246 lines
7.2 KiB
Python
246 lines
7.2 KiB
Python
import numpy as np
|
|
import pandas as pd
|
|
import matplotlib.pyplot as plt
|
|
from pyFTS.common import FuzzySet,SortedCollection,tree
|
|
from pyFTS.probabilistic import kde
|
|
|
|
|
|
class ProbabilityDistribution(object):
|
|
"""
|
|
Represents a discrete or continous probability distribution
|
|
If type is histogram, the PDF is discrete
|
|
If type is KDE the PDF is continuous
|
|
"""
|
|
def __init__(self, type = "KDE", **kwargs):
|
|
self.uod = kwargs.get("uod", None)
|
|
|
|
self.data = []
|
|
|
|
self.type = type
|
|
|
|
self.bins = kwargs.get("bins", None)
|
|
self.labels = kwargs.get("bins_labels", None)
|
|
|
|
data = kwargs.get("data", None)
|
|
|
|
if self.type == "KDE":
|
|
self.kde = kde.KernelSmoothing(kwargs.get("h", 0.5), kwargs.get("kernel", "epanechnikov"))
|
|
_min = np.nanmin(data)
|
|
_min = _min * .7 if _min > 0 else _min * 1.3
|
|
_max = np.nanmax(data)
|
|
_max = _max * 1.3 if _max > 0 else _max * .7
|
|
self.uod = [_min, _max]
|
|
|
|
self.nbins = kwargs.get("num_bins", 100)
|
|
|
|
if self.bins is None:
|
|
self.bins = np.linspace(int(self.uod[0]), int(self.uod[1]), int(self.nbins)).tolist()
|
|
self.labels = [str(k) for k in self.bins]
|
|
|
|
if self.uod is not None:
|
|
self.resolution = (self.uod[1] - self.uod[0]) / self.nbins
|
|
|
|
self.bin_index = SortedCollection.SortedCollection(iterable=sorted(self.bins))
|
|
self.quantile_index = None
|
|
self.distribution = {}
|
|
self.cdf = None
|
|
self.qtl = None
|
|
self.count = 0
|
|
for k in self.bins: self.distribution[k] = 0
|
|
|
|
if data is not None:
|
|
self.append(data)
|
|
|
|
self.name = kwargs.get("name", "")
|
|
|
|
def set(self, value, density):
|
|
k = self.bin_index.find_ge(value)
|
|
self.distribution[k] = density
|
|
|
|
def append(self, values):
|
|
if self.type == "histogram":
|
|
for k in values:
|
|
v = self.bin_index.find_ge(k)
|
|
self.distribution[v] += 1
|
|
self.count += 1
|
|
else:
|
|
self.data.extend(values)
|
|
self.distribution = {}
|
|
dens = self.density(self.bins)
|
|
for v,d in enumerate(dens):
|
|
self.distribution[self.bins[v]] = d
|
|
|
|
def append_interval(self, intervals):
|
|
if self.type == "histogram":
|
|
for interval in intervals:
|
|
for k in self.bin_index.inside(interval[0], interval[1]):
|
|
self.distribution[k] += 1
|
|
self.count += 1
|
|
|
|
def density(self, values):
|
|
ret = []
|
|
scalar = False
|
|
|
|
if not isinstance(values, list):
|
|
values = [values]
|
|
scalar = True
|
|
|
|
for k in values:
|
|
if self.type == "histogram":
|
|
v = self.bin_index.find_ge(k)
|
|
ret.append(self.distribution[v] / (self.count + 1e-5))
|
|
elif self.type == "KDE":
|
|
v = self.kde.probability(k, self.data)
|
|
ret.append(v)
|
|
else:
|
|
v = self.bin_index.find_ge(k)
|
|
ret.append(self.distribution[v])
|
|
|
|
if scalar:
|
|
return ret[0]
|
|
|
|
return ret
|
|
|
|
def differential_offset(self, value):
|
|
nbins = []
|
|
dist = {}
|
|
|
|
for k in self.bins:
|
|
nk = k+value
|
|
nbins.append(nk)
|
|
dist[nk] = self.distribution[k]
|
|
|
|
self.bins = nbins
|
|
self.distribution = dist
|
|
self.labels = [str(k) for k in self.bins]
|
|
|
|
self.bin_index = SortedCollection.SortedCollection(iterable=sorted(self.bins))
|
|
self.quantile_index = None
|
|
self.cdf = None
|
|
self.qtl = None
|
|
|
|
def expected_value(self):
|
|
return np.nansum([v * self.distribution[v] for v in self.bins])
|
|
|
|
def build_cdf_qtl(self):
|
|
ret = 0.0
|
|
self.cdf = {}
|
|
self.qtl = {}
|
|
for k in sorted(self.bins):
|
|
ret += self.density(k)
|
|
if k not in self.cdf:
|
|
self.cdf[k] = ret
|
|
|
|
if str(ret) not in self.qtl:
|
|
self.qtl[str(ret)] = []
|
|
|
|
self.qtl[str(ret)].append(k)
|
|
|
|
_keys = [float(k) for k in sorted(self.qtl.keys())]
|
|
|
|
self.quantile_index = SortedCollection.SortedCollection(iterable=_keys)
|
|
|
|
def cummulative(self, values):
|
|
if self.cdf is None:
|
|
self.build_cdf_qtl()
|
|
|
|
if isinstance(values, list):
|
|
ret = []
|
|
for val in values:
|
|
k = self.bin_index.find_ge(val)
|
|
ret.append(self.cdf[k])
|
|
else:
|
|
k = self.bin_index.find_ge(values)
|
|
return self.cdf[values]
|
|
|
|
def quantile(self, values):
|
|
if self.qtl is None:
|
|
self.build_cdf_qtl()
|
|
|
|
if isinstance(values, list):
|
|
ret = []
|
|
for val in values:
|
|
k = self.quantile_index.find_ge(val)
|
|
ret.append(self.qtl[str(k)][0])
|
|
else:
|
|
k = self.quantile_index.find_ge(values)
|
|
ret = self.qtl[str(k)]
|
|
|
|
return ret
|
|
|
|
def entropy(self):
|
|
h = -sum([self.distribution[k] * np.log(self.distribution[k]) if self.distribution[k] > 0 else 0
|
|
for k in self.bins])
|
|
return h
|
|
|
|
def crossentropy(self,q):
|
|
h = -sum([self.distribution[k] * np.log(q.distribution[k]) if self.distribution[k] > 0 else 0
|
|
for k in self.bins])
|
|
return h
|
|
|
|
def kullbackleiblerdivergence(self,q):
|
|
h = sum([self.distribution[k] * np.log(self.distribution[k]/q.distribution[k]) if self.distribution[k] > 0 else 0
|
|
for k in self.bins])
|
|
return h
|
|
|
|
def empiricalloglikelihood(self):
|
|
_s = 0
|
|
for k in self.bins:
|
|
if self.distribution[k] > 0:
|
|
_s += np.log(self.distribution[k])
|
|
return _s
|
|
|
|
def pseudologlikelihood(self, data):
|
|
|
|
densities = self.density(data)
|
|
|
|
_s = 0
|
|
for k in densities:
|
|
if k > 0:
|
|
_s += np.log(k)
|
|
return _s
|
|
|
|
def averageloglikelihood(self, data):
|
|
|
|
densities = self.density(data)
|
|
|
|
_s = 0
|
|
for k in densities:
|
|
if k > 0:
|
|
_s += np.log(k)
|
|
return _s / len(data)
|
|
|
|
def plot(self,axis=None,color="black",tam=[10, 6], title = None):
|
|
|
|
if axis is None:
|
|
fig = plt.figure(figsize=tam)
|
|
axis = fig.add_subplot(111)
|
|
|
|
if self.type == "histogram":
|
|
ys = [self.distribution[k]/self.count for k in self.bins]
|
|
else:
|
|
ys = [self.distribution[k] for k in self.bins]
|
|
yp = [0 for k in self.data]
|
|
axis.plot(self.data, yp, c="red")
|
|
|
|
if title is None:
|
|
title = self.name
|
|
axis.plot(self.bins, ys, c=color)
|
|
axis.set_title(title)
|
|
|
|
axis.set_xlabel('Universe of Discourse')
|
|
axis.set_ylabel('Probability')
|
|
|
|
def __str__(self):
|
|
ret = ""
|
|
for k in sorted(self.bins):
|
|
ret += str(round(k,2)) + ':\t'
|
|
if self.type == "histogram":
|
|
ret += str(round(self.distribution[k] / self.count,3))
|
|
elif self.type == "KDE":
|
|
ret += str(round(self.density(k),3))
|
|
else:
|
|
ret += str(round(self.distribution[k], 6))
|
|
ret += '\n'
|
|
return ret
|