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The viterbi algorithm for HMM in Haskell language
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data Tag = TagStart | TagStop | Tag Int deriving (Eq, Show) | |
type Word = String | |
class CorpusModel m where | |
tags :: m -> [Tag] | |
tag_name :: m -> Tag -> String | |
tag_count_u :: m -> Tag -> Int | |
tag_count_b :: m -> (Tag, Tag) -> Int | |
tag_count_t :: m -> (Tag, Tag, Tag) -> Int | |
word_tag_count :: m -> Word -> Tag -> Int | |
viterbi :: CorpusModel m => m -> [Word] -> [Tag] | |
viterbi m s = let -- list all possible ends tag pairs, and find the maximum one. | |
candidates = [(taccum (len+1) t1 t2 TagStop, (t1, t2)) | t1 <- validtags, t2 <- validtags] | |
(_, (t1, t2)) = maximumBy value_compare candidates | |
-- utility step function that extract the previous tag | |
-- from tag pair (t1,t2) at step n. | |
step (n,t1,t2) = fromJust $ snd $ pi_cached !# n !# (t1,t2) | |
-- repeat the above step utils the full path of tags are extracted, | |
-- note that this path is reversed. | |
path = t2 : t1 : map step (zip3 (reverse [3..len]) (tail path) path) | |
in reverse path | |
where | |
validtags = tags m | |
len = length s | |
min_tag = TagStart | |
max_tag = maximum validtags | |
tag_range = ((min_tag,min_tag),(max_tag,max_tag)) | |
sentence = listArray (1,len) s | |
-- word probability | |
wprob n = let cnt = word_tag_count m (sentence !# n) | |
in \t -> (fromIntegral (cnt t) / fromIntegral (tag_count_u m t)) :: Double | |
-- one-step transition probability | |
tprob t1 t2 t3 = (fromIntegral (tag_count_t m (t1,t2,t3)) / fromIntegral (tag_count_b m (t1,t2))):: Double | |
-- accumulated transition probability | |
taccum 1 t1 t2 t3 = tprob t1 t2 t3 | |
taccum n t1 t2 t3 = get_value (pi_cached !# (n-1) !# (t1, t2)) * tprob t1 t2 t3 | |
pi :: Int -> (Tag,Tag) -> (Double, Maybe Tag) | |
pi n (t2,t3) | t3 `elem` [TagStart, TagStop] = (0, Nothing) | |
| n == 1 && t2 /= TagStart = (0, Nothing) | |
| n > 1 && t2 `elem` [TagStart, TagStop] = (0, Nothing) | |
-- (n = 1 ==> t2 = TagStart) && (n > 1 ==> t2 /= TagStart,TagStop) | |
| otherwise = let wprobn = wprob n | |
in if n <= 2 then | |
(taccum n TagStart t2 t3 * wprobn t3, Just TagStart) | |
else | |
let candidates = [(taccum n t1 t2 t3 * wprobn t3, Just t1) | t1 <- validtags] | |
in maximumBy value_compare candidates | |
-- cached pi values | |
-- by the lazy semantics, each value is computed only when it is necessary and always computed only once. | |
pi_cached :: Array Int (Array (Tag,Tag) (Double, Maybe Tag)) | |
pi_cached = listArray (1,len) | |
( flip map [1..len] (\n -> | |
listArray tag_range $ map (pi n) (range tag_range))) | |
get_value (v, _) = v | |
value_compare a b = compare (get_value a) (get_value b) |
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