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There used to be an earlier era of machine learning that wasn't as statistical. Ng, and most other current ML researchers, now heavily draw on mainstream statistics. It really does make sense to do logistic regression as the foundation for later stuff.

The terminology confusions, I think, stems from the earlier era of ML research.

What did the earlier era use?

In a case like this, perhaps a perceptron?

Which is Ng's class's next chapter after logistic regression. :-)

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