You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
294 lines
10 KiB
Plaintext
294 lines
10 KiB
Plaintext
5 years ago
|
.. Copyright (C) 2001-2019 NLTK Project
|
||
|
|
.. For license information, see LICENSE.TXT
|
||
|
|
|
||
|
|
=======
|
||
|
|
Metrics
|
||
|
|
=======
|
||
|
|
|
||
|
|
The `nltk.metrics` package provides a variety of *evaluation measures*
|
||
|
|
which can be used for a wide variety of NLP tasks.
|
||
|
|
|
||
|
|
>>> from __future__ import print_function
|
||
|
|
>>> from nltk.metrics import *
|
||
|
|
|
||
|
|
------------------
|
||
|
|
Standard IR Scores
|
||
|
|
------------------
|
||
|
|
|
||
|
|
We can use standard scores from information retrieval to test the
|
||
|
|
performance of taggers, chunkers, etc.
|
||
|
|
|
||
|
|
>>> reference = 'DET NN VB DET JJ NN NN IN DET NN'.split()
|
||
|
|
>>> test = 'DET VB VB DET NN NN NN IN DET NN'.split()
|
||
|
|
>>> print(accuracy(reference, test))
|
||
|
|
0.8
|
||
|
|
|
||
|
|
|
||
|
|
The following measures apply to sets:
|
||
|
|
|
||
|
|
>>> reference_set = set(reference)
|
||
|
|
>>> test_set = set(test)
|
||
|
|
>>> precision(reference_set, test_set)
|
||
|
|
1.0
|
||
|
|
>>> print(recall(reference_set, test_set))
|
||
|
|
0.8
|
||
|
|
>>> print(f_measure(reference_set, test_set))
|
||
|
|
0.88888888888...
|
||
|
|
|
||
|
|
Measuring the likelihood of the data, given probability distributions:
|
||
|
|
|
||
|
|
>>> from nltk import FreqDist, MLEProbDist
|
||
|
|
>>> pdist1 = MLEProbDist(FreqDist("aldjfalskfjaldsf"))
|
||
|
|
>>> pdist2 = MLEProbDist(FreqDist("aldjfalssjjlldss"))
|
||
|
|
>>> print(log_likelihood(['a', 'd'], [pdist1, pdist2]))
|
||
|
|
-2.7075187496...
|
||
|
|
|
||
|
|
|
||
|
|
----------------
|
||
|
|
Distance Metrics
|
||
|
|
----------------
|
||
|
|
|
||
|
|
String edit distance (Levenshtein):
|
||
|
|
|
||
|
|
>>> edit_distance("rain", "shine")
|
||
|
|
3
|
||
|
|
>>> edit_distance_align("shine", "shine")
|
||
|
|
[(0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5)]
|
||
|
|
>>> edit_distance_align("rain", "brainy")
|
||
|
|
[(0, 0), (1, 1), (1, 2), (2, 3), (3, 4), (4, 5), (4, 6)]
|
||
|
|
>>> edit_distance_align("", "brainy")
|
||
|
|
[(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6)]
|
||
|
|
>>> edit_distance_align("", "")
|
||
|
|
[(0, 0)]
|
||
|
|
|
||
|
|
Other distance measures:
|
||
|
|
|
||
|
|
>>> s1 = set([1,2,3,4])
|
||
|
|
>>> s2 = set([3,4,5])
|
||
|
|
>>> binary_distance(s1, s2)
|
||
|
|
1.0
|
||
|
|
>>> print(jaccard_distance(s1, s2))
|
||
|
|
0.6
|
||
|
|
>>> print(masi_distance(s1, s2))
|
||
|
|
0.868
|
||
|
|
|
||
|
|
----------------------
|
||
|
|
Miscellaneous Measures
|
||
|
|
----------------------
|
||
|
|
|
||
|
|
Rank Correlation works with two dictionaries mapping keys to ranks.
|
||
|
|
The dictionaries should have the same set of keys.
|
||
|
|
|
||
|
|
>>> spearman_correlation({'e':1, 't':2, 'a':3}, {'e':1, 'a':2, 't':3})
|
||
|
|
0.5
|
||
|
|
|
||
|
|
Windowdiff uses a sliding window in comparing two segmentations of the same input (e.g. tokenizations, chunkings).
|
||
|
|
Segmentations are represented using strings of zeros and ones.
|
||
|
|
|
||
|
|
>>> s1 = "000100000010"
|
||
|
|
>>> s2 = "000010000100"
|
||
|
|
>>> s3 = "100000010000"
|
||
|
|
>>> s4 = "000000000000"
|
||
|
|
>>> s5 = "111111111111"
|
||
|
|
>>> windowdiff(s1, s1, 3)
|
||
|
|
0.0
|
||
|
|
>>> abs(windowdiff(s1, s2, 3) - 0.3) < 1e-6 # windowdiff(s1, s2, 3) == 0.3
|
||
|
|
True
|
||
|
|
>>> abs(windowdiff(s2, s3, 3) - 0.8) < 1e-6 # windowdiff(s2, s3, 3) == 0.8
|
||
|
|
True
|
||
|
|
>>> windowdiff(s1, s4, 3)
|
||
|
|
0.5
|
||
|
|
>>> windowdiff(s1, s5, 3)
|
||
|
|
1.0
|
||
|
|
|
||
|
|
----------------
|
||
|
|
Confusion Matrix
|
||
|
|
----------------
|
||
|
|
|
||
|
|
>>> reference = 'This is the reference data. Testing 123. aoaeoeoe'
|
||
|
|
>>> test = 'Thos iz_the rifirenci data. Testeng 123. aoaeoeoe'
|
||
|
|
>>> print(ConfusionMatrix(reference, test))
|
||
|
|
| . 1 2 3 T _ a c d e f g h i n o r s t z |
|
||
|
|
--+-------------------------------------------+
|
||
|
|
|<8>. . . . . 1 . . . . . . . . . . . . . . |
|
||
|
|
. | .<2>. . . . . . . . . . . . . . . . . . . |
|
||
|
|
1 | . .<1>. . . . . . . . . . . . . . . . . . |
|
||
|
|
2 | . . .<1>. . . . . . . . . . . . . . . . . |
|
||
|
|
3 | . . . .<1>. . . . . . . . . . . . . . . . |
|
||
|
|
T | . . . . .<2>. . . . . . . . . . . . . . . |
|
||
|
|
_ | . . . . . .<.>. . . . . . . . . . . . . . |
|
||
|
|
a | . . . . . . .<4>. . . . . . . . . . . . . |
|
||
|
|
c | . . . . . . . .<1>. . . . . . . . . . . . |
|
||
|
|
d | . . . . . . . . .<1>. . . . . . . . . . . |
|
||
|
|
e | . . . . . . . . . .<6>. . . 3 . . . . . . |
|
||
|
|
f | . . . . . . . . . . .<1>. . . . . . . . . |
|
||
|
|
g | . . . . . . . . . . . .<1>. . . . . . . . |
|
||
|
|
h | . . . . . . . . . . . . .<2>. . . . . . . |
|
||
|
|
i | . . . . . . . . . . 1 . . .<1>. 1 . . . . |
|
||
|
|
n | . . . . . . . . . . . . . . .<2>. . . . . |
|
||
|
|
o | . . . . . . . . . . . . . . . .<3>. . . . |
|
||
|
|
r | . . . . . . . . . . . . . . . . .<2>. . . |
|
||
|
|
s | . . . . . . . . . . . . . . . . . .<2>. 1 |
|
||
|
|
t | . . . . . . . . . . . . . . . . . . .<3>. |
|
||
|
|
z | . . . . . . . . . . . . . . . . . . . .<.>|
|
||
|
|
--+-------------------------------------------+
|
||
|
|
(row = reference; col = test)
|
||
|
|
<BLANKLINE>
|
||
|
|
|
||
|
|
>>> cm = ConfusionMatrix(reference, test)
|
||
|
|
>>> print(cm.pretty_format(sort_by_count=True))
|
||
|
|
| e a i o s t . T h n r 1 2 3 c d f g _ z |
|
||
|
|
--+-------------------------------------------+
|
||
|
|
|<8>. . . . . . . . . . . . . . . . . . 1 . |
|
||
|
|
e | .<6>. 3 . . . . . . . . . . . . . . . . . |
|
||
|
|
a | . .<4>. . . . . . . . . . . . . . . . . . |
|
||
|
|
i | . 1 .<1>1 . . . . . . . . . . . . . . . . |
|
||
|
|
o | . . . .<3>. . . . . . . . . . . . . . . . |
|
||
|
|
s | . . . . .<2>. . . . . . . . . . . . . . 1 |
|
||
|
|
t | . . . . . .<3>. . . . . . . . . . . . . . |
|
||
|
|
. | . . . . . . .<2>. . . . . . . . . . . . . |
|
||
|
|
T | . . . . . . . .<2>. . . . . . . . . . . . |
|
||
|
|
h | . . . . . . . . .<2>. . . . . . . . . . . |
|
||
|
|
n | . . . . . . . . . .<2>. . . . . . . . . . |
|
||
|
|
r | . . . . . . . . . . .<2>. . . . . . . . . |
|
||
|
|
1 | . . . . . . . . . . . .<1>. . . . . . . . |
|
||
|
|
2 | . . . . . . . . . . . . .<1>. . . . . . . |
|
||
|
|
3 | . . . . . . . . . . . . . .<1>. . . . . . |
|
||
|
|
c | . . . . . . . . . . . . . . .<1>. . . . . |
|
||
|
|
d | . . . . . . . . . . . . . . . .<1>. . . . |
|
||
|
|
f | . . . . . . . . . . . . . . . . .<1>. . . |
|
||
|
|
g | . . . . . . . . . . . . . . . . . .<1>. . |
|
||
|
|
_ | . . . . . . . . . . . . . . . . . . .<.>. |
|
||
|
|
z | . . . . . . . . . . . . . . . . . . . .<.>|
|
||
|
|
--+-------------------------------------------+
|
||
|
|
(row = reference; col = test)
|
||
|
|
<BLANKLINE>
|
||
|
|
|
||
|
|
>>> print(cm.pretty_format(sort_by_count=True, truncate=10))
|
||
|
|
| e a i o s t . T h |
|
||
|
|
--+---------------------+
|
||
|
|
|<8>. . . . . . . . . |
|
||
|
|
e | .<6>. 3 . . . . . . |
|
||
|
|
a | . .<4>. . . . . . . |
|
||
|
|
i | . 1 .<1>1 . . . . . |
|
||
|
|
o | . . . .<3>. . . . . |
|
||
|
|
s | . . . . .<2>. . . . |
|
||
|
|
t | . . . . . .<3>. . . |
|
||
|
|
. | . . . . . . .<2>. . |
|
||
|
|
T | . . . . . . . .<2>. |
|
||
|
|
h | . . . . . . . . .<2>|
|
||
|
|
--+---------------------+
|
||
|
|
(row = reference; col = test)
|
||
|
|
<BLANKLINE>
|
||
|
|
|
||
|
|
>>> print(cm.pretty_format(sort_by_count=True, truncate=10, values_in_chart=False))
|
||
|
|
| 1 |
|
||
|
|
| 1 2 3 4 5 6 7 8 9 0 |
|
||
|
|
---+---------------------+
|
||
|
|
1 |<8>. . . . . . . . . |
|
||
|
|
2 | .<6>. 3 . . . . . . |
|
||
|
|
3 | . .<4>. . . . . . . |
|
||
|
|
4 | . 1 .<1>1 . . . . . |
|
||
|
|
5 | . . . .<3>. . . . . |
|
||
|
|
6 | . . . . .<2>. . . . |
|
||
|
|
7 | . . . . . .<3>. . . |
|
||
|
|
8 | . . . . . . .<2>. . |
|
||
|
|
9 | . . . . . . . .<2>. |
|
||
|
|
10 | . . . . . . . . .<2>|
|
||
|
|
---+---------------------+
|
||
|
|
(row = reference; col = test)
|
||
|
|
Value key:
|
||
|
|
1:
|
||
|
|
2: e
|
||
|
|
3: a
|
||
|
|
4: i
|
||
|
|
5: o
|
||
|
|
6: s
|
||
|
|
7: t
|
||
|
|
8: .
|
||
|
|
9: T
|
||
|
|
10: h
|
||
|
|
<BLANKLINE>
|
||
|
|
|
||
|
|
|
||
|
|
--------------------
|
||
|
|
Association measures
|
||
|
|
--------------------
|
||
|
|
|
||
|
|
These measures are useful to determine whether the coocurrence of two random
|
||
|
|
events is meaningful. They are used, for instance, to distinguish collocations
|
||
|
|
from other pairs of adjacent words.
|
||
|
|
|
||
|
|
We bring some examples of bigram association calculations from Manning and
|
||
|
|
Schutze's SNLP, 2nd Ed. chapter 5.
|
||
|
|
|
||
|
|
>>> n_new_companies, n_new, n_companies, N = 8, 15828, 4675, 14307668
|
||
|
|
>>> bam = BigramAssocMeasures
|
||
|
|
>>> bam.raw_freq(20, (42, 20), N) == 20. / N
|
||
|
|
True
|
||
|
|
>>> bam.student_t(n_new_companies, (n_new, n_companies), N)
|
||
|
|
0.999...
|
||
|
|
>>> bam.chi_sq(n_new_companies, (n_new, n_companies), N)
|
||
|
|
1.54...
|
||
|
|
>>> bam.likelihood_ratio(150, (12593, 932), N)
|
||
|
|
1291...
|
||
|
|
|
||
|
|
For other associations, we ensure the ordering of the measures:
|
||
|
|
|
||
|
|
>>> bam.mi_like(20, (42, 20), N) > bam.mi_like(20, (41, 27), N)
|
||
|
|
True
|
||
|
|
>>> bam.pmi(20, (42, 20), N) > bam.pmi(20, (41, 27), N)
|
||
|
|
True
|
||
|
|
>>> bam.phi_sq(20, (42, 20), N) > bam.phi_sq(20, (41, 27), N)
|
||
|
|
True
|
||
|
|
>>> bam.poisson_stirling(20, (42, 20), N) > bam.poisson_stirling(20, (41, 27), N)
|
||
|
|
True
|
||
|
|
>>> bam.jaccard(20, (42, 20), N) > bam.jaccard(20, (41, 27), N)
|
||
|
|
True
|
||
|
|
>>> bam.dice(20, (42, 20), N) > bam.dice(20, (41, 27), N)
|
||
|
|
True
|
||
|
|
>>> bam.fisher(20, (42, 20), N) > bam.fisher(20, (41, 27), N) # doctest: +SKIP
|
||
|
|
False
|
||
|
|
|
||
|
|
For trigrams, we have to provide more count information:
|
||
|
|
|
||
|
|
>>> n_w1_w2_w3 = 20
|
||
|
|
>>> n_w1_w2, n_w1_w3, n_w2_w3 = 35, 60, 40
|
||
|
|
>>> pair_counts = (n_w1_w2, n_w1_w3, n_w2_w3)
|
||
|
|
>>> n_w1, n_w2, n_w3 = 100, 200, 300
|
||
|
|
>>> uni_counts = (n_w1, n_w2, n_w3)
|
||
|
|
>>> N = 14307668
|
||
|
|
>>> tam = TrigramAssocMeasures
|
||
|
|
>>> tam.raw_freq(n_w1_w2_w3, pair_counts, uni_counts, N) == 1. * n_w1_w2_w3 / N
|
||
|
|
True
|
||
|
|
>>> uni_counts2 = (n_w1, n_w2, 100)
|
||
|
|
>>> tam.student_t(n_w1_w2_w3, pair_counts, uni_counts2, N) > tam.student_t(n_w1_w2_w3, pair_counts, uni_counts, N)
|
||
|
|
True
|
||
|
|
>>> tam.chi_sq(n_w1_w2_w3, pair_counts, uni_counts2, N) > tam.chi_sq(n_w1_w2_w3, pair_counts, uni_counts, N)
|
||
|
|
True
|
||
|
|
>>> tam.mi_like(n_w1_w2_w3, pair_counts, uni_counts2, N) > tam.mi_like(n_w1_w2_w3, pair_counts, uni_counts, N)
|
||
|
|
True
|
||
|
|
>>> tam.pmi(n_w1_w2_w3, pair_counts, uni_counts2, N) > tam.pmi(n_w1_w2_w3, pair_counts, uni_counts, N)
|
||
|
|
True
|
||
|
|
>>> tam.likelihood_ratio(n_w1_w2_w3, pair_counts, uni_counts2, N) > tam.likelihood_ratio(n_w1_w2_w3, pair_counts, uni_counts, N)
|
||
|
|
True
|
||
|
|
>>> tam.poisson_stirling(n_w1_w2_w3, pair_counts, uni_counts2, N) > tam.poisson_stirling(n_w1_w2_w3, pair_counts, uni_counts, N)
|
||
|
|
True
|
||
|
|
>>> tam.jaccard(n_w1_w2_w3, pair_counts, uni_counts2, N) > tam.jaccard(n_w1_w2_w3, pair_counts, uni_counts, N)
|
||
|
|
True
|
||
|
|
|
||
|
|
|
||
|
|
For fourgrams, we have to provide more count information:
|
||
|
|
|
||
|
|
>>> n_w1_w2_w3_w4 = 5
|
||
|
|
>>> n_w1_w2, n_w1_w3, n_w2_w3 = 35, 60, 40
|
||
|
|
>>> n_w1_w2_w3, n_w2_w3_w4 = 20, 10
|
||
|
|
>>> pair_counts = (n_w1_w2, n_w1_w3, n_w2_w3)
|
||
|
|
>>> triplet_counts = (n_w1_w2_w3, n_w2_w3_w4)
|
||
|
|
>>> n_w1, n_w2, n_w3, n_w4 = 100, 200, 300, 400
|
||
|
|
>>> uni_counts = (n_w1, n_w2, n_w3, n_w4)
|
||
|
|
>>> N = 14307668
|
||
|
|
>>> qam = QuadgramAssocMeasures
|
||
|
|
>>> qam.raw_freq(n_w1_w2_w3_w4, pair_counts, triplet_counts, uni_counts, N) == 1. * n_w1_w2_w3_w4 / N
|
||
|
|
True
|