Please make it fastly urgent dear please 573. Explain the significance of the forward-backward algorithm in HMMs.
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HMMs are statistical models where the system being modeled is assumed to be a Markov process with unobserved (hidden) states. Show more…
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Problem 1. Hidden Markov Models (30pts). Assume that we have the Hidden Markov Model (HMM) depicted in the figure below. The transition, emission and prior probabilities are given in the table below. a. If each of the states can take on k different values and a total of m different observations are possible (across all states), how many parameters are required to fully define this HMM? Justify your answer (5pts). b. Using the forward algorithm, compute the probability that we observe the sequence O1 = 1, O2 = 1, and O3 = 0. Show your work (i.e., show each of your alphas) (10pts). c. Use the Viterbi algorithm to compute (and report) the most likely sequence of states. Show your work (i.e., show each of your Vs) (10pts). d. Is the most likely sequence of states the same as the sequence comprised of the most likely setting for each individual state? Does this make sense? Provide a 1-2 sentence justification for your answer (5 pts).
Dominador T.
--TT--GA-G TATT--CAC-A -CATGGCA--- GC-T---ACGA --GT--CT--- AC-TA-CA--A GC-GT-CT--- -C-T--CA-G ** * *
Supreeta N.
To better understand the HMM underlying the protein family application consider the following (much smaller scale) model: The states and their transition probabilities are depicted on the right. There are three classes of states: rectangles, circles and hexagons. Each emit different symbols with different frequencies. Rectangles will emit the symbols 1, 2, 3 with equal probabilities, hexagons emit a 2 with probability 0.4 and a 4 with probability 0.6, circles always emit 0's. Every process starts in state A1 and ends in A2. That is, both A1 and A2 emit a single symbol only. (a) Carefully define the state space S and the emission alphabet A for this example. Explicitly write down the parameters λ = (P, B, π). (b) Find the most likely state path q = (q1, ..., q5) that led to the sequence of emissions O = (3, 0, 4, 2, 1). For this state path, find P(q|O, λ).
Adi S.
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