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Water Hose and Balloon Metaphor

In order to provide some intuition for the Arc Force and Node Force computed by BayesiaLab, we will use the water hose and balloon metaphor:

Imagine that we have a Bayesian network in which the variables are balloons and the arcs are perforated water hoses. The size of the holes in the hose represents the uncertainty of contained in conditional probability table associated with the child node.

  • For a deterministic relationship (i.e. we know with certainty the state of one variable given the state of the other one), there are no holes at all in the hose, and therefore, no water is lost between these two nodes. 
  • Conversely, for an entirely uncertain relationship where information on one variable does not yield any information regarding the other one (this “relation” cannot be machine learned as there is no correlation in the dataset), the size of the holes would be such that no water coming from one node would reach the other one.

Now, let’s suppose we are sending a constant flow of water into the system. The thickness of a hose will be inversely proportional to the size of its hole, and the pressure in a balloon, and therefore it size, will be directly dependent on the number of connected hoses and the size of their holes.

The BayesiaLab's mapping based on node and arc forces allows then to quickly see what are the most important variables, even in high dimensional spaces (here Country, Age and Gender)