Lecture 6

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Unformatted text preview: ecognition, where W = word and Q = phoneme. • Most likely sequence of states (Viterbi/ MAP, max-product): arg max P (q1:t, w1:t|e1:t) q1:t,w1:t • Most likely sequence of words (Marginal MAP, max-sum-product): P (w1:t, q1:t|e1:t) arg max w1:t q1:t • Max-product often used as computationally simpler approximation to max-sum-product (or can use A∗ decoding). Complexity of exact inference Decision problems • Determinining if PB (X = x) > 0 for some (discrete) variable X and some Bayes net B is NP-complete. • Defn: a decision problem is a task of the form: does there exist a solution which satisfies these conditions? • What does this mean? • Example: boolean satisfiability: • Roughly: The best algorithm for exact inference (in discrete-state models) probably takes exponential time, in the worst case. • More formally: we need a review of basic computational complexity theory. (q1 ∨ ¬q2 ∨ q3) ∧ ¬qq ∨ q2 ∨ ¬q3 is satisfiable (q1 = q2 = q3=true) • 3-SAT is boolean satisfiability where φ = C1 ∧ C2 . . . ∧ Cn, and every clause Ci has 3 literals. P vs NP Proving NP-completeness • Defn: A decision problem Π is in P if it can be solved in polynomial time. • Defn: Π is in NP if it can be solved in polynomial...
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This document was uploaded on 03/28/2014 for the course CS 532 at The University of British Columbia.

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