# What is a discrimination threshold of binary classifier?

With respect to ROC can anyone please tell me what the phrase "discrimination threshold of binary classifier system" means? I know what a binary classifier is.

## 2 Answers

Just to add a bit.

Like it was mentioned before, if you have a classifier (probabilistic) your output is a probability (a number between 0 and 1), ideally you want to say that everything larger than 0.5 is part of one class and anything less than 0.5 is the other class.

But if you are classifying cancer rates, you are deeply concerned with false negatives (telling some he does not have cancer, when he does) while a false positive (telling someone he does have cancer when he doesn't) is not as critical (IDK - being told you've cancer coudl be psychologically very costly). So you might artificially move that threshold from 0.5 to higher or lower values, to change the sensitivity of the model in general.

By doing this, you can generate the ROC plot for different thresholds.

• To add to this, this resource includes a visual demonstration of how an ROC curve is constructed by varying the thresholds (about 2/3 down the page): r-bloggers.com/roc-curves-and-classification Feb 4, 2015 at 17:21
• What if the binary classifier is not probabilistic? Jun 22, 2017 at 13:08

Classifiers often return probabilities of belonging to a class. For example in logistic regression the predicted values are the predicted probability of belonging to the non-reference class or $\text{Pr}(Y = 1)$. The discrimination threshold is just the cutoff imposed on the predicted probabilities for assigning observations to each class.