On minimum Kantorovich distance estimators

By Federico Bassetti, A. Bodini, E. Regazzini. 2006

102 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/59350bfcaafb7e2f943db50558965e7df62a3ba8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Finance

In Statistics and Probability

Citations in the corpus

Stochastic Optimization for Large-scale Optimal Transport (2016, background): “Solving these semi-discrete problems efficiently could have a significant impact for applications to density fitting with an OT loss [2] for machine learning applications, see [13].”
A Fast Proximal Point Method for Computing Exact Wasserstein Distance (2018, background): “Given a dataset { x i } and some noise { z j } (Bassetti et al., 2006; Goodfellow et al., 2014), our goal is to ﬁnd a parameterized function g θ ( · ) that minimize where Usually, g θ is parameterized by a neural network with parameter θ , and the minimization over θ is done by stochastic gradient…”
Wasserstein Training of Restricted Boltzmann Machines (2016, background): “This choice was considered in theory by [2], who proved its statistical consistency, but was never considered practically to the best of our knowledge.”
A Fast Proximal Point Method for Computing Wasserstein Distance (2018, background): “Given a dataset { x i } and some noise { z j } [4, 15], our goal is to ﬁnd a parameterized function where Usually, g θ is parameterized by a neural network with parameter θ , and the minimization over θ is done by stochastic gradient descent.”
Learning with a Wasserstein Loss (2015, background): “The closest work to this paper is a theoretical study [14] of an estimator that minimizes the optimal transport cost between the empirical distribution and the estimated distribution in the setting of statistical parameter estimation.”
Computational Optimal Transport (2018, methodology): “The class of estimators obtained using L = Lc, often called “minimum Kantorovich estimators,” was initially introduced in [Bassetti et al., 2006]; see also [Canas and Rosasco, 2012].”
GAN and VAE from an Optimal Transport Point of View (2017, unknown): “…y j ∈ X ⊂ R p , and a parametric family of probability distributions ( µ θ ) θ ∈ Θ ⊂ P ( X ), Θ ⊂ R q , a Minimum Kantorovitch Estimator (MKE) [2, 11, 3] for θ is deﬁned as any solution of the problem min where W c is the Wasserstein cost on P ( X ) for some ground cost function c : X × X → R…”
Interpolating between Optimal Transport and MMD using Sinkhorn Divergences (2018, background): “…wide range of situations, from computer graphics (Bonneel et al., 2016) to supervised learning (Frogner et al., 2015), unsupervised density ﬁtting (Bassetti et al., 2006) and generative model learning (Montavon et al., 2016; Arjovsky et al., 2017; Salimans et al., 2018; Genevay et al., 2018;…”
Learning Generative Models with Sinkhorn Divergences (2017, methodology): “To remedy these issues, and in line with several recent proposals [2, 26, 4, 1], we propose to shift away from information divergence based methods (among which the MLE) and consider instead the geometry of optimal transport [36, 31] to define such a fitting criterion.”