-
Notifications
You must be signed in to change notification settings - Fork 7
/
qwk.py
214 lines (178 loc) · 8.07 KB
/
qwk.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
import numpy
from functools import reduce
def confusion_matrix(rater_a, rater_b,
min_rating=None, max_rating=None):
"""
Returns the confusion matrix between rater's ratings
"""
assert (len(rater_a) == len(rater_b))
if min_rating is None:
min_rating = min(reduce(min, rater_a), reduce(min, rater_b))
if max_rating is None:
max_rating = max(reduce(max, rater_a), reduce(max, rater_b))
num_ratings = max_rating - min_rating + 1
conf_mat = [[0 for i in range(num_ratings)]
for j in range(num_ratings)]
for a, b in zip(rater_a, rater_b):
conf_mat[a - min_rating][b - min_rating] += 1
return conf_mat
def histogram(ratings, min_rating=None, max_rating=None):
"""
Returns the counts of each type of rating that a rater made
"""
if min_rating is None: min_rating = reduce(min, ratings)
if max_rating is None: max_rating = reduce(max, ratings)
num_ratings = max_rating - min_rating + 1
hist_ratings = [0 for x in range(num_ratings)]
for r in ratings:
hist_ratings[r - min_rating] += 1
return hist_ratings
def quadratic_weighted_kappa(rater_a, rater_b,
min_rating=None, max_rating=None):
"""
Calculates the quadratic weighted kappa
scoreQuadraticWeightedKappa calculates the quadratic weighted kappa
value, which is a measure of inter-rater agreement between two raters
that provide discrete numeric ratings. Potential values range from -1
(representing complete disagreement) to 1 (representing complete
agreement). A kappa value of 0 is expected if all agreement is due to
chance.
scoreQuadraticWeightedKappa(rater_a, rater_b), where rater_a and rater_b
each correspond to a list of integer ratings. These lists must have the
same length.
The ratings should be integers, and it is assumed that they contain
the complete range of possible ratings.
score_quadratic_weighted_kappa(X, min_rating, max_rating), where min_rating
is the minimum possible rating, and max_rating is the maximum possible
rating
"""
assert (len(rater_a) == len(rater_b))
if min_rating is None:
min_rating = min(reduce(min, rater_a), reduce(min, rater_b))
if max_rating is None:
max_rating = max(reduce(max, rater_a), reduce(max, rater_b))
conf_mat = confusion_matrix(rater_a, rater_b,
min_rating, max_rating)
num_ratings = len(conf_mat)
num_scored_items = float(len(rater_a))
hist_rater_a = histogram(rater_a, min_rating, max_rating)
hist_rater_b = histogram(rater_b, min_rating, max_rating)
numerator = 0.0
denominator = 0.0
for i in range(num_ratings):
for j in range(num_ratings):
expected_count = (hist_rater_a[i] * hist_rater_b[j]
/ num_scored_items)
d = pow(i - j, 2.0) / pow(num_ratings - 1, 2.0)
numerator += d * conf_mat[i][j] / num_scored_items
denominator += d * expected_count / num_scored_items
return 1.0 - numerator / denominator
def linear_weighted_kappa(rater_a, rater_b,
min_rating=None, max_rating=None):
"""
Calculates the linear weighted kappa
linear_weighted_kappa calculates the linear weighted kappa
value, which is a measure of inter-rater agreement between two raters
that provide discrete numeric ratings. Potential values range from -1
(representing complete disagreement) to 1 (representing complete
agreement). A kappa value of 0 is expected if all agreement is due to
chance.
linear_weighted_kappa(rater_a, rater_b), where rater_a and rater_b
each correspond to a list of integer ratings. These lists must have the
same length.
The ratings should be integers, and it is assumed that they contain
the complete range of possible ratings.
linear_weighted_kappa(X, min_rating, max_rating), where min_rating
is the minimum possible rating, and max_rating is the maximum possible
rating
"""
assert (len(rater_a) == len(rater_b))
if min_rating is None:
min_rating = min(reduce(min, rater_a), reduce(min, rater_b))
if max_rating is None:
max_rating = max(reduce(max, rater_a), reduce(max, rater_b))
conf_mat = confusion_matrix(rater_a, rater_b,
min_rating, max_rating)
num_ratings = len(conf_mat)
num_scored_items = float(len(rater_a))
hist_rater_a = histogram(rater_a, min_rating, max_rating)
hist_rater_b = histogram(rater_b, min_rating, max_rating)
numerator = 0.0
denominator = 0.0
for i in range(num_ratings):
for j in range(num_ratings):
expected_count = (hist_rater_a[i] * hist_rater_b[j]
/ num_scored_items)
d = abs(i - j) / float(num_ratings - 1)
numerator += d * conf_mat[i][j] / num_scored_items
denominator += d * expected_count / num_scored_items
return 1.0 - numerator / denominator
def kappa(rater_a, rater_b,
min_rating=None, max_rating=None):
"""
Calculates the kappa
kappa calculates the kappa
value, which is a measure of inter-rater agreement between two raters
that provide discrete numeric ratings. Potential values range from -1
(representing complete disagreement) to 1 (representing complete
agreement). A kappa value of 0 is expected if all agreement is due to
chance.
kappa(rater_a, rater_b), where rater_a and rater_b
each correspond to a list of integer ratings. These lists must have the
same length.
The ratings should be integers, and it is assumed that they contain
the complete range of possible ratings.
kappa(X, min_rating, max_rating), where min_rating
is the minimum possible rating, and max_rating is the maximum possible
rating
"""
assert (len(rater_a) == len(rater_b))
if min_rating is None:
min_rating = min(reduce(min, rater_a), reduce(min, rater_b))
if max_rating is None:
max_rating = max(reduce(max, rater_a), reduce(max, rater_b))
conf_mat = confusion_matrix(rater_a, rater_b,
min_rating, max_rating)
num_ratings = len(conf_mat)
num_scored_items = float(len(rater_a))
hist_rater_a = histogram(rater_a, min_rating, max_rating)
hist_rater_b = histogram(rater_b, min_rating, max_rating)
numerator = 0.0
denominator = 0.0
for i in range(num_ratings):
for j in range(num_ratings):
expected_count = (hist_rater_a[i] * hist_rater_b[j]
/ num_scored_items)
if i == j:
d = 0.0
else:
d = 1.0
numerator += d * conf_mat[i][j] / num_scored_items
denominator += d * expected_count / num_scored_items
return 1.0 - numerator / denominator
def mean_quadratic_weighted_kappa(kappas, weights=None):
"""
Calculates the mean of the quadratic
weighted kappas after applying Fisher's r-to-z transform, which is
approximately a variance-stabilizing transformation. This
transformation is undefined if one of the kappas is 1.0, so all kappa
values are capped in the range (-0.999, 0.999). The reverse
transformation is then applied before returning the result.
mean_quadratic_weighted_kappa(kappas), where kappas is a vector of
kappa values
mean_quadratic_weighted_kappa(kappas, weights), where weights is a vector
of weights that is the same size as kappas. Weights are applied in the
z-space
"""
kappas = numpy.array(kappas, dtype=float)
if weights is None:
weights = numpy.ones(numpy.shape(kappas))
else:
weights = weights / numpy.mean(weights)
# ensure that kappas are in the range [-.999, .999]
kappas = numpy.array([min(x, .999) for x in kappas])
kappas = numpy.array([max(x, -.999) for x in kappas])
z = 0.5 * numpy.log((1 + kappas) / (1 - kappas)) * weights
z = numpy.mean(z)
kappa = (numpy.exp(2 * z) - 1) / (numpy.exp(2 * z) + 1)
return kappa