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Mathematical optimization in classification and regression trees.

Emilio Carrizosa1, Cristina Molero-Río1, Dolores Romero Morales2

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Summary
This summary is machine-generated.

This paper reviews optimization methods for classification and regression trees, enhancing their flexibility. Novel formulations improve handling of cost-sensitivity, explainability, fairness, and complex data.

Keywords:
Classification and regression treesContinuous nonlinear optimizationExplainabilityMixed-integer linear optimizationSparsityTree ensembles

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Area of Science:

  • Machine Learning
  • Continuous Optimization
  • Mixed-Integer Linear Optimization

Background:

  • Classification and regression trees are standard Machine Learning tools.
  • Existing methods have limitations in flexibility and incorporating advanced properties.

Purpose of the Study:

  • To review recent advancements in optimization for tree-based models.
  • To explore novel formulations using Continuous and Mixed-Integer Linear Optimization.
  • To enhance the flexibility and applicability of tree models.

Main Methods:

  • Review of recent contributions in Continuous Optimization.
  • Review of recent contributions in Mixed-Integer Linear Optimization.
  • Comparison of formulations based on decision variables, constraints, and algorithms.

Main Results:

  • Novel optimization formulations offer enhanced flexibility for tree models.
  • These formulations facilitate incorporation of cost-sensitivity, explainability, and fairness.
  • The methods are effective for handling complex data types, including functional data.

Conclusions:

  • Optimization paradigms provide powerful tools for advancing tree-based Machine Learning.
  • New formulations significantly improve the capabilities of classification and regression trees.
  • This research opens avenues for more sophisticated and interpretable tree models.