I think mine is the Metropolis algorithm. Mostly because that first time you realize you can make the denominator disappear is a magical moment.
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As a purely pedagogical device (to illustrate overfitting, role of loss functions, deficiencies in probability-free ML, importance that managers give to interpretability etc.), CART.
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Oh yea. TBH I still reach for it pretty often during initial analysis for anything with at least three or four dimensions...
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Binary search? Probably the only algorithm I implement IRL ever.
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After that study about binary search algos in the wild, I assume I've never done this correctly.
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