We investigate the use of entropy-regularized optimal transport (EOT) cost in developing generative models to learn implicit distributions. Two generative models are proposed. One uses EOT cost directly in an one-shot optimization problem and the other uses EOT cost iteratively in an adversarial game...
Optimal transportRandomized shortest pathsDistances between nodesThe present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into a set of input ...
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove linear convergence of the algorithm with respect to the ...
Wasserstein distanceoptimal transportdensity forecastingmodel combinationWe propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretCumings-Menon, RyanShin, MinchulSocial Science Electronic Publishing...
The "proximity" between probability laws is quantified by the Wasserstein distance, a notion pertaining to optimal transport theory. The combination of the classical entropic regularization technique in this field with recent results from convex duality theory allows to reformulate the distributionally ...
q-DOT Deformed q-optimal transport L-BFGS Limited-memory BFGS OT Optimal transport Appendix A. Derivation of Deformed q Entropy Given a functional relationship π = ∇ Ω ⋆ ( η ) = exp q ( η / λ ) in Equation (20), we derive the deformed q entropy. First, the derivative of...
Keywords: entropy regularization; Wasserstein distance; optimal transport; density forecasting; forecast combination; model combination; quantile aggregation1. Introduction In this paper, we study a class of density forecast combination methods based on a Wasserstein metric. In the univariate case, an equa...