Could you guide us through the Naive Bayes algorithm and the basis for setting its classification threshold?

Question

Anonymous · Accepted Answer

Naive Bayes computes the probability of the class given the features:
P(class | features) = P(features | class) * P(class) / P(features).
Navie Bayes assumes that all the features are independent given the class so
that the likelihood can be computed easily as a product of all the individual
likelihood of features. For each class, it computes a product of all individual
features given the class and the prior probability of that class.
The class with the highest probability is chosen as the resulting class.
For a binary classification problem, the default threshold is 0.5, but it can be
tuned manually (eg. 0.7) to balance precision and recall given the problem's
requirement.  For a multi-class problem, the default threshold is 1 / number of
classes, and we can use the one-vs-rest technique.

Anonymous · Answer

In Naive bayes, the probablity of a sample to a class is calculated as
P(class | sample) = P(sample | class) P(class) / P(sample)
It assumes the samples are independent. In general, the threshold is kept in 0.5
insuring a balance between detection of classes. For example, in case of
Ham/Spam classifier, 0.5 allows for a balance between TP and FP of both classes.
However, if we would like to detect as many as Spam and keen to accpt some Ham
may be classified as Spam, then we can play with threshold

Could you guide us through the Naive Bayes algorithm and the basis for setting its classification threshold?

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