Many problem classes in machine learning are inherently high dimensional. Natural language processing problems, for instance, often involve the extraction of meaning from words, which can appear in an intractably large number of potential sequences in writing. Even if we limit ourselves to parsing only the 1000 most common words in texts, a short paragraph of 50 words will have 10150 possible permutations, which is more than the number of atoms of the observable universe. We are unlikely to make progress in such a setting without reframing the problem or reducing ...
8. Dimensionality Reduction
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