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We are given a big collection of strings, and an intensity associated with each string in the collection. In a sense, a 'distribution' on the dictionary. We are given that the intensity of each string is the sum of intensities of the features the string possesses, and that the collection of features that contribute significantly to the intensity is very small (order 100) compared to the size of the dictionary (order 100,000).

As a simple example, maybe the features that determine the intensity of a string are the presence of certain sub-strings.

  • having cat or dog as a sub-string might add value $a$
  • having atdo adds value $b$.

Then:

  • The strings cat and dog both have intensity $a$
  • The string catdog has intensity $2a+b$.

The problem is we don't know what the features that matter are. Given a distribution on a large dictionary, what techniques exist to automatically learn what features determine the intensity of string?

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