NLP.Scores

Scoring functions commonly used for evaluation of NLP systems. Most functions in this module work on lists, but some take a precomputed table of Counts. This will give a speedup if you want to compute multiple scores on the same data. For example to compute the Mutual Information, Variation of Information and the Adujusted Rand Index on the same pair of clusterings:

>>> let cs = counts $ zip "abcabc" "abaaba"
>>> mapM_ (print . ($ cs)) [mi, ari, vi]

Scores for classification and ranking

accuracy :: (Eq a, Fractional n) => [a] -> [a] -> n

Accuracy: the proportion of elements in the first list equal to elements at corresponding positions in second list. Lists should be of equal lengths.

recipRank :: (Eq a, Fractional n) => a -> [a] -> n

Reciprocal rank: the reciprocal of the rank at which the first arguments occurs in the list given as the second argument.

avgPrecision :: (Fractional n, Ord a) => Set a -> [a] -> n

Average precision. http://en.wikipedia.org/wiki/Information_retrieval#Average_precision

Scores for clustering

ari :: (Ord a, Ord b) => Counts a b -> Double

Adjusted Rand Index: http://en.wikipedia.org/wiki/Rand_index

mi :: (Ord a, Ord b) => Counts a b -> Double

Mutual information: MI(X,Y) = H(X) - H(X|Y) = H(Y) - H(Y|X). Also known as information gain.

vi :: (Ord a, Ord b) => Counts a b -> Double

Variation of information: VI(X,Y) = H(X) + H(Y) - 2 MI(X,Y)

Auxiliary types and functions

type Count = Double

A count

data Counts a b

Count table

sum :: Num a => [a] -> a

The sum of a list of numbers (without overflowing stack, unlike sum).

mean :: (Fractional n, Real a) => [a] -> n

The mean of a list of numbers.

jaccard :: (Fractional n, Ord a) => Set a -> Set a -> n

Jaccard coefficient J(A,B) = |AB| / |A union B|

entropy :: [Count] -> Double

Entropy: H(X) = -SUM_i P(X=i) log_2(P(X=i))