91 q proof the quantity argmaxrq mtt1 r q ri

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∗ ∗ Then we can find a state value qt+1 (1) at t + 1 such that (qt (1), qt+1 (1)) is a pair of state values of a Viterbi path using the following procedure: ∗ ∗ qt+1 (1) ∈ argmax mt,t+1 (qt (1), q ). (9.1) q Proof. ∗∗ The quantity argmaxr,q mt,t+1 (r, q ) = {(ri , qi )}i is a set of pairs, each of which is compatible with some Viterbi path. Moreover, any Viterbi path must, at times t and t + 1, have value corresponding to one of the ∗ ∗ pairs. Therefore, there is some i such that qt (1) = ri , and the argmax in ∗ Equation (9.1) chooses the corresponding qi which hence is compatible with some Viterbi path. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 9 - Feb 6th, 2013 page 9-11 (of 180) k-best without the penalty Island Summary Scratch Computing Viterbi from max-margin - any case We start this process with the singleton max-marginal on the left ∗ q1 (1) ∈ argmax m1 (q ), (9.2) q and then repeat the following recursion, for t = 2 . . . T , as follows ∗ ∗ qt (1) ∈ argmax mt−1,t (qt−1 (1), q ), (9.3) q which, thanks to to Proposition 9.3.1, is guaranteed to be a Viterbi path. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lec...
View Full Document

This document was uploaded on 04/05/2014.

Ask a homework question - tutors are online