N (2)

Question 1

What are the parameters of a discrete HMM?

Answer 1

• State transition probabilities
• Discrete output probabilities
• B = {bi(k)} = {P(ot=k|xt=i)}

N states and K observation types are involved in the model.

Question 2

In a discrete HMM, what does B represent?

Answer 2

B = {bi(k)} = {P(ot=k|xt=i)}

It denotes the discrete output probabilities for each state.

Question 3

What are the parameters of a continuous HMM?

Answer 3

• State-transition probabilities
• Continuous output probability densities

The state-transition probabilities are represented as A = {j, aij, ni} = {P(x+=j|x+-1=i)}.

Question 4

In a continuous HMM, what does A represent?

Answer 4

A = {j, aij, ni} = {P(x+=j|x+-1=i)}

It describes the state-transition probabilities.

Question 5

What is the output probability density function for each state i in a continuous HMM?

Answer 5

p(ot|xt=i)

The output pdf can be Gaussian, represented as bilot) = N(otiMi, Ei).

Question 6

In a continuous HMM, the output pdf for state i can be represented as __________.

Answer 6

bilot) = N(otiMi, Ei)

This indicates that the output is normally distributed with mean Mi and variance Si.

Question 7

What is the notation used for state transition probabilities in a discrete HMM?

Answer 7

aij

These probabilities define the likelihood of transitioning from one state to another.

Question 8

What does N represent in the context of HMMs?

Answer 8

The number of states

N is a crucial parameter that defines the structure of the model.

Question 9

What is the range for i and j in the state transition probabilities for HMMs?

Answer 9

1 ≤ i, j ≤ N

This indicates that both indices must fall within the total number of states.

Question 10

What is the range for k in the discrete output probabilities for HMMs?

Answer 10

1 ≤ k ≤ K

K represents the number of observation types.