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Stabler - Lx 185/209 2003 And of course, the language grows continually: Number of unique bigrams, character 6-grams or uniquely tagged words Number of word types 450000 400000 350000 300000 250000 200000 150000 100000 50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 character 6-grams word bigrams tag trigrams uniquely tagged words 0 0 1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 Number of characters (bytes) 0 0 200000 400000 600000 800000 1000000 Number of word tokens Brown 131 LOB WSJ Shakespeare Austen Bible
Stabler - Lx 185/209 2003 8.1.4 Probability measures and Bayes’ Theorem (28) A sample space Ω is a set of outcomes. An event A ⊆ Ω. Letting 2Ω be the set of subsets of Ω, thepowersetofΩ, thenaneventA∈2Ω . (29) Given events A, B, the usual notions A ∩ B,A ∪ B apply. For the complement of A let’s write A = Ω − A. Sometimes set subtraction A − B = A ∩ B is written A\B, but since we are not using the dash for complements, we can use it for subtraction without excessive ambiguity. (30) (2Ω , ⊆) is a Boolean (set) algebra, that is, it is a collection of subsets of Ω such that a. Ω ∈ 2Ω b. A0,A1 ∈ 2 Ω implies A0 ∪ A1 ∈ 2 Ω c. A ∈ 2 Ω implies A ∈ 2 Ω The English mathematician George Boole (1815-1864) is best known for his work in propositional logic and algebra. In 1854 he published An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities. (31) When A ∩ B =∅, A and B are (mutually) disjoint. A0,A1,...,An is a sequence of (mutually) disjoint events if for all 0 ≤ i, j ≤ n where i = j, thepairAiand Aj is disjoint. (32) When Ω is countable (finite or countably infinite), it is discrete. Otherwise Ω is continuous. (33) [0, 1] is the closed interval {x ∈ R| 0 ≤ x ≤ 1} (0, 1) is the open interval {x ∈ R| 0
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Notes on computati
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Stabler - Lx 185/209 2003 Linguisti
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Stabler - Lx 185/209 2003 1 Setting
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Stabler - Lx 185/209 2003 1.2 Propo
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Stabler - Lx 185/209 2003 10. Call
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Stabler - Lx 185/209 2003 compute s
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Stabler - Lx 185/209 2003 Exercises
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Stabler - Lx 185/209 2003 15.1 Mono
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Index (x, y), openintervalfromx to
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