Data Science Algorithms

Optimal counterfactual explanations for k-Nearest Neighbors using Mathematical Optimization and Constraint Programming

  • Thibaut Vidal
  • Ricardo Fukasawa
  • Louis-Martin Rousseau
  • Claudio Contardo
    • Categories Applications - Science and Engineering, Data Science Algorithms Tags , , , ,

    Within the topic of explainable AI, counterfactual explanations to classifiers have received significant recent attention. We study counterfactual explanations that try to explain why a data point received an undesirable classification by providing the closest data point that would have received a desirable one. Within the context of one the simplest and most popular classification … Read more

    An Integer Programming Approach To Subspace Clustering With Missing Data

  • Akhilesh Soni
  • Jeff Linderoth
  • James R. Luedtke
  • Daniel Pimentel-Alarcon
    • Categories Data Science Algorithms, Integer Programming Tags , ,

    In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD is to cluster the vectors according to their subspace membership and recover the underlying basis, which can … Read more

    Conjecturing-Based Discovery of Patterns in Data

  • J. Paul Brooks
  • David Edwards
  • C. E. Larson
  • Nico Van Cleemput
    • Categories Applications - OR and Management Sciences, Data Science Algorithms, Optimization in Data Science Tags , , , ,

    We propose the use of a conjecturing machine that suggests feature relationships in the form of bounds involving nonlinear terms for numerical features and boolean expressions for categorical features. The proposed Conjecturing framework recovers known nonlinear and boolean relationships among features from data. In both settings, true underlying relationships are revealed. We then compare the … Read more

    Learning the Follower’s Objective Function in Sequential Bilevel Games

  • Ioana Molan
  • Martin Schmidt
  • Johannes Thürauf
    • Categories Data Science Algorithms, Other Topics

    We consider bilevel optimization problems in which the leader has no or only partial knowledge about the objective function of the follower. The studied setting is a sequential one in which the bilevel game is played repeatedly. This allows the leader to learn the objective function of the follower over time. We focus on two … Read more

    Stability-Adjusted Cross-Validation for Sparse Linear Regression

  • Ryan Cory-Wright
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms

    Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To select the sparsity and robustness of linear regressors, techniques like k-fold cross-validation are commonly used for hyperparameter tuning. However, cross-validation substantially increases the … Read more

    The Online Shortest Path Problem: Learning Travel Times Using A Multi-Armed Bandit Framework

  • Tomas Lagos
  • Ramon Auad
  • Felipe Lagos
    • Categories Applications - OR and Management Sciences, Data Science Algorithms, Transportation Tags , , , , ,

    In the age of e-commerce, many logistic companies must operate in large road networks without accurate knowledge of travel times for their specific fleet of vehicles. Moreover, millions of dollars are spent on routing services that do not accurately capture the specific characteristics of the companies’ drivers and the types of vehicles they must use. … Read more

    Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

  • Martin Schmidt
  • Jan Pablo Burgard
  • Maria Eduarda Pinheiro
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Data Science Applications Tags , , ,

    Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more

    Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training

  • Serge Gratton
  • Alena Kopanicakova
  • Philippe L. Toint
    • Categories Data Science Algorithms, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , ,

    A class of multi-level algorithms for unconstrained nonlinear optimization is presented which does not require the evaluation of the objective function. The class contains the momentum-less AdaGrad method as a particular (single-level) instance. The choice of avoiding the evaluation of the objective function is intended to make the algorithms of the class less sensitive to … Read more

    A classification method based on a cloud of spheres

  • Tiago Dias
  • Paula Alexandra Amaral
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Quadratic Programming Tags , , ,

    In this article we propose a binary classification model to distinguish a specific class that corresponds to a characteristic that we intend to identify (fraud, spam, disease). The classification model is based on a cloud of spheres that circumscribes the points of the class to be identified. It is intended to build a model based … Read more