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I often read the Matthews correlation coefficient is one of the most generally used validity estimates of confusion matrices in machine learning.

However, I couldn't find a reference which states what a good value of this coefficient should be. What is the status on that issue?

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Well, the value should certainly be bigger than 0.

Are you comparing your predictor to some existing predictors? Then you want your MCC to be bigger than those predictors' MCCs.

But possibly you have no other predictors to compare against, and you want to know when you can tell your boss/thesis adviser that you have reached a milestone.

If you work in industry you should always attempt to calculate the "business value" of your predictions, in terms of time or money saved, or revenue generated or whatever. It may not be the case that said value is a function of the MCC i.e. there are different $(TP, TN, FP, FN)$ tuples which give the same MCC but different values of "business value", but you may be able to establish target ranges. For example, "An MCC of 0.8 will save us between $100 and $120 per month".

If you are working in an academic context then your adviser should be able to help you out. Make sure you do some background research into attempts by other people first!

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