Contents
Why are the number of parameters in the Bayesian network 12 instead of 8?
Therefore, the independence assumptions in the Bayesian network helps us avoid specifying the joint distribution. What I cannot understand is why in the final calculation the number of parameters to define interview table is 12 instead of 8?
How are Bayesian networks used in decision making?
Bayesian Networks help us in decision making and simplify complex problems encoding various independencies. As we read that Joint Distribution is not capable to give us an inference which is interpretable. Furthermore, Bayesian Networks (Acyclic Graphs) provide a basis for Restricted Boltzmann Machines.
What is conditional parameterization in the real world?
This process is known as Conditional Parameterization. (But it does not reduce the number of parameters!) In the real world scenario, we make certain assumptions regarding the random variables involved in the joint distribution, whether or not they are dependent on each other or not.
How is the graphical representation of a probabilistic network?
The graphical representation is as follows: In this case, we did a very naive assumption that all random variables are independent of each other, which highly simplifies the chain rule notation to represent the model.
How many parameters are needed for the offer table?
Similarly, the Offer table has six entries, but only 1 independent parameter per row is required, which makes 3 (1 x 3) independent parameters. Therefore, the total number of parameters is 1 (Experience) + 1 (Grades)+ 12 (Interview) + 3 (Offer) amount to 17, which is a lot lesser than 24 parameters to fully specify the joint distribution.
How many parameters are in a conditional probability table?
Let’s go through each conditional probability table, one parameter at a time. Experience and Grades take two values, and therefore need one independent parameter each. The Interview table has 12 (3 x 4) parameters. However, each row sums up to 1, and therefore, we need two independent parameters per row.
How many parameters are needed for the interview table?
Experience and Grades take two values, and therefore need one independent parameter each. The Interview table has 12 (3 x 4) parameters. However, each row sums up to 1, and therefore, we need two independent parameters per row. The whole table needs 8 (2 x 4) independent parameters.