Inference in bayes nets

Question 1

What is inference in bayes nets?

Answer 1

• It is answering probabilistic questions using bayes questions
• The answer is a complete joint probability distribution (Posterior distribution) over the query variables.
• Answer P(Q1, Q2, …| E1, E2)
• Answer argmax(q) P(Q1=q1, Q2=q2…|E1=e1…)

Question 2

What in inference of bayes nets what are evidence, query and hidden variables?

Answer 2

• Evidence: Variables we know the value of.
• Query: Variables we want to find the values of
• Hidden: Variables that are neither evidence or query

Question 3

What is in inference Enumeration?

Answer 3

• Finds all possibilities, adds them up and comes up with an answer
  1) We take a conditional probability and turn it into unconditional probability
  2) Enumerate all atomic probabilities and calculate the sum of products. Example: sumsum P(+b,+j,+m,e,a)
  3) Turn the sum into the terms of the probability distribution. Example: sumsum P(+b)P(e)P(a|+b,e)P(+j,a)P(+m|a)

Question 4

How to speed up enumeration?

Answer 4

• Pull out terms that are constant in the sum:
  p(+b) sum (a) p(a). This reduces the cost of doing each row in the table
• Max independence

Question 5

Causal direction

Answer 5

• The bayes network is more compact and easier to infer something when it follows the causal direction

Question 6

Variable elimination

Answer 6

• It is another method for computing a bayes net.
• In practice it is faster than enumeration. But it is NP-hars
• It is about combining parts of the net into smaller parts and then use enumeration and then combine again.
  1) Joining factor: A factor is one of the tables of one of the probabilities. Choose two factors and form a new factor with the joint probability of the variables.
  2) Eliminatation: the new factor and reduce it buy summing out variables

Question 7

Approximate Inference Sampling

Answer 7

• Run experiments, record the results and estimate the probabilities based on the results
• It can calculate the full probability distribution
• To calculate a conditional probability use rejection sampling, that means to use only samples that work with the probability

Question 8

likelihood weighting

Answer 8

Way to produce only samples that work