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Several machine learning methods leverage the idea of locality by using k-nearest neighbor (KNN) techniques to design better pattern recognition models. However, the choice of KNN parameters such as k is often made experimentally, e.g., via cross-validation, leading to local neighborhoods without a clear geometric interpretation. In this paper, we replace KNN with our recently introduced polytope neighborhood scheme - Non Negative Kernel regression (NNK). NNK formulates neighborhood selection as a sparse signal approximation problem and is adaptive to the local distribution of samples in the neighborhood of the data point of interest. We analyze the benefits of local neighborhood construction based on NNK. In particular, we study the generalization properties of local interpolation using NNK and present data dependent bounds in the non asymptotic setting. The applicability of NNK in transductive few shot learning setting and for measuring distance between two datasets is demonstrated. NNK exhibits robust, superior performance in comparison to standard locally weighted neighborhood methods.
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Data-Driven Optimal Transport Cost Selection For Distributionally Robust Optimization
Some recent works showed that several machine learning algorithms, such as square-root Lasso, Support Vector Machines, and regularized logistic regression, among many others, can be represented exactly as distributionally robust optimization (DRO) problems. The distributional uncertainty set is defined as a neighborhood centered at the empirical distribution, and the neighborhood is measured by optimal transport distance. In this paper, we propose a methodology which learns such neighborhood in a natural data-driven way. We show rigorously that our framework encompasses adaptive regularization as a particular case. Moreover, we demonstrate empirically that our proposed methodology is able to improve upon a wide range of popular machine learning estimators.
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- PAR ID:
- 10175309
- Date Published:
- Journal Name:
- 2019 Winter Simulation Conference
- Page Range / eLocation ID:
- 3740 to 3751
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/WSC40007.2019.9004785
