# Number of parameters in Bayesian Classifier

## Problem

Assume we have a Bayesian classifier with the three following features to determine whether a software user is a student, an admin, or an infiltrator (3 classifications).

LoginFrequency = { Never, Daily, Weekly }

LoginLocation = { Home, InCity, InState InCountry, OutOfCountry }

LoginDuration = { Seconds, Minutes, Hours, Days, Weeks }

1. Assuming the features aren't independent, how many parameters need to be estimated, in total, to classify amongst the 3 types of users?

2. What about if we assume the features are independent?

## Attempt

I'm having problems understanding how to count the number of estimated parameters in either case.

My guess for (2) is $${\displaystyle \prod_{i=1}^{3} X_i}$$, where each $$X_i$$ is the number of values per feature, giving us $$3 \times 5 \times 5 = 75$$, which seems pretty wrong. As for (1), I don't know where to begin.

## Notes

I'm only 2 weeks into a graduate ML course as an undergrad, and we've missed a lecture due to a snow storm so, as you might assume, I'm still much of a beginner. Hence, any help would be greatly appreciated.

• Please see stats.stackexchange.com/tags/self-study/info . Here it would be useful to explain the reasoning behind the guess and/or what do you understand a Bayesian classifier to be and what kind of parameters it would have. – Juho Kokkala Feb 6 at 7:27

By the definition, events $$A$$ and $$B$$ are independent if
$$p(A, B) = p(A) \, p(B)$$