Unbalanced CO-optimal Transport

Eulerian models and algorithms for unbalanced optimal transport

Co-clustering through Optimal Transport

In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy regularized optimal transport between empirical measures defined on data instances and features in order to obtain an estimated joint probability density func...

Supplementary material for the paper: Co-clustering through Optimal Transport

For the sake of completeness, we first present the Sinkhorn’s theorem and explain how it was used to derive the solution of the regularized optimal transport. Theorem ((Sinkhorn & Knopp, 1967)). If A is an n × n matrix with strictly positive elements, then there exist diagonal matrices D1 and D2 with strictly positive diagonal elements such that D1 ∗ A ∗ D2 is doubly stochastic. The matrices D1...

Markov-Perfect Optimal Fiscal Policy: The Case of Unbalanced Budgets∗

In most developed economies, income tax rates and government debt levels are positive and sizable. In the US, effective income tax rates have been in the order of 20%, and outstanding public debt represents about 60% of GDP. The main question we pose in this paper is: can these numbers be accounted for as the outcome of a government’s welfare maximization program in a neoclassical economy? To a...

Optimal SVM parameter selection for non-separable and unbalanced datasets.

This article presents a study of three validation metrics used for the selection of optimal parameters of a support vector machine (SVM) classifier in the case of non-separable and unbalanced datasets. This situation is often encountered when the data is obtained experimentally or clinically. The three metrics selected in this work are the area under the ROC curve (AUC), accuracy, and balanced ...