I deal with the binary classification problem of predicting if a sample is positive or negative. For me it is important to view false positives. Therefore I would allow to have less true positives. So, the question is not about improving the overall performance of the classifier, but to give more weight to false positives and be able to set a parameter for the tradeoff.
I see two options to obtain this:
Train a classifier that can output a probability for each sample. Then on the prediction of a separate training set, I'd tune a threshold that provides the required false positive rate. This learned threshold is then used to classify the test set.
Train the classifier with different loss for positives and negatives. No tuning required.
Are there other options, that I should consider? With with should I go?