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Normally, people use 'accuracy' to describe the output quality (from a model or methodology https://en.wikipedia.org/wiki/Precision_and_recall) for categorical data.

However, I am wondering could the concept of 'accuracy' extend to the numerical data? For example, if the real value is 5.0 while the (model) predicted value is 20.0, could we define the accuracy for this case?

If not, what's the best metrics to describe the quality of the model predicted outputs? Thanks!

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Accuracy in machine learning is typically used to refer to classification, where ware trying to predict categorical data. It implicitly refers to the 0-1 loss, where there is a penalty if the prediction is wrong (no matter by how much) and no penalty if the prediction is correct.

For numerical data, that rarely corresponds to something we'd care about. Instead, we typically care about how large the error in our prediction is. Thus, the 0-1 loss is too simplistic, and we should instead use a loss function that is well-suited to numerical data. For example, we might instead use the MSE loss, aka the squared error loss.

The difference is that prediction of a categorical variable is called a classification problem, while prediction of a numerical variable is called a regression problem. Different losses and metrics are applicable to the former vs the latter.

See also https://en.wikipedia.org/wiki/Accuracy_and_precision.

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