Types of inference in Bayes network

Types of inference in Bayes network in Artificial Intelligence

PATTERNS OF INFERENCE IN BAYES NETWORK

There are mainly three types of inference in Bayes network.
Inorder to explain the patterns of inference let us consider an example Bayes network. The network is shown in the Fig. 3.5.1.

Fig 3.5.1: A Bayes Network

In the above Figure. 3.5.1 M is the movement of arm, L is the term, which represents a block is liftable, B represents battery and G represents gauge which indicates when battery if full. Now we explain the three patterns of inference.

Causal or Top-down Inference:

Let us calculate P(M | L) that is the probability that the arm moves given that black is liftable.

The arm can only be moved by the cause the block is liftable this calculation is an example of causal reasoning.
P(M | L), L is called the evidence and M is called as query node, as the question is about the probability of M.
Next chain rule is used. to condition M on the Other parent B and also L.

P(M | L) = P(M | B, L) P(B | L) + P(M | ᆨB, L) P(ᆨB | L). As B has no parents
P(B | L)= P(B), in the same way P(ᆨB | L) = P(ᆨB).
⇒ P(M | L) = P(M | B, L) P(B) + P(M | ᆨB, L) P(ᆨB)

from the above Figure, 3.5.1 these values are substituted,

P(M | L) = 0.9 X 0.5 + 0 X 0.5 = 0.45
∴ P(M | L) = 0.45

The operations that are performed are.

Rewriting the given condition probability of the query node Q in the form of joint probability of Q if evidence is given and the parents which are not evidence given the evidence.
This point probability is expressed in the form of probability of Q which is conditioned on all of its parents.

Diagnostic or Bottom-up Inference

Let us calculate that the block cannot be lifted if it is given that the arm can't move. i.e. P(ᆨL | ᆨM).
Here an effect is used to infer a cause, so this is called diagnostic reasoning.

$P(\neg L|\neg M){\rm{ = }}\frac{{{\rm{P(}}\neg M|\neg L)P(\neg )}}{{P(\neg M)}}(\therefore {\rm{ Bayes rules}})$

Now this can be converted into casual relationship like P(ᆨM | ᆨL) and the value can be used to find the P(ᆨL | ᆨM) as 0.63934.

Explaining Away

If there is another evidence say ᆨB that the battery is not charged.
Then this evidence explains, ᆨM, making ᆨL less certain.
This inference uses bottom up reasoning in which top-down reasoning may be used.
According to Bayes rule,

$P(\neg L|\neg B,\neg M){\rm{ = }}\frac{{P(\neg M,\neg B|\neg L)P(\neg L)}}{{P(\neg B,\neg M)}}$

From the definition of conditional probability it implies.

$\frac{{P(\neg M,\neg B|\neg L)P(\neg L)}}{{P(\neg B,\neg M)}}{\rm{ = }}\frac{{P(\neg M,\neg B|\neg L)P(\neg B|\neg L)P(\neg L)}}{{P(\neg B,\neg M)}}$

As B has no parents P(ᆨB | ᆨL) =P(ᆨB)

$\therefore P(L,\neg B|{\rm{ }}\neg B,M) = \frac{{P(\neg M,\neg B|\neg L)P(\neg B|\neg L)P(\neg L)}}{{P(\neg B,\neg M)}} = \frac{{1X0.5X0.5}}{{P(\neg B,\neg M)}}$