10 Questions
What is the goal of the likelihood computation in hidden Markov models?
To determine the probability of the observation sequence given the hidden Markov model
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 $M$?
$p(X|M) = \sum_{Q\in Q} P(X, Q|M)$
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?
$N^T$
Which of the following is a key challenge in computing the likelihood of the observation sequence in a hidden Markov model?
The need to sum over all possible state sequences
What is the purpose of the forward algorithm in hidden Markov models?
To compute the likelihood of the observation sequence given the hidden Markov model
What is the purpose of the Viterbi algorithm in hidden Markov models?
To find the most likely state sequence given the observation sequence
Which of the following is a key difference between the forward algorithm and the Viterbi algorithm in hidden Markov models?
The forward algorithm computes the likelihood, while the Viterbi algorithm finds the most likely state sequence
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?
It represents the probability of observing $x_t$ given that the current state is $q_t$
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?
It represents the probability of transitioning from state $q_{t-1}$ to state $q_t$
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?
It represents the probability of the initial state $q_1
Learn about computation complexity in multiplication and the Forward algorithm in Hidden Markov Models. Understand the recursive computation of probabilities and how to exploit the Markov assumption for efficient calculations.
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