What is the Bayes decision boundary?
Naive Bayes is a linear classifier The boundary of the ellipsoids indicate regions of equal probabilities P(x|y). The red decision line indicates the decision boundary where P(y=1|x)=P(y=2|x).
How Bayes theorem is used in proper decision making?
Bayes’ theorem thus gives the probability of an event based on new information that is, or may be related, to that event. The formula can also be used to see how the probability of an event occurring is affected by hypothetical new information, supposing the new information will turn out to be true.
Which is a linear decision boundary of naive Bayes?
Naive Bayes is a linear classifier Naive Bayes leads to a linear decision boundary in many common cases. Illustrated here is the case where P(xα | y) is Gaussian and where σα, c is identical for all c (but can differ across dimensions α). The boundary of the ellipsoids indicate regions of equal probabilities P(x | y).
How is the loss function related to the Bayes decision rule?
The risk corresponding to this loss function is precisely the average probability of error because the conditional risk for the two-category classification is and P (wj|x) is the conditional probability that action ai is correct. The Bayes decision rule to minimize risk calls for selecting the action that minimizes the conditional risk.
Which is the ideal case for Bayesian decision theory?
It is considered the ideal case in which the probability structure underlying the categories is known perfectly. While this sort of stiuation rarely occurs in practice, it permits us to determine the optimal (Bayes) classifier against which we can compare all other classifiers.
Which is the model of the Bayes classifier?
Model P(xα ∣ y): P(xα = j | y = c) = [θjc]α and Kα ∑ j = 1[θjc]α = 1 where [θjc]α is the probability of feature α having the value j, given that the label is c . And the constraint indicates that xα must have one of the categories {1, …, Kα} .