bayes

Question 1

name 3 problems with Bayesion / belief networks:

Answer 1

• The construction of the network is done manually
• The estimations of probability is not always easy without the data
• The product of probabilities leads to a propagation of errors in long chains.

Question 2

what are bayesian networks / belief networks?

Answer 2

data structures that represent the dependencies among variables in a directed, acyclic graph, where every link represents a direct influence from the parent to the child node. The child node can then represent the conditional distribution for each parent values in a conditional probability table (CPT)

Question 3

what 2 methods can be used to apply bayes’ on continuous data?

Answer 3

1. Binning: divide the range of continuous data into a discrete number of bins, then apply the discrete method.
2. Mixture of Gaussians: make an assumption regarding the PDF and derive the corresponding parameters.

Question 4

what is bayes’ formula / rule

Answer 4

P(A|B) = (P(B | A)P(A))/P(B)

Question 5

what does P(A|B) = P(A^B) / P(B) actually say?

Answer 5

the probability of A given B, is the probability that A and B appear at the same time, divided by the probability that B appears on its own (prior).

Question 6

definition of posterior probabilities:

Answer 6

P(A|B) = P(A ^ B) / P(B)

Question 7

Prior probabilities are

Answer 7

beliefs prior to arrival of any evidence. For example the probability that it is sunny outside.

Question 8

Posterior or conditional probabilities are

Answer 8

the probability based on evidence, for example the probability that it is sunny outside, given that we’re in December.

Question 9

name 3 problems with Bayesion / belief networks:

Answer 9

• The construction of the network is done manually
• The estimations of probability is not always easy without the data
• The product of probabilities leads to a propagation of errors in long chains.

Question 10

what is p(X|C)

Answer 10

the conditional likelihood of the data given the class

Question 11

p(C|X)

Answer 11

posterior: probability of the class after seeing the data

Question 12

p(C)

Answer 12

probability of the class before seeing anything

Question 13

p(X)

Answer 13

probability of the data

Question 14

naive bayes assumptions

Answer 14

no pair of predicting features is dependent

each feature is given the same importance, contributing equally to the outcome