N (4)

Question 1

What are the maximum-likelihood estimates derived for the Gaussian classifier?

Answer 1

• Class mean Mi
• Variance S

These estimates are based on sample moments.

Question 2

In the multivariate case, what are the maximum-likelihood estimates for the class mean vector and covariance matrix?

Answer 2

• Class mean vector u;
• Covariance matrix di

These estimates are derived similarly to the univariate case.

Question 3

What does the notation T represent in the context of vector estimation?

Answer 3

Vector transpose

It is used in the formulation of maximum-likelihood estimates.

Question 4

In Baum-Welch training, what type of distribution is used for observations produced by an HMM?

Answer 4

Continuous multivariate Gaussian distribution

The observations are modeled as bi (01) = N (Ot; M¡, Z¡).

Question 5

What does vt(i) denote in the context of Baum-Welch training?

Answer 5

Likelihood of occupying state i at time t

This likelihood is used to allocate observations to states probabilistically.

Question 6

How are the maximum-likelihood estimates of the Gaussian output pdf parameters calculated in Baum-Welch training?

Answer 6

Weighted averages

These averages are normalized by the total likelihood of all paths passing through state i.