Maximum Likelihood (ML) and Maximum A Posteriori (MAP) Criteria

Maximum Likelihood (ML) and Maximum A Posteriori (MAP) criteria are two fundamental methods commonly used in machine learning. The Maximum Likelihood criterion serves as a parameter estimation approach that assumes observed data were generated under known parameter conditions, utilizing this data to select parameters that best fit the observations. In MATLAB implementation, this typically involves optimizing likelihood functions using functions like fmincon or mle, where the algorithm maximizes the joint probability of observed data given model parameters.

The Maximum A Posteriori criterion integrates prior knowledge with sample data to estimate parameters, making it particularly effective for handling small or incomplete datasets. In MATLAB simulations, MAP estimation can be implemented by combining likelihood functions with prior distributions through Bayesian inference, often using probability distribution objects from the Statistics and Machine Learning Toolbox. Both criteria are frequently applied in machine learning for model selection and parameter optimization tasks. Conducting MATLAB simulations with these methods helps researchers better understand and master these concepts through practical implementation, including visualization of convergence behavior and comparison of estimation accuracy under different data conditions.