This lab focuses on the implementation of the Support Vector Machine (SVM) in AMPL, exploring both its primal and dual quadratic formulations.
Support Vector Machines are powerful supervised learning models used for classification. They can be formulated as quadratic optimization problems:
- Primal formulation: Direct optimization over the separating hyperplane parameters with margin maximization and slack variables for soft margins.
- Dual formulation: Optimization expressed in terms of Lagrange multipliers, allowing the use of kernel functions and efficient solutions for high-dimensional data.
In this lab, both formulations are implemented in AMPL, providing hands-on experience with mathematical programming techniques for machine learning.
- Understand the mathematical foundations of SVMs as quadratic programming problems.
- Implement the primal and dual SVM formulations in AMPL.
- Compare the two formulations in terms of constraints, variables, and computational aspects.
- Gain familiarity with optimization modelling for machine learning tasks.
- Support Vector Machines (SVM)
- Primal and Dual Formulations
- Quadratic Programming
- AMPL
- Optimization in Machine Learning