Bonneel et al., 2015; Kolouri et al., 2016; Carriere et al., 2017; Karras et al., 2017; Şimşekli et al., 2018; Deshpande et al., 2018; Kolouri et al., 2018; 2019).”
Sliced Wasserstein Distance for Learning Gaussian Mixture Models (2017, methodology): “The Sliced p-Wasserstein distance as defined above is symmetric, and it satisfies sub-additivity and coincidence axioms, and hence it is a true metric [29].”