Need of Probabilistic Reasoning in AI
- Unpredictable outcomes
- Predicates are too large to handle
- Unknown error occurs
In probabilistic reasoning, there are two methods to solve difficulties with uncertain knowledge
- Bayes’ rule
- Bayesian Statistics
- Probability: Probability can be defined as chance of occurrence of an uncertain event. It is the numerical measure of the likelihood that an event will occur. The value of probability always remains between 0 and 1.
0 ≤ P(X) ≤ 1, where P(X) is the probability of an event X.
- P(X) = 0, indicates total uncertainty in an event X.
- P(X) =1, indicates total certainty in an event X
Bayesian Belief Network
Bayesian Network can be used for building models from data and experts opinions, and it consists of two parts:
- Directed Acyclic Graph
- Table of conditional probabilities
The generalized form of Bayesian network that represents and solve decision problems under uncertain knowledge is known as an Influence diagram. Note: It is used to represent conditional dependencies.
A Bayesian network graph is made up of nodes and Arcs (directed links), where:
- Each node corresponds to the random variables, and a variable can be continuous or discrete.
- Arc or directed arrows represent the causal relationship or conditional probabilities between random variables. These directed links or arrows connect the pair of nodes in the graph. These links represent that one node directly influence the other node, and if there is no directed link that means that nodes are independent with each other
- The Bayesian network has mainly two components:
- Causal Component
- Actual numbers
- Each node in the Bayesian network has condition probability distribution P(Xi |Parent(Xi ) ), which determines the effect of the parent on that node.
- Bayesian network is based on Joint probability distribution and conditional probability.