best subset selection

Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications

  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Dabeen Lee
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , , , , ,

    We consider a general conic mixed-binary set where each homogeneous conic constraint involves an affine function of independent continuous variables and an epigraph variable associated with a nonnegative function, $f_j$, of common binary variables. Sets of this form naturally arise as substructures in a number of applications including mean-risk optimization, chance-constrained problems, portfolio optimization, lot-sizing … Read more

    An Alternating Method for Cardinality-Constrained Optimization: A Computational Study for the Best Subset Selection and Sparse Portfolio Problems

  • Carina Moreira Costa
  • Dennis Kreber
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Statistics Tags , , , ,

    Cardinality-constrained optimization problems are notoriously hard to solve both in theory and practice. However, as famous examples such as the sparse portfolio optimization and best subset selection problems show, this class is extremely important in real-world applications. In this paper, we apply a penalty alternating direction method to these problems. The key idea is to … Read more

    A mixed-integer optimization approach to an exhaustive cross-validated model selection for regression

  • Dennis Kreber
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , , ,

    We consider a linear regression model for which we assume that many of the observed regressors are irrelevant for the prediction. To avoid overfitting, we conduct a variable selection and only include the true predictors for the least square fitting. The best subset selection gained much interest in recent years for addressing this objective. For … Read more

    Rank-one Convexification for Sparse Regression

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming, Statistics Tags , , , , ,

    Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an L0 constraint restricting the support of the estimators is a challenging non-convex optimization problem. In this paper, we derive new strong convex relaxations for sparse regression. These relaxations are based … Read more

    Best subset selection of factors affecting influenza spread using bi-objective optimization

  • Aigerim Bogyrbayeva
  • Hadi Charkhgard
  • Walter Silva
  • Shalome Hanisha Anand Tatapudi
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    A typical approach for computing an optimal strategy for non-pharmaceutical interventions during an influenza outbreak is based on statistical ANOVA. In this study, for the first time, we propose to use bi-objective mixed integer linear programming. Our approach employs an existing agent-based simulation model and statistical design of experiments presented in Martinez and Das (2014) … Read more

    Best subset selection via bi-objective mixed integer linear programming

  • Hadi Charkhgard
  • Ali Eshragh
    • Categories Multi-Criteria Optimization, Statistics Tags , ,

    We study the problem of choosing the best subset of p features in linear regression given n observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem either by combining the two objectives using … Read more