Tax evasion represents one of the main problems in modern economies because it results in a loss of State revenue. The aim of this project is to provide an estimate of the Italian VAT Tax Gap for the year 2011. Analysis is performed using a bottomup approach based on compliance controls and estimation is pursued via machine learning techniques. The observed data have been taken from two sources: the register of Irpef1, VAT and Irap2 declarations (available on all units, actual tax revenue due unknown) and the compliance control papers, performed only on a non-random sample of units ([1]) (assessed units, actual tax revenue due known). One of the main problems of this analysis is related to the non-randomness of the compliance controls, that induce a selection bias on the observed sample. The final target of the analysis is to get trustful estimates for the undeclared tax base of the unassessed units. However, our model will focus on the estimation of the potential tax base (BIT) and the undeclared part will be derived as a difference: BIND = BIT