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This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches.
An inductive inference machine
Raymond J. Solomonoff · 1957
Earlier work this paper cites.
Some methods for classification and analysis of multivariate observations
James MacQueen · 1967
Earlier work this paper cites.
Constructing optimal binary decision trees is NP-complete
Laurent Hyafil and Ronald L. Rivest · 1976
Earlier work this paper cites.
An algorithm for constructing optimal binary decision trees
Harold J. Payne and William S. Meisel · 1977
Earlier work this paper cites.
Cluster analysis: An application of Lagrangian relaxation
John M Mulvey and Harlan P Crowder · 1979
Earlier work this paper cites.
Classification and Regression Trees
L Breiman, J Friedman, R Olshen, and C Stone · 1984
Earlier work this paper cites.
The p-median problem for cluster analysis: A comparative test using the mixture model approach
Ted D Klastorin · 1985
Earlier work this paper cites.
A stochastic approximation method
Herbert Robbins and Sutton Monro · 1985
Earlier work this paper cites.
Generalized additive models
Trevor Hastie and Robert Tibshirani · 1986
Earlier work this paper cites.
Heuristic least-cost computation of discrete classification functions with uncertain argument values
Louis Anthony Cox, Yuping Qiu, and Warren Kuehner · 1989
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Generalization and network design strategies
Yann LeCun et al · 1989
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Approximation capabilities of multilayer feedforward networks
Kurt Hornik · 1991
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Teachability in computational learning
Ayumi Shinohara and Satoru Miyano · 1991
Earlier work this paper cites.
Decision tree construction via linear programming
Kristin P Bennett · 1992
Earlier work this paper cites.
Robust linear programming discrimination of two linearly inseparable sets
Kristin P Bennett and Olvi L Mangasarian · 1992
Earlier work this paper cites.
An algorithm for the mixed-integer nonlinear bilevel programming problem
Thomas A Edmunds and Jonathan F Bard · 1992
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Clustering heuristics for set covering
Renata Krystyna Kwatera and Bruno Simeone · 1993
Earlier work this paper cites.
Nonlinear integer bilevel programming
Rong-Hong Jan and Maw-Sheng Chern · 1994
Earlier work this paper cites.
A limited memory algorithm for bound constrained optimization
Richard H Byrd, Peihuang Lu, Jorge Nocedal, and Ciyou Zhu · 1995
Earlier work this paper cites.
The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions
Yang Chen and Michael Florian · 1995
Earlier work this paper cites.
Support-vector networks
Corinna Cortes and Vladimir Vapnik · 1995
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On the complexity of teaching
Sally Goldman and Michael Kearns · 1995
Earlier work this paper cites.
Sparse approximate solutions to linear systems
Balas Kausik Natarajan · 1995
Earlier work this paper cites.
Optimal decision trees
Kristin P. Bennett and J. Blue · 1996
Earlier work this paper cites.
Learning Bayesian networks is NP-complete
David Maxwell Chickering · 1996
Earlier work this paper cites.
Eigenfaces vs. fisherfaces: Recognition using class specific linear projection
Peter N Belhumeur, João P Hespanha, and David J Kriegman · 1997
Earlier work this paper cites.
Cluster analysis and mathematical programming
Pierre Hansen and Brigitte Jaumard · 1997
Earlier work this paper cites.
Permutation-based multivariate regression analysis: The case for least sum of absolute deviations regression
Paul W Mielke and Kenneth J Berry · 1997
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Locating least-distant lines in the plane
Anita Schöbel · 1998
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Statistical Learning Theory
Vladimir Vapnik · 1998
Earlier work this paper cites.
Data clustering: a review
Anil K. Jain, M. N. Narasimha Murty, and Patrick J. Flynn · 1999
Earlier work this paper cites.
Iterative Methods for Optimization
Carl T Kelley · 1999
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Massive data discrimination via linear support vector machines
Paul Bradley and Olvi Mangasarian · 2000
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Large margin rank boundaries forordinal regression
R. Herbrich, T. Graepel, and K. Obermayer · 2000
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The Elements of Statistical Learning
Jerome Friedman, Trevor Hastie, and Robert Tibshirani · 2001
Earlier work this paper cites.
Global optimization of nonlinear bilevel programming problems
Zeynep H Gümüş and Christodoulos A Floudas · 2001
Earlier work this paper cites.
Learning Kernel Classifiers: Theory and Algorithms
Ralf Herbrich · 2001
Earlier work this paper cites.
Prediction of ordinal classes using regression trees
Stefan Kramer, Gerhard Widmer, Bernhard Pfahringer, and Michael De Groeve · 2001
Earlier work this paper cites.
Logistic regression and artificial neural network classification models: a methodology review
Stephan Dreiseitl and Lucila Ohno-Machado · 2002
Earlier work this paper cites.
Review of nonlinear mixed-integer and disjunctive programming techniques
Ignacio E. Grossmann · 2002
Earlier work this paper cites.
Gene selection for cancer classification using support vector machines
Isabelle Guyon, Jason Weston, Stephen Barnhill, and Vladimir Vapnik · 2002
Earlier work this paper cites.
A robust minimax approach to classification
Gert R. G. Lanckriet, Laurent El Ghaoui, Chiranjib Bhattacharyya, and Michael I. Jordan · 2002
Earlier work this paper cites.
Subset Selection in Regression
Alan Miller · 2002
Earlier work this paper cites.
A clustering technique for the identification of piecewise affine systems
Giancarlo Ferrari-Trecate, Marco Muselli, Diego Liberati, and Manfred Morari · 2003
Earlier work this paper cites.
Constraint classification for multiclass classification and ranking
Sariel Har-Peled, Dan Roth, and Dav Zimak · 2003
Earlier work this paper cites.
Ranking with large margin principle: Two approaches
Amnon Shashua and Anat Levin · 2003
Earlier work this paper cites.
Online convex programming and generalized infinitesimal gradient ascent
Martin Zinkevich · 2003
Earlier work this paper cites.
Continuous location of dimensional structures
JM Dıaz-Bánez, Juan A Mesa, and Anita Schöbel · 2004
Earlier work this paper cites.
K-means clustering via principal component analysis
Chris Ding and Xiaofeng He · 2004
Earlier work this paper cites.
Least angle regression
Bradley Efron, Trevor Hastie, Iain Johnstone, Robert Tibshirani, et al · 2004
Earlier work this paper cites.
Evaluating feature selection methods for learning in data mining applications
Selwyn Piramuthu · 2004
Earlier work this paper cites.
A tutorial on support vector regression
Alex J Smola and Bernhard Schölkopf · 2004
Earlier work this paper cites.
1-Norm support vector machines
Ji Zhu, Saharon Rosset, Robert Tibshirani, and Trevor J. Hastie · 2004
Earlier work this paper cites.
Adversarial learning
Daniel Lowd and Christopher Meek · 2005
Earlier work this paper cites.
Regularization and variable selection via the elastic net
Hui Zou and Trevor Hastie · 2005
Earlier work this paper cites.
A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems
Adil M Bagirov and John Yearwood · 2006
Earlier work this paper cites.
The interplay of optimization and machine learning research
Kristin P Bennett and Emilio Parrado-Hernández · 2006
Earlier work this paper cites.
Nightmare at test time: robust learning by feature deletion
Amir Globerson and Sam Roweis · 2006
Earlier work this paper cites.
A tutorial on energy-based learning
Yann LeCun, Sumit Chopra, Raia Hadsell, Marc Aurelio Ranzato, and Fu Jie Huang · 2006
Earlier work this paper cites.
The capacitated centred clustering problem
Marcos Negreiros and Augusto Palhano · 2006
Earlier work this paper cites.
A mixed-integer programming approach to the clustering problem with an application in customer segmentation
Burcu Sağlam, F. Sibel Salman, Serpil Sayın, and Metin Türkay · 2006
Earlier work this paper cites.
A scatter search heuristic for the capacitated clustering problem
Stephan Scheuerer and Rolf Wendolsky · 2006
Earlier work this paper cites.
The doubly regularized support vector machine
Li Wang, Ji Zhu, and Hui Zou · 2006
Earlier work this paper cites.
Classification and regression via integer optimization
Dimitris Bertsimas and Romy Shioda · 2007
Earlier work this paper cites.
Direct convex relaxations of sparse SVM
Antoni B. Chan, Nuno Vasconcelos, and Gert R. G. Lanckriet · 2007
Earlier work this paper cites.
Support vector ordinal regression
Wei Chu and S Sathiya Keerthi · 2007
Earlier work this paper cites.
An application of special ordered sets to a periodic milk collection problem
GDH Claassen and Th HB Hendriks · 2007
Earlier work this paper cites.
Cloves: A cluster-and-search heuristic to solve the vehicle routing problem with delivery and pick-up
K Ganesh and TT Narendran · 2007
Earlier work this paper cites.
New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and technology
Pakize Taylan, G-W Weber, and Amir Beck · 2007
Earlier work this paper cites.
A special ordered set approach for optimizing a discontinuous separable piecewise linear function
I.R. de Farias, M. Zhao, and H. Zhao · 2008
Earlier work this paper cites.
Modern Multivariate Statistical Techniques: Regression, Classification and Manifold Learning
Alan Julian Izenman · 2008
Earlier work this paper cites.
Operations research and data mining
Sigurdur Olafsson, Xiaonan Li, and Shuning Wu · 2008
Earlier work this paper cites.
Bilevel programming with discrete lower level problems
Diana Fanghänel and Stephan Dempe · 2009
Earlier work this paper cites.
The security of machine learning
Marco Barreno, Blaine Nelson, Anthony D. Joseph, and J. Doug Tygar · 2010
Earlier work this paper cites.
Multiple classifier systems under attack
Battista Biggio, Giorgio Fumera, and Fabio Roli · 2010
Earlier work this paper cites.
Binarized support vector machines
Emilio Carrizosa, Belén Martín-Barragán, and Dolores Romero Morales · 2010
Cited alongside, same era.
Clustering search algorithm for the capacitated centered clustering problem
Antonio Augusto Chaves and Luiz Antonio Nogueira Lorena · 2010
Cited alongside, same era.
Learning to classify with missing and corrupted features
Ofer Dekel, Ohad Shamir, and Lin Xiao · 2010
Cited alongside, same era.
Simultaneous classification and feature selection via convex quadratic programming with application to HIV-associated neurocognitive disorder assessment
Michelle Dunbar, John M. Murray, Lucette A. Cysique, Bruce J. Brew, and Vaithilingam Jeyakumar · 2010
Cited alongside, same era.
Learning Bayesian network structure using LP relaxations
Tommi Jaakkola, David Sontag, Amir Globerson, and Marina Meila · 2010
Cited alongside, same era.
Best subset selection via a modern optimization lens
Dimitris Bertsimas, Angela King, and Rahul Mazumder · 2016
Later among the works it cites.
Deep Learning
Ian Goodfellow, Yoshua Bengio, Aaron Courville, and Yoshua Bengio · 2016
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Learning to branch in mixed integer programming
Elias B. Khalil, Pierre Le Bodic, Le Song, George Nemhauser, and Bistra Dilkina · 2016
Later among the works it cites.
Adversarial machine learning at scale
Alexey Kurakin, Ian Goodfellow, and Samy Bengio · 2016
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The teaching dimension of linear learners
Ji Liu and Xiaojin Zhu · 2016
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A model for clustering data from heterogeneous dissimilarities
Éverton Santi, Daniel Aloise, and Simon J. Blanchard · 2016
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Juan Pablo Vielma, Shabbir Ahmed, and George Nemhauser · 2010
Cited alongside, same era.
Multi-label linear discriminant analysis
Hua Wang, Chris Ding, and Heng Huang · 2010
Cited alongside, same era.
Optimization problems in statistical learning: Duality and optimality conditions
Radu Ioan Boţ and Nicole Lorenz · 2011
Cited alongside, same era.
Stackelberg games for adversarial prediction problems
Michael Brückner and Tobias Scheffer · 2011
Cited alongside, same era.
Efficient structure learning of Bayesian networks using constraints
Cassio P de Campos and Qiang Ji · 2011
Cited alongside, same era.
Detecting relevant variables and interactions in supervised classification
Emilio Carrizosa, Belén Martín-Barragán, and Dolores Romero Morales · 2011
Cited alongside, same era.
Bayesian network learning with cutting planes
James Cussens · 2011
Cited alongside, same era.
Learning treewidth-bounded bayesian networks with thousands of variables
Mauro Scanagatta, Giorgio Corani, Cassio P de Campos, and Marco Zaffalon · 2016
Later among the works it cites.
Big data analytics in logistics and supply chain management: Certain investigations for research and applications
Gang Wang, Angappa Gunasekaran, Eric W.T. Ngai, and Thanos Papadopoulos · 2016
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Multi-stage optimization of decision and inhibitory trees for decision tables with many-valued decisions
Mohammad Azad and Mikhail Moshkov · 2017
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Integer linear programming for the Bayesian network structure learning problem
Mark Bartlett and James Cussens · 2017
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Optimal classification trees
Dimitris Bertsimas and Jack Dunn · 2017
Later among the works it cites.
Towards evaluating the robustness of neural networks
Nicholas Carlini and David Wagner · 2017
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Maximum resilience of artificial neural networks
Chih-Hong Cheng, Georg Nührenberg, and Harald Ruess · 2017
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Optimization methods for supervised machine learning: From linear models to deep learning
Frank E. Curtis and Katya Scheinberg · 2017
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An effective algorithm for hyperparameter optimization of neural networks
Gonzalo I. Diaz, Achille Fokoue-Nkoutche, Giacomo Nannicini, and Horst Samulowitz · 2017
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Towards a rigorous science of interpretable machine learning
Finale Doshi-Velez and Been Kim · 2017
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Lagrangian relaxation for SVM feature selection
Manlio Gaudioso, Enrico Gorgone, Martine Labbé, and Antonio M Rodríguez-Chía · 2017
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Extended comparisons of best subset selection, forward stepwise selection, and the lasso
Trevor Hastie, Robert Tibshirani, and Ryan J Tibshirani · 2017
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New diagonal bundle method for clustering problems in large data sets
Napsu Karmitsa, Adil M. Bagirov, and Sona Taheri · 2017
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Reluplex: An efficient SMT solver for verifying deep neural networks
Guy Katz, Clark Barrett, David L. Dill, Kyle Julian, and Mykel J. Kochenderfer · 2017
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Learning to run heuristics in tree search
Elias B. Khalil, Bistra Dilkina, George L. Nemhauser, Shabbir Ahmed, and Yufen Shao · 2017
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On learning and branching: a survey
Andrea Lodi and Giulia Zarpellon · 2017
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Empirical decision model learning
Michele Lombardi, Michela Milano, and Andrea Bartolini · 2017
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Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2017
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Notes on the number of linear regions of deep neural networks
Guido Montúfar · 2017
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Theory of deep learning III: explaining the non-overfitting puzzle
Tomaso Poggio, Kenji Kawaguchi, Qianli Liao, Brando Miranda, Lorenzo Rosasco, Xavier Boix, Jack Hidary, and Hrushikesh Mhaskar · 2017
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Certified defenses for data poisoning attacks
Jacob Steinhardt, Pang Wei W Koh, and Percy S Liang · 2017
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Best subset selection for eliminating multicollinearity
Ryuta Tamura, Ken Kobayashi, Yuichi Takano, Ryuhei Miyashiro, Kazuhide Nakata, and Tomomi Matsui · 2017
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Evaluating robustness of neural networks with mixed integer programming
Vincent Tjeng and Russ Tedrake · 2017
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Ensemble adversarial training: Attacks and defenses
Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, and Patrick McDaniel · 2017
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Learning decision trees with flexible constraints and objectives using integer optimization
Sicco Verwer and Yingqian Zhang · 2017
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Auction optimization using regression trees and linear models as integer programs
Sicco Verwer, Yingqian Zhang, and Qing Chuan Ye · 2017
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A kernel machine method for detecting higher order interactions in multimodal datasets: Application to schizophrenia
Md Ashad Alam, Hui-Yi Lin, Hong-Wen Deng, Vince D Calhoun, and Yu-Ping Wang · 2018
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Machine learning for combinatorial optimization: a methodological tour d’horizon
Yoshua Bengio, Andrea Lodi, and Antoine Prouvost · 2018
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Characterization of the equivalence of robustification and regularization in linear and matrix regression
Dimitris Bertsimas and Martin S. Copenhaver · 2018
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Locating hyperplanes to fitting set of points: A general framework
Víctor Blanco, Justo Puerto, and Román Salmerón · 2018
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Optimal randomized classification trees
Rafael Blanquero, Emilio Carrizosa, Cristina Molero-Rıo, and Dolores Romero Morales · 2018
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Learning a classification of mixed-integer quadratic programming problems
Pierre Bonami, Andrea Lodi, and Giulia Zarpellon · 2018
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Optimization methods for large-scale machine learning
Léon Bottou, Frank E. Curtis, and Jorge Nocedal · 2018
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A unified view of piecewise linear neural network verification
Rudy R Bunel, Ilker Turkaslan, Philip Torr, Pushmeet Kohli, and Pawan K Mudigonda · 2018
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Bi-criteria optimization of decision trees with applications to data analysis
Igor Chikalov, Shahid Hussain, and Mikhail Moshkov · 2018
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Deep neural networks and mixed integer linear optimization
Matteo Fischetti and Jason Jo · 2018
Later among the works it cites.
Bilevel programming for hyperparameter optimization and meta-learning
Luca Franceschi, Paolo Frasconi, Saverio Salzo, Riccardo Grazzi, and Massimilano Pontil · 2018
Later among the works it cites.
High dimensional data classification and feature selection using support vector machines
Bissan Ghaddar and Joe Naoum-Sawaya · 2018
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Optimal decision trees for categorical data via integer programming
Oktay Günlük, Jayant Kalagnanam, Matt Menickelly, and Katya Scheinberg · 2018
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K-beam subgradient descent for minimax optimization
Jihun Hamm and Yung-Kyun Noh · 2018
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Segmented concave least squares: A nonparametric piecewise linear regression
Abolfazl Keshvari · 2018
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Combinatorial attacks on binarized neural networks
Elias Boutros Khalil, Amrita Gupta, and Bistra Dilkina · 2018
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Automated verification of neural networks: Advances, challenges and perspectives
Francesco Leofante, Nina Narodytska, Luca Pulina, and Armando Tacchella · 2018
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Model-based capacitated clustering with posterior regularization
Feng Mai, Michael J. Fry, and Jeffrey W. Ohlmann · 2018
Later among the works it cites.
Bounding and counting linear regions of deep neural networks
Thiago Serra, Christian Tjandraatmadja, and Srikumar Ramalingam · 2018
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Understanding adversarial training: Increasing local stability of supervised models through robust optimization
Uri Shaham, Yutaro Yamada, and Sahand Negahban · 2018
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Big data analytics in supply chain management between 2010 and 2016: Insights to industries
Sunil Tiwari, H.M. Wee, and Yosef Daryanto · 2018
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Accelerating the branch-and-price algorithm using machine learning
Roman Václavík, Antonín Novák, Přemysl Šůcha, and Zdeněk Hanzálek · 2018
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Data poisoning attacks against online learning
Yizhen Wang and Kamalika Chaudhuri · 2018
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Optimization algorithms for data analysis
Stephen J Wright · 2018
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An overview of machine teaching
Xiaojin Zhu, Adish Singla, Sandra Zilles, and Anna N Rafferty · 2018
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Rank-one convexification for sparse regression
Alper Atamturk and Andres Gomez · 2019
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A comparative study of the leading machine learning techniques and two new optimization algorithms
Philipp Baumann, D. S. Hochbaum, and Y. T. Yang · 2019
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Robust classification
Dimitris Bertsimas, Jack Dunn, Colin Pawlowski, and Ying Daisy Zhuo · 2019
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Neural architecture search: A survey
Thomas Elsken, Jan Hendrik Metzen, and Frank Hutter · 2019
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Machine learning meets mathematical optimization to predict the optimal production of offshore wind parks
Martina Fischetti and Marco Fraccaro · 2019
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Learning MILP resolution outcomes before reaching time-limit
Martina Fischetti, Andrea Lodi, and Giulia Zarpellon · 2019
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Training binarized neural networks using MIP and CP
Rodrigo Toro Icarte, León Illanes, Margarita P Castro, Andre A Cire, Sheila A McIlraith, and J Christopher Beck · 2019
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Activation ensembles for deep neural networks
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Fisher-Rao metric, geometry, and complexity of neural networks
Tengyuan Liang, Tomaso Poggio, Alexander Rakhlin, and James Stokes · 2019
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A review on the self and dual interactions between machine learning and optimisation
Heda Song, Isaac Triguero, and Ender Özcan · 2019
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Mixed integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor
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Enhancing transportation systems via deep learning: A survey
Yuan Wang, Dongxiang Zhang, Ying Liu, Bo Dai, and Loo Hay Lee · 2019
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A survey on neural architecture search
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From predictive to prescriptive analytics
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Sparse high-dimensional regression: Exact scalable algorithms and phase transitions
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Sparsity in optimal randomized classification trees
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Deep learning in business analytics and operations research: models, applications and managerial implications
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