Bayesian Networks: a probability rather than just a possibility

They are transparent and white-box in nature. They don’t just solve complex problems, but they also help diagnose how the problem was solved or how the problem itself arose. This is of great value for things such as audits and to better understand businesses and their associated problems. Enters Bayesian Networks (BNs).

A BN is a Probabilistic Graphical Model (PGM) that uses probability (Bayesian statistics) and graph theory for knowledge representation and inferencing.

BNs comprises two parts:

1. Qualitative part – this part is mainly driven by the graph theory that represents the links and (in)dependencies of variables of interest for a problem.
2. Quantitative part – this part deals with the conditional probabilities among the variables of interest.

Figure 1 is an example of how a BN is trying to predict the capital adequacy of an entity. The capital adequacy is an important component to work out the creditability of an entity if they want to be granted credit. Capital adequacy is directly dependant on Total Capital Ratio, Capital at Risk, Judgement (acquired from an analyst), Tier 1Capital Ratio, and Total Assets of an entity.

The yellow ovals (nodes) are the variables of interest and the directed arcs denote the direct dependencies among the nodes. For the model in Figure 1 to be able to do inferencing, the conditional probabilities among the nodes must be defined. Thereafter the model can proceed to explain away.

Bayesian Network applications

Bayesian networks have been most promising in the use of Artificial Intelligence (AI) in games. Under uncertain conditions a BN calculates the probability of a certain variable, which may be the wrong decision, but as more information is uncovered about the world, the network is able to refine

the probabilities of other variables. This subsequently causes the calculated variables to be refined and updated to produce refining and an evolving AI.

There are games that use BNs as a way of intelligently making decisions and controlling and altering behaviours. A prime example is Microsoft’s Forza Motorsport, which uses what they call Drivatars [1]. These Drivatars use BN inference to allow the computer driven cars to monitor and mimic the driving style of a human being.

Solves uncertainties

Typically, BNs will do well with problems that involve uncertainty and incompleteness, such as computer/software virus detection, medical diagnostic systems, decision support systems and credit risk scoring systems.

The power in BNs essentially lie in the mathematical theorem they are based on. Bayesian Networks are based on a mathematical theory known as Bayes’ Theorem, which is used to calculate the probability of an event occurring given a known piece of information. Using this theorem, we can compute the statistical probability of events transpiring if we know very little about the world, which provides some information for reasoning under uncertainty” [2].

Conclusion

The Bayesian network keeps the network “informed” so to speak. If there is a change to one variable in the network it will propagate via its connections to all the relevant parts of the network. This means you can make fewer assumptions when modelling and can therefore better represent and subsequently better solve your problem.

Since the main focus of the network is to look at interdependencies among the variables, adding extra variables as time goes by is less problematic.

This tool really solves quite a few of our complex problems that we face on a daily basis and it warrants a wider use in business.

References

 by Mthokozisi Myeza