The paper discusses the application of Least Squares Support Vector Machines (LS-SVMs) and their comparison with Vapnik's Support Vector Machines (SVMs) in regression and classification tasks. It begins by introducing Vapnik's SVM Regression, which projects data into a higher-dimensional space to find a hyperplane that maximizes the margin and minimizes squared error. The paper then outlines the computational algorithms for LS-SVMs, including the Nyström method and incomplete Cholesky factorization, which are used to reduce computational complexity. Feature selection is also addressed, with a focus on using information gain to identify relevant features. The Bayesian approach to learning is introduced, where the weights of the regression function are estimated using penalized least-squares and maximum likelihood. The paper explains how Bayesian inference can be used to estimate parameters and make predictions, providing a probabilistic interpretation of the results. The relevance vectors, which are the non-zero components of the weight vector, are highlighted as a key feature of the Bayesian approach, offering a more efficient way to approximate functions compared to traditional SVMs. Finally, the paper presents experimental results using RVMs on two datasets: noisy 'sinc' data for regression and Ripley's synthetic data for classification. The results show that RVMs outperform traditional SVMs in both tasks, with fewer relevance vectors required to achieve better performance.The paper discusses the application of Least Squares Support Vector Machines (LS-SVMs) and their comparison with Vapnik's Support Vector Machines (SVMs) in regression and classification tasks. It begins by introducing Vapnik's SVM Regression, which projects data into a higher-dimensional space to find a hyperplane that maximizes the margin and minimizes squared error. The paper then outlines the computational algorithms for LS-SVMs, including the Nyström method and incomplete Cholesky factorization, which are used to reduce computational complexity. Feature selection is also addressed, with a focus on using information gain to identify relevant features. The Bayesian approach to learning is introduced, where the weights of the regression function are estimated using penalized least-squares and maximum likelihood. The paper explains how Bayesian inference can be used to estimate parameters and make predictions, providing a probabilistic interpretation of the results. The relevance vectors, which are the non-zero components of the weight vector, are highlighted as a key feature of the Bayesian approach, offering a more efficient way to approximate functions compared to traditional SVMs. Finally, the paper presents experimental results using RVMs on two datasets: noisy 'sinc' data for regression and Ripley's synthetic data for classification. The results show that RVMs outperform traditional SVMs in both tasks, with fewer relevance vectors required to achieve better performance.