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# I wanted to get across the idea that this was dynamic

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Unformatted text preview: •  Biology: certain kinds of dele'ons or inser'ons are more likely than others Dan Jurafsky Confusion matrix for spelling errors Dan Jurafsky Dan Jurafsky Weighted Min Edit Distance •  Ini'aliza'on: D(0,0) = 0! D(i,0) = D(i-1,0) + del[x(i)]; D(0,j) = D(0,j-1) + ins[y(j)]; 1 < i ≤ N! 1 < j ≤ M •  Recurrence Rela'on: D(i,j)= min D(i-1,j) + del[x(i)]! D(i,j-1) + ins[y(j)]! D(i-1,j-1) + sub[x(i),y(j)]! •  Termina'on: D(N,M) is distance ! ! Dan Jurafsky Where did the name, dynamic programming, come from? …The 1950s were not good years for mathematical research. [the] Secretary of Defense …had a pathological fear and hatred of the word, research… I decided therefore to use the word, “programming”. I wanted to get across the idea that this was dynamic, this was multistage… I thought, let’s … take a word that has an absolutely precise meaning, namely dynamic… it’s impossible to use the word, dynamic, in a pejorative sense. Try thinking of some combination that will possibly give it a pejorative meaning. It’s impossible. Thus, I thought dynamic programming was a good name. It was something not even a Congressman could object to.” Richard Bellman, “Eye of the Hurricane: an autobiography” 1984. Minimum Edit Distance Weighted Minimum Edit Distance Minimum Edit Distance Minimum Edit Distance in Computa'onal Biology Dan Jurafsky Sequence Alignment AGGCTATCACCTGACCTCCAGGCCGATGCCC TAGCTATCACGACCGCGGTCGATTTGCCCGAC -AGGCTATCACCTGACCTCCAGGCCGA--TGCCC--TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC Dan Jurafsky Why sequence alignment? •  Comparing genes or regions from diﬀerent species •  to ﬁnd important regions •  determine func'on •  uncover evolu'onary forces •  Assembling fragments to sequence DNA •  Compare individuals to looking for muta'ons Dan Jurafsky Alignments in two ﬁelds •  In Natural Language Processing •  We generally talk about distance (minimized) •  And weights •  In Computa'onal Biology •  We generally talk about similarity (maximized) •  And score...
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