Description: Jensen’s inequality is a fundamental mathematical tool in the field of optimization and statistics. It is based on the theory of convexity and states that for a convex function, the value of the function at the mean of a set of points is less than or equal to the mean of the function values at those points. This property is crucial in training machine learning models, as it ensures that the solutions found during the optimization process are effective and robust. In the context of optimization algorithms, Jensen’s inequality is used to analyze and improve the convergence of methods, such as gradient descent. By applying this inequality, researchers can establish bounds on the expected performance of a model, facilitating the selection of appropriate hyperparameters and the evaluation of the quality of the solutions found. In summary, Jensen’s inequality not only provides a theoretical framework for understanding the behavior of functions in parameter spaces but also has practical applications in improving the efficiency and effectiveness of machine learning models.
