Minimum Cross-Entropy (MinXEnt)

Context

• Using the Minimum Cross-Entropy (MinXEnt) algorithm, the Target Distribution, which produces the Target Mean/Value, is computed in such a way that the Cross-Entropy between the original probability distribution of the node and the Target Distribution is minimized.
• Like Value Shift, MinXEnt generates Soft Evidence.
  • This means that the Target Distribution they supply should be understood like posterior distribution given evidence set on a “hidden cause”, i.e. evidence on a variable not included in the model.
  • As such, using MinXEnt or Value Shift is suitable for creating evidence that represents changing levels of measures like customer satisfaction.
  • Unlike setting the price of a product, we cannot directly adjust the satisfaction of all customers to a specific level. This would imply setting an unrealistic distribution with low or no uncertainty.
  • More realistically, we would have to assume that higher satisfaction is the result of an enhanced product or better service, i.e. a cause from outside the model.
  • Thus, we need to generate the evidence for customer satisfaction as if it were produced by a hidden cause.
  • This also means that MinXEnt and Value Shift will produce a distribution close to the marginal one if the targeted Numerical Evidence is close to the marginal value.
• The Monitor below shows the distribution with a mean of −0.01 that is “closest” in terms of Cross-Entropy to the original, marginal distribution shown earlier.