Session Detail Information
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Cluster :  Optimization/Integer and Discrete Optimization

Session Information  : Tuesday Nov 03, 11:00 - 12:30

Title:  Machine Learning under a Modern Optimization Lens
Chair: Dimitris Bertsimas,Professor, MIT, 77 Massachusetts Ave., Cambridge MA 02139, United States of America, dbertsim@mit.edu

Abstract Details

Title: Sparse Principal Component Analysis via a Modern Optimization Lens
 Presenting Author: Lauren Berk,Massachusetts Institute of Technology, 77 Massachusetts Avenue, Bldg. E40-149, Cambridge MA 02139, United States of America, lberk@mit.edu
 Co-Author: Dimitris Bertsimas,Professor, MIT, 77 Massachusetts Ave., Cambridge MA 02139, United States of America, dbertsim@mit.edu
 
Abstract: We develop tractable algorithms that provide provably optimal solutions to the exact Sparse Principal Component problems of up to 1000 dimensions, using techniques from Mixed Integer Optimization and first order methods. Unlike earlier SPCA methods, our approach retains complete control over the degree of sparsity of the components, and provides solutions with higher explained variance.
  
Title: Robust Support Vector Machines
 Presenting Author: Colin Pawlowski,MIT, 77 Massachusetts Ave., Cambridge MA 02139, United States of America, cpawlows@mit.edu
 Co-Author: Dimitris Bertsimas,Professor, MIT, 77 Massachusetts Ave., Cambridge MA 02139, United States of America, dbertsim@mit.edu
 
Abstract: We consider a maximal-margin classifier which is the non-regularized formulation of SVM. Using Robust Optimization, we develop new, computationally tractable methods that are immunized against uncertainty in the features and labels of the training data. Experiments on real-world datasets from the UCI Machine Learning Repository show out-of-sample accuracy improvements for robust methods in a significant number of problems analyzed.
  
Title: Optimal Trees
 Presenting Author: Jack Dunn,Operations Research Center, MIT, 77 Mass Ave, Bldg E40-130, Cambridge MA 02139, United States of America, jackdunn@mit.edu
 Co-Author: Dimitris Bertsimas,Professor, MIT, 77 Massachusetts Ave., Cambridge MA 02139, United States of America, dbertsim@mit.edu
 
Abstract: Decision trees are widely used to solve the classical statistical problem of classification. We introduce a new method for constructing optimal decision trees using Mixed-Integer Optimization, and show using real data sets that these trees can offer significant increases in accuracy over current state-of-the-art decision tree methods. We also demonstrate the benefits of using Robust Optimization when constructing these trees.
  
Title: Logistic Regression using Robust Optimization
 Presenting Author: Daisy Zhuo,Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139, United States of America, zhuo@mit.edu
 Co-Author: Dimitris Bertsimas,Professor, MIT, 77 Massachusetts Ave., Cambridge MA 02139, United States of America, dbertsim@mit.edu
 
Abstract: Logistic regression is one of the most commonly used classification methods, yet the solution can be sensitive to inaccuracy and noise in data. Here we propose an approach using Robust Optimization to find stable solutions under uncertainties in data features and labels. Using more than 80 real-world problems, we demonstrate that the robust logistic regressions lower misclassification error significantly in the majority of the data sets.