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Just came across this transcript that states:

The principle is that prediction is the same thing as compression. And what that means is that whenever you have a prediction algorithm, you can also get a correspondingly good compression algorithm for data you already have, and vice versa.

Even though the article gives some examples, I would like to know some answers from this community on the question: Is Prediction the same as Compression?

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Fundamentally, yes. Prediction can be used to compress, and compression is a form of prediction. More generally, any learned pattern can be used to compress and vice versa.

This rabbit hole goes a lot deeper, for example I'd suggest A Tutorial Introduction to the Minimum Description Length Principle as a thorough introduction into trying to learn and choose models using compression.

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Prediction is a very useful part of compression.

Given a sequence of unrelated integers, you can check how they are distributed and compress them say using Hufmann or arithmetic coding.

If the integers are related, you predict their values as good as you can, calculate the prediction errors, and compress the prediction errors; the errors should be smaller numbers than the original ones and therefore compress to a smaller size.

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