Mixed-integer linear programming robust regression with feature selection

We introduce a Mixed-Integer Linear Programming approach for building Regression models. These models can detect potential outliers and have a built-in Feature Selection technique. We demonstrate how to build a linear regression model as well as a multidimensional piece-wise linear regression model that can simulate non-linear models. We compare our techniques with the existing statistical approaches for building regression models with different feature selection algorithms by comparing the results of predictions for 3 real-world data sets. All experiments show that our approach is useful in case where the number of training instances is less than the number of predictors, more stable and provides better results than Stepwise regression, which is the most used linear regression technique in cases when we deal with too many features in the model while having fewer observations.