LM (Levenberg–Marquardt)

Information

• LM (Levenberg-Marquardt) is an optimization algorithm used in nonlinear least squares regression.
• LM is a modification of the Gauss-Newton algorithm, which is used to solve nonlinear least squares problems by iteratively minimizing the sum of squared residuals between the observed and predicted values.
• LM adds a damping parameter to the diagonal of the normal equations, which controls the step size and prevents large oscillations or overshoots in the parameter updates, especially when the Jacobian matrix is ill-conditioned or singular.
• LM can handle both over-determined and under-determined systems, where the number of observations is greater or less than the number of unknowns, by adding or removing constraints on the parameters, respectively.
• LM can also handle noisy or missing data, by using robust or weighted loss functions, or by imputing the missing values based on the known patterns or correlations in the data.
• LM has been widely used in various fields, such as engineering, physics, economics, and machine learning, to estimate the parameters of complex models and to perform feature selection, dimensionality reduction, and model comparison. However, its performance may depend on the choice of the initial parameters, the scaling of the variables, and the convergence criteria, which can affect the speed, accuracy, and stability of the algorithm.