155 lines
6.1 KiB
Python
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, n_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[ci] for ci in range(n_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, n_classes=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
|
|
|