Semanlink - Information theory

> We define the relevant information in a signal x ∈ X as being the information that this signal provides about another signal y ∈ Y. Examples include the information that face images provide about the names of the people portrayed, or the information that speech sounds provide about the words spoken. **Understanding the signal x requires more than just predicting y, it also requires specifying which features of X play a role in the prediction. We formalize this problem as that of finding a short code for X that preserves the maximum information about Y.** That is, we squeeze the information that X provides about Y through a ‘bottleneck’ formed by a limited set of codewords X ̃... This approach yields an exact set of self consistent equations for the coding rules X → X ̃ and X ̃ → Y .

(from the intro) : how to define "meaningful / relevant" information? An issue left out of information theory by Shannon (focus on the problem of transmitting information rather than judging its value to the recipient) ->leads to
consider statistical and information theoretic principles as almost irrelevant
for the question of meaning.

> In contrast, **we argue here that information theory,
in particular lossy source compression, provides a natural quantitative
approach to the question of “relevant information.”** Specifically, we formulate
a **variational principle** for the extraction or efficient representation of
relevant information.

2019-08-15 About

Deep InfoMax: Learning good representations through mutual information maximization - Microsoft Research

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