Random Forests (RF) is a popular machine learning method for classification and regression problems. It involves a bagging application to decision tree models. One of the primary advantages of the Random Forests model is the reduction in the variance of the forecast. In large scale applications of the model with millions of data points and hundreds of features, the size of the fitted objects can get very large and reach the limits on the available space in production setups, depending on the number and depth of the trees. This could be especially challenging when trained models need to be downloaded on-demand to small devices with limited memory. There is a need to approximate the trained RF models to significantly reduce the model size without losing too much of prediction accuracy. In this project we study methods that approximate each fitted tree in the Random Forests model using the multinomial allocation of the data points to the leafs. Specifically, we begin by studying whether fitting a multinomial logistic regression (and subsequently, a generalized additive model (GAM) extension) to the output of each tree helps reduce the size while preserving the prediction quality.