I like the example about the History exam, good one.
If someone fancies a more mathematical and in-deep explanation, I recommend the free online book neuralnetworksanddeeplearning.com and in particular chapter 6
Great examples! They made the point of overfitting really clear.
Does this make machine learning an unsolvable problem?
No. We can solve by reducing the model complexity, by gathering more data, by fixing bad data (outliers, missing values, etc).
The multiplication example makes so much sense, Manuel!
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