Example of Parameter Optimization for Least Squares Support Vector Machine Using Bayesian Inference

This article demonstrates how to implement Bayesian inference in MATLAB to optimize parameters for Least Squares Support Vector Machines (LS-SVM). Bayesian inference is a widely adopted statistical methodology that estimates unknown parameters based on observed data. The MATLAB implementation typically involves constructing probabilistic models for hyperparameters (such as regularization and kernel parameters) and using evidence approximation techniques to maximize marginal likelihood. Through Bayesian inference, we can achieve faster convergence to optimal SVM parameters compared to traditional grid search methods. The implementation often utilizes MATLAB's optimization toolbox and probability distribution functions to compute posterior distributions efficiently. Additionally, we will explain the fundamental principles of support vector machines and their practical applications, including kernel function selection (RBF, polynomial) and the mathematical formulation of LS-SVM's linear system solution. This article will provide practical MATLAB code snippets demonstrating key steps: data preprocessing, evidence maximization using fmincon or Bayesian optimization functions, and parameter validation through cross-validation. By studying this material, readers will gain comprehensive understanding of implementing Bayesian inference and parameter optimization for support vector machines in MATLAB environments.