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Wasserstein Logistic Regression with Mixed Features
Aras Selvi · Mohammad Reza Belbasi · Martin Haugh · Wolfram Wiesemann

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #726

Recent work has leveraged the popular distributionally robust optimization paradigm to combat overfitting in classical logistic regression. While the resulting classification scheme displays a promising performance in numerical experiments, it is inherently limited to numerical features. In this paper, we show that distributionally robust logistic regression with mixed (\emph{i.e.}, numerical and categorical) features, despite amounting to an optimization problem of exponential size, admits a polynomial-time solution scheme. We subsequently develop a practically efficient cutting plane approach that solves the problem as a sequence of polynomial-time solvable exponential conic programs. Our method retains many of the desirable theoretical features of previous works, but---in contrast to the literature---it does not admit an equivalent representation as a regularized logistic regression, that is, it represents a genuinely novel variant of the logistic regression problem. We show that our method outperforms both the unregularized and the regularized logistic regression on categorical as well as mixed-feature benchmark instances.

Author Information

Aras Selvi (Imperial College London)
Aras Selvi

Aras Selvi is a Ph.D. candidate at Imperial College London (Department of Analytics and Operations, Business School) as a member of the group “Models and Algorithms for Decision-Making under Uncertainty” supervised by Professor Wolfram Wiesemann. His research interests include robust and distributionally robust optimization, machine learning, computational privacy, and their intersections. He is a recipient of The Alan Turing Institute Ph.D. Enrichment Placement program (2022/23).

Mohammad Reza Belbasi (Imperial College London, Imperial College London)
Martin Haugh (Imperial College London)

Martin Haugh is an Associate Professor of Analytics and Operations Research at Imperial College Business School where he has been since September 2017. Prior to that he spent more than 10 years in the Department of IE & OR at Columbia University as well as 4 years working as a quant in the hedge fund industry in New York and London. He has a Ph.D. in Operations Research from MIT (2001) and MSc degrees in Applied Statistics and Mathematics from the University of Oxford and University College Cork, respectively. His research interests are in quantitative finance & risk management, dynamic programming, and data science.

Wolfram Wiesemann (Imperial College)

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