# Coupling of Loss Function & Evaluation Metrics With some problems we have a cost function that is nicely tied to a different final metric. Think about image classification accuracy and a cross entropy loss. Those are different but nicely coupled. Why? To start, notice that we must separate the model prediction and a DECISION being made. The decision being made requires, in this case, that we make a specific prediction of what single class the image represents. That means we want the true class ONLY to have high probability. Well, cross entropy is good for that! It specifically INCENTIVIZES large probability mass to be assigned to the true class! So it turns out that our model loss function is naturally, nicely coupled to our decision metrics (where our decision metric quantifies how well we used the information yielded via our model predictions. We must always use the information remember!). How is this different in our problem? How will we use the information? To start, image classification got LUCKY! That task requires learning something that really only requires the true label, which we OBSERVE. Our problem requires the true distribution, which we don’t observe. We only observe samples. In a sense image classification isn’t very stochastic. We KNOW there is only a single thing in the image. Really note that this is a clean, convenient coupling between model loss function and decision metric --- Date: 20230207 Links to: [Machine Learning MOC](Machine%20Learning%20MOC.md) Tags: References: * [machine learning - Proper scoring rule when there is a decision to make (e.g. spam vs ham email) - Cross Validated](https://stats.stackexchange.com/questions/464636/proper-scoring-rule-when-there-is-a-decision-to-make-e-g-spam-vs-ham-email?noredirect=1&lq=1)