Estimation of linear model hyperparameters for noise or correlated feature selection problem

The problem of feature selection in linear regression models has been solved. To select the features, the authors estimate the covariance matrix of the model parameters. Dependent variable and model parameters are assumed to be normally distributed vectors. Laplace approximation is used for estimation of the covariance matrix: logarithm of the error function is approximated by the normal distribution function. The problem of noise or correlated features is also examined, since in this case, the covariance matrix of the model parameters becomes singular. An algorithm for feature selection is suggested. The results of the study for a time series are given in the computational experiment.