
A Consistent Extension of Discrete Optimal Transport Maps for Machine Learning Applications
Optimal transport maps define a onetoone correspondence between probab...
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Evaluating Bregman Divergences for Probability Learning from Crowd
The crowdsourcing scenarios are a good example of having a probability d...
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Robustifying Conditional Portfolio Decisions via Optimal Transport
We propose a datadriven portfolio selection model that integrates side ...
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Learning Probability Measures with respect to Optimal Transport Metrics
We study the problem of estimating, in the sense of optimal transport me...
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An optimal transport approach to data compression in distributionally robust control
We consider the problem of controlling a stochastic linear timeinvarian...
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Stein Points
An important task in computational statistics and machine learning is to...
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Partial Wasserstein Covering
We consider a general task called partial Wasserstein covering with the ...
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SPOT: A framework for selection of prototypes using optimal transport
In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important problem in several machine learning applications where human understanding of the learning models and underlying data distribution is essential for decision making. We model the prototype selection problem as learning a sparse (empirical) probability distribution having the minimum OT distance from the target distribution. The learned probability measure supported on the chosen prototypes directly corresponds to their importance in representing the target data. We show that our objective function enjoys a key property of submodularity and propose an efficient greedy method that is both computationally fast and possess deterministic approximation guarantees. Empirical results on several real world benchmarks illustrate the efficacy of our approach.
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