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Questions and Answers
What is the goal of the likelihood computation in hidden Markov models?
What is the goal of the likelihood computation in hidden Markov models?
- To find the optimal state sequence that maximizes the likelihood of the observation sequence
- To estimate the parameters of the hidden Markov model
- To determine the probability of the observation sequence given the hidden Markov model (correct)
- To determine the most likely state sequence given the observation sequence
What is the formula used to compute the likelihood of the observation sequence $X = (x_1, x_2, ..., x_T)$ given the hidden Markov model $M$?
What is the formula used to compute the likelihood of the observation sequence $X = (x_1, x_2, ..., x_T)$ given the hidden Markov model $M$?
- $p(X|M) = \prod_{t=1}^T P(x_t|q_t)$
- $p(X|M) = P(q_1)P(x_1|q_1) \prod_{t=2}^T P(q_t|q_{t-1})P(x_t|q_t)$
- $p(X|M) = \sum_{Q\in Q} P(X, Q|M)$ (correct)
- $p(X|M) = \max_{Q\in Q} P(X, Q|M)
How many possible state sequences $Q = (q_1, q_2, ..., q_T)$ are there for an observation sequence of length $T$ in a hidden Markov model with $N$ states?
How many possible state sequences $Q = (q_1, q_2, ..., q_T)$ are there for an observation sequence of length $T$ in a hidden Markov model with $N$ states?
- $N$
- $N^2$
- $T^N$
- $N^T$ (correct)
Which of the following is a key challenge in computing the likelihood of the observation sequence in a hidden Markov model?
Which of the following is a key challenge in computing the likelihood of the observation sequence in a hidden Markov model?
What is the purpose of the forward algorithm in hidden Markov models?
What is the purpose of the forward algorithm in hidden Markov models?
What is the purpose of the Viterbi algorithm in hidden Markov models?
What is the purpose of the Viterbi algorithm in hidden Markov models?
Which of the following is a key difference between the forward algorithm and the Viterbi algorithm in hidden Markov models?
Which of the following is a key difference between the forward algorithm and the Viterbi algorithm in hidden Markov models?
What is the role of the observation probability $P(x_t|q_t)$ in the computation of the likelihood of the observation sequence in a hidden Markov model?
What is the role of the observation probability $P(x_t|q_t)$ in the computation of the likelihood of the observation sequence in a hidden Markov model?
What is the role of the transition probability $P(q_t|q_{t-1})$ in the computation of the likelihood of the observation sequence in a hidden Markov model?
What is the role of the transition probability $P(q_t|q_{t-1})$ in the computation of the likelihood of the observation sequence in a hidden Markov model?
What is the purpose of the initial state probability $P(q_1)$ in the computation of the likelihood of the observation sequence in a hidden Markov model?
What is the purpose of the initial state probability $P(q_1)$ in the computation of the likelihood of the observation sequence in a hidden Markov model?
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