Information Gain

Definition

The Information Gain regarding evidence EE is the difference between the:

  • Log-Loss LLU(E)L{L_U}\left( E \right), given an unconnected network UU, i.e., a so-called straw model, in which all nodes are marginally independent;

  • Log-Loss LLB(E)L{L_B}\left( E \right) given a reference network BB.

IGB(E)=logโก2(P(e1,...,en)โˆi=1nP(ei))=LLU(E)โˆ’LLB(E)IG_B(E) = {\log _2}\left( {{{P({e_1},...,{e_n})} \over {\prod\limits_{i = 1}^n {P({e_i})} }}} \right) = L{L_U}(E) - L{L_B}(E)

In earlier versions of BayesiaLab, Information Gain was named Consistency.

Interpretation

The Log-Loss reflects the "cost" in bits of applying the network BB to evidence EE, i.e., the number of bits that are needed to encode evidence EE. The lower the probability of evidence EE, the higher the Log-Loss.

As a result, a positive value of Information Gain would reflect a "cost-saving" for encoding evidence EE by virtue of having network BB. In other words, encoding EE with network BB is less "costly" than encoding it with the straw model UU. Therefore, evidence EE would be consistent with network BB.

Conversely, a negative Information Gain indicates a so-called conflict, Log-Loss of evidence EE is higher with the straw model UU compared to the reference network BB. Note that conflicting evidence does not necessarily mean that the reference network is wrong. Rather, it probably indicates that such a set of evidence belongs to the tail of the distribution that is represented by the reference network BB.

However, if evidence EE is drawn from the original data on which the reference network BB was originally learned, the probability of observing conflicting evidence should be smaller than the probability of observing consistent evidence.

So, for a network model to be useful, there should generally be more sets of evidence with a positive Information Gain, i.e., consistent observations, than sets of evidence with a negative Information Gain, i.e., conflicting observations.

Therefore, the mean value of the Information Gain of a reference network BB compared to a straw model UU is a useful performance indicator of the reference network BB.

Related BayesiaLab Functions

  • Information Gain and Evidence Analysis

  • Network Performance

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