that isit is the maximum likelihood estimate of thb thn argmax th = ln gi (yi thunder the assumption that (thfor some parameter thwe have from theorem that the estimated in-sample generalization risk can be approximated as ln ( thn ex (thn rtn (thn ln = this leads to the heuristic of selecting the learner ( thn with the smallest value of the aicn ln gi (yi thn ( - = example (normal linear modelfor the normal linear model (xbs (see ( ))with -dimensional vector bwe have (yi > ) gi (yi bs exp |{ ps =th so that the aic is ky xb bk ln( pn ln qb ( where ( bb is the maximum likelihood estimate and + is the number of parameters (including for model comparison we may remove the ln( pterm if all the models are normal linear models certain software packages report the aic without the ln term in ( this may lead to sub-optimal model selection if normal models are compared with nonnormal ones categorical features suppose thatas described in the data is given in the form of spreadsheet or data frame with rows and columnswhere the first element of row is the response variable yi and the remaining elements form the vector of explanatory variables > when all the explanatory variables (featurespredictorsare quantitativethen the model matrix can be directly read off from the data frame as the matrix with rows > howeverwhen some explanatory variables are qualitative (categorical)such one-toone correspondence between data frame and model matrix no longer holds the solution is to include indicator or dummy variables