Understand
Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017) 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 is defined as a neighborhood centered at the empirical distribution.
- 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.
Built on
The elements of statistical learning
Friedman, J., Hastie, T., and Tibshirani, R. (2001) · 2001
Earlier work this paper cites.
Distance metric learning with application to clustering with side-information
Xing, E. P., Ng, A. Y., Jordan, M. I., and Russell, S. (2002) · 2002
Earlier work this paper cites.
Learning a distance metric from relative comparisons
Schultz, M. and Joachims, T. (2004) · 2004
Earlier work this paper cites.
The adaptive lasso and its oracle properties
Zou, H. (2006) · 2006
Earlier work this paper cites.
Optimal transport: old and new
Villani, C. (2008) · 2008
Earlier work this paper cites.
Similar
A survey on metric learning for feature vectors and structured data
Bellet, A., Habrard, A., and Sebban, M. (2013) · 2013
Cited alongside, same era.
Kullback-leibler divergence constrained distributionally robust optimization
Hu, Z. and Hong, L. J. (2013) · 2013
Cited alongside, same era.
UCI machine learning repository
Lichman, M. (2013) · 2013
Cited alongside, same era.
Geometry and properties of generalized ridge regression in high dimensions
Ishwaran, H. and Rao, J. S. (2014) · 2014
Cited alongside, same era.
Esfahani, P. M. and Kuhn, D. (2015) · 2015
Cited alongside, same era.
Ridge regression: applications to nonorthogonal problems
Hoerl, A. E. and Kennard, R. W. (1970a)
Cited in the paper.
Ridge regression: Biased estimation for nonorthogonal problems
Hoerl, A. E. and Kennard, R. W. (1970b)
Cited in the paper.
Then
Distributionally robust logistic regression
Shafieezadeh-Abadeh, S., Esfahani, P. M., and Kuhn, D. (2015) · 2015
Later among the works it cites.
Robust wasserstein profile inference and applications to machine learning
Blanchet, J., Kang, Y., and Murthy, K. (2016) · 2016
Later among the works it cites.
Less than a single pass: Stochastically controlled stochastic gradient method
Lei, L. and Jordan, M. I. (2016) · 2016
Later among the works it cites.
A mahalanobis metric learning-based polynomial kernel for classification of hyperspectral images
Li, L., Sun, C., Lin, L., Li, J., and Jiang, S. (2016) · 2016
Later among the works it cites.
Distributionally robust semi-supervised learning
Blanchet, J. and Kang, Y. (2017) · 2017
Closest in time.
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