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Abstract Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The transform is defined by computing the optimal transport of each distribution to a fixed reference distribution and has a number of benefits when it comes to speed of computation and to determining classification boundaries. In this paper, we characterize a number of settings in which LOT embeds families of distributions into a space in which they are linearly separable. This is true in arbitrary dimension, and for families of distributions generated through perturbations of shifts and scalings of a fixed distribution. We also prove conditions under which the $L^2$ distance of the LOT embedding between two distributions in arbitrary dimension is nearly isometric to Wasserstein-2 distance between those distributions. This is of significant computational benefit, as one must only compute $$N$$ optimal transport maps to define the $N^2$ pairwise distances between $$N$$ distributions. We demonstrate the benefits of LOT on a number of distribution classification problems.
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Better Input Modeling via Model Averaging
Rather than the standard practice of selecting a single “best-fit” distribution from a candidate set, frequentist model averaging (FMA) forms a mixture distribution that is a weighted average of the candidate distributions with the weights tuned by cross-validation. In previous work we showed theoretically and empirically that FMA in the probability space leads to higher fidelity input distributions. In this paper we show that FMA can also be implemented in the quantile space, leading to fits that emphasize tail behavior. We also describe an R package for FMA that is easy to use and available for download.
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- Award ID(s):
- 1634982
- PAR ID:
- 10122981
- Date Published:
- Journal Name:
- Proceedings of the 2018 Winter Simulation Conference
- Page Range / eLocation ID:
- 1575-1586
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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