Bayesian networks

These are also called Belief Networks or Probabilistic Inference Networks. Initially developed by Pearl (1988).
The basic idea is:

• Knowledge in the world is modular -- most events are conditionally independent of most other events.
• Adopt a model that can use a more local representation to allow interactions between events that only affect each other.
• Some events may only be unidirectional others may be bidirectional -- make a distinction between these in model.
• Events may be causal and thus get chained together in a network.

Implementation

• A Bayesian Network is a directed acyclic graph:
  • A graph where the directions are links which indicate dependencies that exist between nodes.
  • Nodes represent propositions about events or events themselves.
  • Conditional probabilities quantify the strength of dependencies.

Consider the following example:

• The probability,  that my car won't start.
• If my car won't start then it is likely that
  • The battery is flat or
  • The staring motor is broken.

In order to decide whether to fix the car myself or send it to the garage I make the following decision:

• If the headlights do not work then the battery is likely to be flat so i fix it myself.
• If the starting motor is defective then send car to garage.
• If battery and starting motor both gone send car to garage.

The network to represent this is as follows:

Fig. 21 A simple Bayesian network

Reasoning in Bayesian nets

• Probabilities in links obey standard conditional probability axioms.
• Therefore follow links in reaching hypothesis and update beliefs accordingly.
• A few broad classes of algorithms have bee used to help with this:
  • Pearls's message passing method.
  • Clique triangulation.
  • Stochastic methods.
  • Basically they all take advantage of clusters in the network and use their limits on the influence to constrain the search through net.
  • They also ensure that probabilities are updated correctly.
• Since information is local information can be readily added and deleted with minimum effect on the whole network. ONLY affected nodes need updating.