# Source code for nltk.metrics.scores

```# Natural Language Toolkit: Evaluation
#
# Copyright (C) 2001-2023 NLTK Project
# Author: Edward Loper <edloper@gmail.com>
#         Steven Bird <stevenbird1@gmail.com>
# URL: <https://www.nltk.org/>

import operator
from functools import reduce
from math import fabs
from random import shuffle

try:
from scipy.stats.stats import betai
except ImportError:
betai = None

from nltk.util import LazyConcatenation, LazyMap

[docs]def accuracy(reference, test):
"""
Given a list of reference values and a corresponding list of test
values, return the fraction of corresponding values that are
equal.  In particular, return the fraction of indices
``0<i<=len(test)`` such that ``test[i] == reference[i]``.

:type reference: list
:param reference: An ordered list of reference values.
:type test: list
:param test: A list of values to compare against the corresponding
reference values.
:raise ValueError: If ``reference`` and ``length`` do not have the
same length.
"""
if len(reference) != len(test):
raise ValueError("Lists must have the same length.")
return sum(x == y for x, y in zip(reference, test)) / len(test)

[docs]def precision(reference, test):
"""
Given a set of reference values and a set of test values, return
the fraction of test values that appear in the reference set.
In particular, return card(``reference`` intersection ``test``)/card(``test``).
If ``test`` is empty, then return None.

:type reference: set
:param reference: A set of reference values.
:type test: set
:param test: A set of values to compare against the reference set.
:rtype: float or None
"""
if not hasattr(reference, "intersection") or not hasattr(test, "intersection"):
raise TypeError("reference and test should be sets")

if len(test) == 0:
return None
else:
return len(reference.intersection(test)) / len(test)

[docs]def recall(reference, test):
"""
Given a set of reference values and a set of test values, return
the fraction of reference values that appear in the test set.
In particular, return card(``reference`` intersection ``test``)/card(``reference``).
If ``reference`` is empty, then return None.

:type reference: set
:param reference: A set of reference values.
:type test: set
:param test: A set of values to compare against the reference set.
:rtype: float or None
"""
if not hasattr(reference, "intersection") or not hasattr(test, "intersection"):
raise TypeError("reference and test should be sets")

if len(reference) == 0:
return None
else:
return len(reference.intersection(test)) / len(reference)

[docs]def f_measure(reference, test, alpha=0.5):
"""
Given a set of reference values and a set of test values, return
the f-measure of the test values, when compared against the
reference values.  The f-measure is the harmonic mean of the
``precision`` and ``recall``, weighted by ``alpha``.  In particular,
given the precision *p* and recall *r* defined by:

- *p* = card(``reference`` intersection ``test``)/card(``test``)
- *r* = card(``reference`` intersection ``test``)/card(``reference``)

The f-measure is:

- *1/(alpha/p + (1-alpha)/r)*

If either ``reference`` or ``test`` is empty, then ``f_measure``
returns None.

:type reference: set
:param reference: A set of reference values.
:type test: set
:param test: A set of values to compare against the reference set.
:rtype: float or None
"""
p = precision(reference, test)
r = recall(reference, test)
if p is None or r is None:
return None
if p == 0 or r == 0:
return 0
return 1.0 / (alpha / p + (1 - alpha) / r)

[docs]def log_likelihood(reference, test):
"""
Given a list of reference values and a corresponding list of test
probability distributions, return the average log likelihood of
the reference values, given the probability distributions.

:param reference: A list of reference values
:type reference: list
:param test: A list of probability distributions over values to
compare against the corresponding reference values.
:type test: list(ProbDistI)
"""
if len(reference) != len(test):
raise ValueError("Lists must have the same length.")

# Return the average value of dist.logprob(val).
total_likelihood = sum(dist.logprob(val) for (val, dist) in zip(reference, test))

[docs]def approxrand(a, b, **kwargs):
"""
Returns an approximate significance level between two lists of
independently generated test values.

Approximate randomization calculates significance by randomly drawing
from a sample of the possible permutations. At the limit of the number
of possible permutations, the significance level is exact. The
approximate significance level is the sample mean number of times the
statistic of the permutated lists varies from the actual statistic of
the unpermuted argument lists.

:return: a tuple containing an approximate significance level, the count
of the number of times the pseudo-statistic varied from the
actual statistic, and the number of shuffles
:rtype: tuple
:param a: a list of test values
:type a: list
:param b: another list of independently generated test values
:type b: list
"""
shuffles = kwargs.get("shuffles", 999)
# there's no point in trying to shuffle beyond all possible permutations
shuffles = min(shuffles, reduce(operator.mul, range(1, len(a) + len(b) + 1)))
stat = kwargs.get("statistic", lambda lst: sum(lst) / len(lst))
verbose = kwargs.get("verbose", False)

if verbose:
print("shuffles: %d" % shuffles)

actual_stat = fabs(stat(a) - stat(b))

if verbose:
print("actual statistic: %f" % actual_stat)
print("-" * 60)

c = 1e-100
lst = LazyConcatenation([a, b])
indices = list(range(len(a) + len(b)))

for i in range(shuffles):
if verbose and i % 10 == 0:
print("shuffle: %d" % i)

shuffle(indices)

pseudo_stat_a = stat(LazyMap(lambda i: lst[i], indices[: len(a)]))
pseudo_stat_b = stat(LazyMap(lambda i: lst[i], indices[len(a) :]))
pseudo_stat = fabs(pseudo_stat_a - pseudo_stat_b)

if pseudo_stat >= actual_stat:
c += 1

if verbose and i % 10 == 0:
print("pseudo-statistic: %f" % pseudo_stat)
print("significance: %f" % ((c + 1) / (i + 1)))
print("-" * 60)

significance = (c + 1) / (shuffles + 1)

if verbose:
print("significance: %f" % significance)
if betai:
for phi in [0.01, 0.05, 0.10, 0.15, 0.25, 0.50]:
print(f"prob(phi<={phi:f}): {betai(c, shuffles, phi):f}")

return (significance, c, shuffles)

[docs]def demo():
print("-" * 75)
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("Reference =", reference)
print("Test    =", test)
print("Accuracy:", accuracy(reference, test))

print("-" * 75)
reference_set = set(reference)
test_set = set(test)
print("Reference =", reference_set)
print("Test =   ", test_set)
print("Precision:", precision(reference_set, test_set))
print("   Recall:", recall(reference_set, test_set))
print("F-Measure:", f_measure(reference_set, test_set))
print("-" * 75)

if __name__ == "__main__":
demo()
```