Why is the threshold t added and how does it improve the model？
I wanted to account for misclassification costs in the model, since in the reality of the upsell business there is a disproportionate cost associated with making a false positive versus a false negative error. In general there are two approaches I could have taken, the first being a cost-sensitive approach such as rebalancing the data by class weighting, under-sampling, or over-sampling techniques. In this case, observations from the less costly class are given higher importance during training. However, I chose a cost-insensitive approach by adding a threshold. In this case, probability estimates, outputted by the classifier that learned from the training set as given, are used to obtain a probability cut-off (the mentioned threshold t) in order to compute cost-optimal decisions. I favored this approach because I did not want to modify the dataset as there was already not a very large data sample. Implementing an optimized threshold in the model will minimize misclassification costs. Therefore, although the accuracy of the model will be reduced, the business loss of the upsell process will be minimized, and therefore the upsell process will be more profitable if the model with the added threshold is used.
