A training set is what you use to provide an Machine Learning algorhythm to get to the expected goal. A great example, it would be to use a set of 10 million images of dogs and cats, until you think it can recognize and tell apart dogs from cats nearly flawlessly, or at least, with enough accuracy to be not stupid, and put “dog” on a lion, and “cat” on a great dane.
An external test set is what you use to test if it’s actually there. It’s a set of images that is taken from a logical environment to debug if your machine learned right. That set may include very feline-looking dogs, and very canine-looking cats, along with images with definitely neither, to know how it deals with cases like that.
I assume you are talking about machine learning.
A training set is the set of data you use to train a machine learning algorithm – think of it as studying for a test by using old tests. A test set is what you use to confirm that the algorithm has learned to apply to real situations rather than just overfitting to the test set – to continue the test analogy, the real test has to be different from the old tests you use to study, so that you actually have to learn the material rather than just memorize the answer.
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