QuaPy/quapy/functional.py

155 lines
6.1 KiB
Python

import itertools
from collections import defaultdict
import numpy as np
def artificial_prevalence_sampling(dimensions, n_prevalences=21, repeat=1, return_constrained_dim=False):
s = np.linspace(0., 1., n_prevalences, endpoint=True)
s = [s] * (dimensions - 1)
prevs = [p for p in itertools.product(*s, repeat=1) if sum(p)<=1]
if return_constrained_dim:
prevs = [p+(1-sum(p),) for p in prevs]
prevs = np.asarray(prevs).reshape(len(prevs), -1)
if repeat>1:
prevs = np.repeat(prevs, repeat, axis=0)
return prevs
def prevalence_linspace(n_prevalences=21, repeat=1, smooth_limits_epsilon=0.01):
"""
Produces a uniformly separated values of prevalence. By default, produces an array 21 prevalences, with step 0.05
and with the limits smoothed, i.e.:
[0.01, 0.05, 0.10, 0.15, ..., 0.90, 0.95, 0.99]
:param n_prevalences: the number of prevalence values to sample from the [0,1] interval (default 21)
:param repeat: number of times each prevalence is to be repeated (defaults to 1)
:param smooth_limits_epsilon: the quantity to add and subtract to the limits 0 and 1
:return: an array of uniformly separated prevalence values
"""
p = np.linspace(0., 1., num=n_prevalences, endpoint=True)
p[0] += smooth_limits_epsilon
p[-1] -= smooth_limits_epsilon
if p[0] > p[1]:
raise ValueError(f'the smoothing in the limits is greater than the prevalence step')
if repeat > 1:
p = np.repeat(p, repeat)
return p
def prevalence_from_labels(labels, classes_):
if labels.ndim != 1:
raise ValueError(f'param labels does not seem to be a ndarray of label predictions')
unique, counts = np.unique(labels, return_counts=True)
by_class = defaultdict(lambda:0, dict(zip(unique, counts)))
prevalences = np.asarray([by_class[class_] for class_ in classes_], dtype=np.float)
prevalences /= prevalences.sum()
return prevalences
def prevalence_from_probabilities(posteriors, binarize: bool = False):
if posteriors.ndim != 2:
raise ValueError(f'param posteriors does not seem to be a ndarray of posteior probabilities')
if binarize:
predictions = np.argmax(posteriors, axis=-1)
return prevalence_from_labels(predictions, np.arange(posteriors.shape[1]))
else:
prevalences = posteriors.mean(axis=0)
prevalences /= prevalences.sum()
return prevalences
def HellingerDistance(P, Q):
return np.sqrt(np.sum((np.sqrt(P) - np.sqrt(Q))**2))
def uniform_prevalence_sampling(n_classes, size=1):
if n_classes == 2:
u = np.random.rand(size)
u = np.vstack([1-u, u]).T
else:
# from https://cs.stackexchange.com/questions/3227/uniform-sampling-from-a-simplex
u = np.random.rand(size, n_classes-1)
u.sort(axis=-1)
_0s = np.zeros(shape=(size, 1))
_1s = np.ones(shape=(size, 1))
a = np.hstack([_0s, u])
b = np.hstack([u, _1s])
u = b-a
if size == 1:
u = u.flatten()
return u
#return np.asarray([uniform_simplex_sampling(n_classes) for _ in range(size)])
uniform_simplex_sampling = uniform_prevalence_sampling
def strprev(prevalences, prec=3):
return '['+ ', '.join([f'{p:.{prec}f}' for p in prevalences]) + ']'
def adjusted_quantification(prevalence_estim, tpr, fpr, clip=True):
den = tpr - fpr
if den == 0:
den += 1e-8
adjusted = (prevalence_estim - fpr) / den
if clip:
adjusted = np.clip(adjusted, 0., 1.)
return adjusted
def normalize_prevalence(prevalences):
prevalences = np.asarray(prevalences)
n_classes = prevalences.shape[-1]
accum = prevalences.sum(axis=-1, keepdims=True)
prevalences = np.true_divide(prevalences, accum, where=accum>0)
allzeros = accum.flatten()==0
if any(allzeros):
if prevalences.ndim == 1:
prevalences = np.full(shape=n_classes, fill_value=1./n_classes)
else:
prevalences[accum.flatten()==0] = np.full(shape=n_classes, fill_value=1./n_classes)
return prevalences
def num_prevalence_combinations(n_prevpoints:int, n_classes:int, n_repeats:int=1):
"""
Computes the number of prevalence combinations in the n_classes-dimensional simplex if nprevpoints equally distant
prevalences are generated and n_repeats repetitions are requested
:param n_classes: number of classes
:param n_prevpoints: number of prevalence points.
:param n_repeats: number of repetitions for each prevalence combination
:return: The number of possible combinations. For example, if n_classes=2, n_prevpoints=5, n_repeats=1, then the
number of possible combinations are 5, i.e.: [0,1], [0.25,0.75], [0.50,0.50], [0.75,0.25], and [1.0,0.0]
"""
__cache={}
def __f(nc,np):
if (nc,np) in __cache: # cached result
return __cache[(nc,np)]
if nc==1: # stop condition
return 1
else: # recursive call
x = sum([__f(nc-1, np-i) for i in range(np)])
__cache[(nc,np)] = x
return x
return __f(n_classes, n_prevpoints) * n_repeats
def get_nprevpoints_approximation(combinations_budget:int, n_classes:int, n_repeats:int=1):
"""
Searches for the largest number of (equidistant) prevalence points to define for each of the n_classes classes so that
the number of valid prevalences generated as combinations of prevalence points (points in a n_classes-dimensional
simplex) do not exceed combinations_budget.
:param n_classes: number of classes
:param n_repeats: number of repetitions for each prevalence combination
:param combinations_budget: maximum number of combinatios allowed
:return: the largest number of prevalence points that generate less than combinations_budget valid prevalences
"""
assert n_classes > 0 and n_repeats > 0 and combinations_budget > 0, 'parameters must be positive integers'
n_prevpoints = 1
while True:
combinations = num_prevalence_combinations(n_prevpoints, n_classes, n_repeats)
if combinations > combinations_budget:
return n_prevpoints-1
else:
n_prevpoints += 1