def _skewed_distributions(ax):
dist1 = scstats.norm()
dist2 = scstats.gumbel_l(loc = 2.0)
y1 = dist1.pdf(x)
y2 = dist2.pdf(x)
ax.plot(x, y1)
ax.fill_between(x, y1, alpha = 0.5, label = 'Before')
ax.plot(x, y2)
ax.fill_between(x, y2, alpha = 0.5, label = 'After')
ax.set_xlim((-5, 5))
ax.legend()
return ax
def sample(self, k):
X = self.gaussian.rvs(k)
# to unfirom
norm = stats.norm()
U = norm.cdf(X)
m1 = stats.gumbel_l()
m2 = stats.beta(a=10, b=2)
Y0 = m1.ppf(U[:, 0])
Y1 = m2.ppf(U[:, 1])
return (Y0, Y1)
def optimize_loc(res_loc, res_scale, load_distro, conf_target, eps):
"""Auxiliary function to be used with the scipy.optimize.bisect function
to find the location parameters of the resistance distribution that
matches a required confidence level.
res_loc, res_scale: locations and scale parameters of the distribution
load_distro: load distribution (frozen scipy.stats distribution)
conf_target: confidence level target
eps: limit integration domain where load and resistance pdfs are > eps"""
res_distro = ss.gumbel_l(loc=res_loc, scale=res_scale)
x, dx = np.linspace(min(load_distro.ppf(eps), res_distro.ppf(eps)),
max(load_distro.ppf(1 - eps), res_distro.ppf(1 - eps)),
2000,
retstep=True)
confidence = 1.0 - pfail(load_distro.pdf, res_distro.cdf, x, dx)
return confidence - conf_target
def __init__(self, mean, stdev, dtype='normal', weib_loc=0):
if dtype == 'normal':
self.dist = ss.norm(loc=mean, scale=stdev)
elif dtype == 'gumbel_r':
beta = stdev * sqrt(6) / pi
mu = mean - euler_gamma * beta
self.dist = ss.gumbel_r(loc=mu, scale=beta)
elif dtype == 'gumbel_l':
beta = stdev * sqrt(6) / pi
mu = mean + euler_gamma * beta
self.dist = ss.gumbel_l(loc=mu, scale=beta)
elif dtype == 'weibull':
self.dist = weibull(mean, stdev, weib_loc)
else:
print('Error dtype.')
def optimize_loc(res_loc, res_scale, load_distro, conf_target, eps):
"""Auxiliary function to be used with the scipy.optimize.bisect function
to find the location parameters of the resistance distribution that
matches a required confidence level.
res_loc, res_scale: locations and scale parameters of the distribution
load_distro: load distribution (frozen scipy.stats distribution)
conf_target: confidence level target
eps: limit integration domain where load and resistance pdfs are > eps"""
res_distro = ss.gumbel_l(loc=res_loc, scale=res_scale)
x, dx = np.linspace(
min(load_distro.ppf(eps), res_distro.ppf(eps)),
max(load_distro.ppf(1-eps), res_distro.ppf(1-eps)),
2000, retstep=True)
confidence = 1.0 - pfail(load_distro.pdf, res_distro.cdf, x, dx)
return confidence - conf_target
def __init__(self, mean, stdev, dtype='normal', weib_loc=0):
if dtype == 'normal':
self.dist = ss.norm(loc=mean, scale=stdev)
elif dtype == 'gumbel_r':
beta = stdev*sqrt(6)/pi
mu = mean - euler_gamma * beta
self.dist = ss.gumbel_r(loc=mu, scale=beta)
elif dtype == 'gumbel_l':
beta = stdev*sqrt(6)/pi
mu = mean + euler_gamma * beta
self.dist = ss.gumbel_l(loc=mu, scale=beta)
elif dtype == 'weibull':
self.dist = weibull(mean, stdev, weib_loc)
else:
print('Error dtype.')
(len(bad_sample) - 1) / len(bad_sample), len(bad_sample)))),
'*')
##
## Using Kolmogorov-Smirnov test
## The D statistic is the absolute max distance (supremum) between the CDFs of the two samples.
## The closer this number is to 0 the more likely it is that the two samples were drawn from the
## same distribution.
## The p-value returned by the k-s test has the same interpretation as other p-values. You reject
## the null hypothesis that the two samples were drawn from the same distribution if the p-value
## is less than your significance level. You can find tables online for the conversion of the
## D statistic into a p-value if you are interested in the procedure.
##
##
stats, pvalue = ss.kstest(rvs=good_sample,
cdf=ss.gumbel_l(*ss.gumbel_l.fit(good_sample)).cdf)
print('The maximumdistance between CDFs is %.2f.' % stats, end='')
print('The sample is Gumbel distributed for a significance level of %.2f' %
pvalue)
stats, pvalue = ss.kstest(rvs=bad_sample,
cdf=ss.gumbel_l(*ss.gumbel_l.fit(bad_sample)).cdf)
print('The maximumdistance between CDFs is %.2f.' % stats, end='')
print('The sample is Gumbel distributed for a significance level of %.2f' %
pvalue)
##
## Using Anderson-Darling test
## The assumption regarding the distribution of the sample is rejected if the output value
## is larger than the critical values for the required significance level.
## For gumbel distributions, the critical values and significance levels are:
load_loc = 100 # location parameter for the load distribution
load_scale = 5 # scale parameter for the load distribution
res_scale = 3.5 # scale parameter for the resistance distribution
eps = 1e-8 # domain = pdf > eps, for load and resistance
# frozen load distribution
load_distro = ss.gumbel_r(loc=load_loc, scale=load_scale)
# finds the location parameter for the resistance distribution that
# gives the required conf_target
res_loc = sp.optimize.bisect(optimize_loc,
load_loc,
load_distro.ppf(1 - eps),
args=(res_scale, load_distro, conf_target,
eps))
# frozen resistance distribution
res_distro = ss.gumbel_l(loc=res_loc, scale=res_scale)
# recalculates the domain and the confidence level
x, dx = np.linspace(min(load_distro.ppf(eps), res_distro.ppf(eps)),
max(load_distro.ppf(1 - eps), res_distro.ppf(1 - eps)),
200,
retstep=True)
confidence = 1.0 - pfail(load_distro.pdf, res_distro.cdf, x, dx)
# %% plotting
plt.plot(x, load_distro.pdf(x), label='load pdf')
plt.plot(x, res_distro.pdf(x), label='resistance pdf')
plt.grid()
plt.legend(loc='best')
plt.show()
print('Confidence %.3f%%' % (100 * confidence))
pfailure = pfail_dblchk(load_distro.pdf, res_distro.pdf, x)
def case3(output=True):
accuracy_in_each_turn = list()
precision_in_each_turn_spam = list()
recall_in_each_turn_spam = list()
precision_in_each_turn_ham = list()
recall_in_each_turn_ham = list()
m = np.loadtxt(open("resources/normalized_data.csv", "rb"), delimiter=',')
shuffled = np.random.permutation(m)
valid.validate_cross_validation(NUMBER_OF_ROUNDS, TRAIN_TEST_RATIO)
# equiprobable priors
prior_spam = 0.5
prior_ham = 0.5
for i in xrange(NUMBER_OF_ROUNDS):
# we're using cross-validation so each iteration we take a different
# slice of the data to serve as test set
train_set, test_set = prep.split_sets(shuffled, TRAIN_TEST_RATIO, i)
#parameter estimation
#but now we take ALL attributes into consideration
sample_means_word_spam = list()
sample_means_word_ham = list()
sample_variances_word_spam = list()
sample_variances_word_ham = list()
# all but the last one
for attr_index in xrange(57):
sample_means_word_spam.append(
nb.take_mean_spam(train_set, attr_index, SPAM_ATTR_INDEX))
sample_means_word_ham.append(
nb.take_mean_ham(train_set, attr_index, SPAM_ATTR_INDEX))
sample_variances_word_spam.append(
nb.take_variance_spam(train_set, attr_index, SPAM_ATTR_INDEX))
sample_variances_word_ham.append(
nb.take_variance_ham(train_set, attr_index, SPAM_ATTR_INDEX))
#sample standard deviations from sample variances
sample_std_devs_spam = map(lambda x: x**(1 / 2.0),
sample_variances_word_spam)
sample_std_devs_ham = map(lambda x: x**(1 / 2.0),
sample_variances_word_ham)
hits = 0.0
misses = 0.0
#number of instances correctly evaluated as spam
correctly_is_spam = 0.0
#total number of spam instances
is_spam = 0.0
#total number of instances evaluated as spam
guessed_spam = 0.0
#number of instances correctly evaluated as ham
correctly_is_ham = 0.0
#total number of ham instances
is_ham = 0.0
#total number of instances evaluated as ham
guessed_ham = 0.0
# now we test the hypothesis against the test set
for row in test_set:
# ou seja, o produto de todas as prob. condicionais das palavras dada a classe
# eu sei que ta meio confuso, mas se olhar com cuidado eh bonito fazer isso tudo numa linha soh! =)
product_of_all_conditional_probs_spam = reduce(
lambda acc, cur: acc * stats.gumbel_l(
sample_means_word_spam[cur], sample_std_devs_spam[cur]).
pdf(row[CASE_2_ATTRIBUTE_INDEXES[cur]]), xrange(10), 1)
# nao precisa dividir pelo termo de normalizacao pois so queremos saber qual e o maior!
posterior_spam = prior_spam * product_of_all_conditional_probs_spam
product_of_all_conditional_probs_ham = reduce(
lambda acc, cur: acc * stats.gumbel_l(
sample_means_word_ham[cur], sample_std_devs_ham[cur]).pdf(
row[CASE_2_ATTRIBUTE_INDEXES[cur]]), xrange(10), 1)
posterior_ham = prior_ham * product_of_all_conditional_probs_ham
# whichever is greater - that will be our prediction
if posterior_spam > posterior_ham:
guess = 1
else:
guess = 0
if (row[SPAM_ATTR_INDEX] == guess):
hits += 1
else:
misses += 1
# we'll use these to calculate metrics
if (row[SPAM_ATTR_INDEX] == 1):
is_spam += 1
if guess == 1:
guessed_spam += 1
correctly_is_spam += 1
else:
guessed_ham += 1
else:
is_ham += 1
if guess == 1:
guessed_spam += 1
else:
guessed_ham += 1
correctly_is_ham += 1
#accuracy = number of correctly evaluated instances/
# number of instances
#
#
accuracy = hits / (hits + misses)
#precision_spam = number of correctly evaluated instances as spam/
# number of spam instances
#
#
# in order to avoid divisions by zero in case nothing was found
if (is_spam == 0):
precision_spam = 0
else:
precision_spam = correctly_is_spam / is_spam
#recall_spam = number of correctly evaluated instances as spam/
# number of evaluated instances como spam
#
#
# in order to avoid divisions by zero in case nothing was found
if (guessed_spam == 0):
recall_spam = 0
else:
recall_spam = correctly_is_spam / guessed_spam
#precision_ham = number of correctly evaluated instances as ham/
# number of ham instances
#
#
# in order to avoid divisions by zero in case nothing was found
if (is_ham == 0):
precision_ham = 0
else:
precision_ham = correctly_is_ham / is_ham
#recall_ham = number of correctly evaluated instances as ham/
# number of evaluated instances como ham
#
#
# in order to avoid divisions by zero in case nothing was found
if (guessed_ham == 0):
recall_ham = 0
else:
recall_ham = correctly_is_ham / guessed_ham
accuracy_in_each_turn.append(accuracy)
precision_in_each_turn_spam.append(precision_spam)
recall_in_each_turn_spam.append(recall_spam)
precision_in_each_turn_ham.append(precision_ham)
recall_in_each_turn_ham.append(recall_ham)
# calculation of means for each metric at the end
mean_accuracy = np.mean(accuracy_in_each_turn)
std_dev_accuracy = np.std(accuracy_in_each_turn)
variance_accuracy = np.var(accuracy_in_each_turn)
mean_precision_spam = np.mean(precision_in_each_turn_spam)
std_dev_precision_spam = np.std(precision_in_each_turn_spam)
variance_precision_spam = np.var(precision_in_each_turn_spam)
mean_recall_spam = np.mean(recall_in_each_turn_spam)
std_dev_recall_spam = np.std(recall_in_each_turn_spam)
variance_recall_spam = np.var(recall_in_each_turn_spam)
mean_precision_ham = np.mean(precision_in_each_turn_ham)
std_dev_precision_ham = np.std(precision_in_each_turn_ham)
variance_precision_ham = np.var(precision_in_each_turn_ham)
mean_recall_ham = np.mean(recall_in_each_turn_ham)
std_dev_recall_ham = np.std(recall_in_each_turn_ham)
variance_recall_ham = np.var(recall_in_each_turn_ham)
if output:
print "\033[1;32m"
print '============================================='
print 'CASE 3 - ALL ATTRIBUTES - USING GUMBEL LEFT MODEL'
print '============================================='
print "\033[00m"
print 'MEAN ACCURACY: ' + str(round(mean_accuracy, 5))
print 'STD. DEV. OF ACCURACY: ' + str(round(std_dev_accuracy, 5))
print 'VARIANCE OF ACCURACY: ' + str(round(variance_accuracy, 8))
print ''
print 'MEAN PRECISION FOR SPAM: ' + str(round(mean_precision_spam, 5))
print 'STD. DEV. OF PRECISION FOR SPAM: ' + str(
round(std_dev_precision_spam, 5))
print 'VARIANCE OF PRECISION FOR SPAM: ' + str(
round(variance_precision_spam, 8))
print ''
print 'MEAN RECALL FOR SPAM: ' + str(round(mean_recall_spam, 5))
print 'STD. DEV. OF RECALL FOR SPAM: ' + str(
round(std_dev_recall_spam, 5))
print 'VARIANCE OF RECALL FOR SPAM: ' + str(
round(variance_recall_spam, 8))
print ''
print 'MEAN PRECISION FOR HAM: ' + str(round(mean_precision_ham, 5))
print 'STD. DEV. OF PRECISION FOR HAM: ' + str(
round(std_dev_precision_ham, 5))
print 'VARIANCE OF PRECISION FOR HAM: ' + str(
round(variance_precision_ham, 8))
print ''
print 'MEAN RECALL FOR HAM: ' + str(round(mean_recall_ham, 5))
print 'STD. DEV. OF RECALL FOR HAM: ' + str(
round(std_dev_recall_ham, 5))
print 'VARIANCE OF RECALL FOR HAM: ' + str(
round(variance_recall_ham, 8))
# 1.305*np.std(data_tp[data_tp['wd'] == wd][c])
# for wd in set(data_tp['wd'])])
# MLE's
mx = max([
ss.gumbel_r(*ss.gumbel_r.fit(data_tp[data_tp['wd'] == wd]
[c])).ppf(0.9)
for wd in set(data_tp['wd'])
])
else:
# # moment estimators
# mx = min([np.mean(data_tp[data_tp['wd'] == wd][c]) +
# 1.305*np.std(data_tp[data_tp['wd'] == wd][c])
# for wd in set(data_tp['wd'])])
# MLE's
mx = min([
ss.gumbel_l(*ss.gumbel_l.fit(data_tp[data_tp['wd'] == wd]
[c])).ppf(0.1)
for wd in set(data_tp['wd'])
])
rw.extend([mx])
stdev.loc[i] = rw
i += 1
# adjust and sort index
stdev = stdev.sort_index(by=['Hs', 'Tp'])
stdev = stdev.reset_index()
del stdev['index']
# %%
# this works, but how to apply +/- depending on max/min
stdev3 = (1.305 * data.groupby(['Hs', 'Tp', 'wd'])[['Tmax', 'Tmin']].std() +
data.groupby(['Hs', 'Tp', 'wd'])[['Tmax', 'Tmin']].mean()).max(
def case1(index=CASE_1_ATTRIBUTE_INDEX,output=True,ret='accuracy'):
accuracy_in_each_turn = list()
precision_in_each_turn_spam = list()
recall_in_each_turn_spam = list()
precision_in_each_turn_ham = list()
recall_in_each_turn_ham = list()
m = np.loadtxt(open("resources/normalized_data.csv","rb"),delimiter=',')
shuffled = np.random.permutation(m)
valid.validate_cross_validation(NUMBER_OF_ROUNDS,TRAIN_TEST_RATIO)
# equiprobable priors
prior_spam = 0.5
prior_ham = 0.5
for i in xrange(NUMBER_OF_ROUNDS):
# we're using cross-validation so each iteration we take a different
# slice of the data to serve as test set
train_set,test_set = prep.split_sets(shuffled,TRAIN_TEST_RATIO,i)
#parameter estimation
sample_mean_word_spam = nb.take_mean_spam(train_set,index,SPAM_ATTR_INDEX)
sample_mean_word_ham = nb.take_mean_ham(train_set,index,SPAM_ATTR_INDEX)
sample_variance_word_spam = nb.take_variance_spam(train_set,index,SPAM_ATTR_INDEX)
sample_variance_word_ham = nb.take_variance_ham(train_set,index,SPAM_ATTR_INDEX)
#sample standard deviations from sample variance
sample_std_dev_spam = sample_variance_word_spam ** (1/2.0)
sample_std_dev_ham = sample_variance_word_ham ** (1/2.0)
hits = 0.0
misses = 0.0
#number of instances corretcly evaluated as spam
correctly_is_spam = 0.0
#total number of spam instances
is_spam = 0.0
#total number of instances evaluated as spam
guessed_spam = 0.0
#number of instances correctly evaluated as ham
correctly_is_ham = 0.0
#total number of ham instances
is_ham = 0.0
#total number of instances evaluated as ham
guessed_ham = 0.0
# now we test the hypothesis against the test set
for row in test_set:
# nao precisa dividir pelo termo de normalizacao pois so queremos saber qual e o maior!
posterior_spam = prior_spam * stats.gumbel_l(sample_mean_word_spam, sample_std_dev_spam).pdf(row[index])
posterior_ham = prior_ham * stats.gumbel_l(sample_mean_word_ham, sample_std_dev_ham).pdf(row[index])
# whichever is greater - that will be our evaluation
if posterior_spam > posterior_ham:
guess = 1
else:
guess = 0
if(row[SPAM_ATTR_INDEX] == guess):
hits += 1
else:
misses += 1
# we'll use these to calculate metrics
if (row[SPAM_ATTR_INDEX] == 1 ):
is_spam += 1
if guess == 1:
guessed_spam += 1
correctly_is_spam += 1
else:
guessed_ham += 1
else:
is_ham += 1
if guess == 1:
guessed_spam += 1
else:
guessed_ham += 1
correctly_is_ham += 1
#accuracy = number of correctly evaluated instances/
# number of instances
#
#
accuracy = hits/(hits+misses)
#precision_spam = number of correctly evaluated instances as spam/
# number of spam instances
#
#
# in order to avoid divisions by zero in case nothing was found
if(is_spam == 0):
precision_spam = 0
else:
precision_spam = correctly_is_spam/is_spam
#recall_spam = number of correctly evaluated instances as spam/
# number of evaluated instances como spam
#
#
# in order to avoid divisions by zero in case nothing was found
if(guessed_spam == 0):
recall_spam = 0
else:
recall_spam = correctly_is_spam/guessed_spam
#precision_ham = number of correctly evaluated instances as ham/
# number of ham instances
#
#
# in order to avoid divisions by zero in case nothing was found
if(is_ham == 0):
precision_ham = 0
else:
precision_ham = correctly_is_ham/is_ham
#recall_ham = number of correctly evaluated instances as ham/
# number of evaluated instances como ham
#
#
# in order to avoid divisions by zero in case nothing was found
if(guessed_ham == 0):
recall_ham = 0
else:
recall_ham = correctly_is_ham/guessed_ham
accuracy_in_each_turn.append(accuracy)
precision_in_each_turn_spam.append(precision_spam)
recall_in_each_turn_spam.append(recall_spam)
precision_in_each_turn_ham.append(precision_ham)
recall_in_each_turn_ham.append(recall_ham)
# calculation of means for each metric at the end
mean_accuracy = np.mean(accuracy_in_each_turn)
std_dev_accuracy = np.std(accuracy_in_each_turn)
variance_accuracy = np.var(accuracy_in_each_turn)
mean_precision_spam = np.mean(precision_in_each_turn_spam)
std_dev_precision_spam = np.std(precision_in_each_turn_spam)
variance_precision_spam = np.var(precision_in_each_turn_spam)
mean_recall_spam = np.mean(recall_in_each_turn_spam)
std_dev_recall_spam = np.std(recall_in_each_turn_spam)
variance_recall_spam = np.var(recall_in_each_turn_spam)
mean_precision_ham = np.mean(precision_in_each_turn_ham)
std_dev_precision_ham = np.std(precision_in_each_turn_ham)
variance_precision_ham = np.var(precision_in_each_turn_ham)
mean_recall_ham = np.mean(recall_in_each_turn_ham)
std_dev_recall_ham = np.std(recall_in_each_turn_ham)
variance_recall_ham = np.var(recall_in_each_turn_ham)
if output:
print "\033[1;32m"
print '============================================='
print 'CASE 1 - ONE ATTRIBUTE - USING GUMBEL LEFT MODEL'
print '============================================='
print "\033[00m"
print 'MEAN ACCURACY: '+str(round(mean_accuracy,5))
print 'STD. DEV. OF ACCURACY: '+str(round(std_dev_accuracy,5))
print 'VARIANCE OF ACCURACY: '+str(round(variance_accuracy,8))
print ''
print 'MEAN PRECISION FOR SPAM: '+str(round(mean_precision_spam,5))
print 'STD. DEV. OF PRECISION FOR SPAM: '+str(round(std_dev_precision_spam,5))
print 'VARIANCE OF PRECISION FOR SPAM: '+str(round(variance_precision_spam,8))
print ''
print 'MEAN RECALL FOR SPAM: '+str(round(mean_recall_spam,5))
print 'STD. DEV. OF RECALL FOR SPAM: '+str(round(std_dev_recall_spam,5))
print 'VARIANCE OF RECALL FOR SPAM: '+str(round(variance_recall_spam,8))
print ''
print 'MEAN PRECISION FOR HAM: '+str(round(mean_precision_ham,5))
print 'STD. DEV. OF PRECISION FOR HAM: '+str(round(std_dev_precision_ham,5))
print 'VARIANCE OF PRECISION FOR HAM: '+str(round(variance_precision_ham,8))
print ''
print 'MEAN RECALL FOR HAM: '+str(round(mean_recall_ham,5))
print 'STD. DEV. OF RECALL FOR HAM: '+str(round(std_dev_recall_ham,5))
print 'VARIANCE OF RECALL FOR HAM: '+str(round(variance_recall_ham,8))
# we'll only use these return values to compute rankings
# for example in script which_attribute_case_1
if ret == 'utility':
return mean_accuracy * mean_precision_ham
elif ret =='accuracy':
return mean_accuracy
else:
print 'UNKNOWN METRIC: '+ret
sys.exit()
# Calculate a few first moments: mean, var, skew, kurt = gumbel_l.stats(moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(gumbel_l.ppf(0.01), gumbel_l.ppf(0.99), 100) ax.plot(x, gumbel_l.pdf(x), 'r-', lw=5, alpha=0.6, label='gumbel_l pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = gumbel_l() ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = gumbel_l.ppf([0.001, 0.5, 0.999]) np.allclose([0.001, 0.5, 0.999], gumbel_l.cdf(vals)) # True # Generate random numbers: r = gumbel_l.rvs(size=1000) # And compare the histogram: ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
print "mean = ", trace.mean()
for bin in [10,20,50,100]:
hist,bin_edges=np.histogram(trace,bins=bin)
a=np.argmax(hist)
print "maxlike = ", bin_edges[a], bin_edges[a+1], (bin_edges[a]+bin_edges[a+1])/2.0
plt.subplot(2,len(things)/2,plot_idx)
if plot_idx==2:
n, bins, patches = plt.hist(np.array(trace), 50, normed=1, facecolor='green', alpha=0.75)
X = sp.gumbel_l.fit(np.array(trace))
print X
dist = sp.gumbel_l(X[0],X[1])
x = np.array(bins)
y = dist.pdf(x)
print y
plt.plot(x, y,'k--',linewidth=2)
X = sp.norm.fit(np.array(trace))
print X
dist = sp.norm(X[0],X[1])
x = np.array(bins)
y = dist.pdf(x)
plt.plot(x, y,'r--',linewidth=2)
X = sp.genextreme.fit(np.array(trace))
print X
dist = sp.genextreme(X[0],X[1],X[2])
# -*- coding: utf-8 -*- """ Created on Thu Oct 5 20:20:31 2017 @author: raf """ import numpy as np from scipy import stats as ss from matplotlib import pyplot as plt import quantilelib as ql n = 50 sample = ss.gumbel_l.rvs(size=n, loc=100, random_state=1234) sample.sort() y = ql.llsurvivals(n) plt.plot(sample, y, 'o') # fit that shit params = ss.gumbel_l.fit(sample) fitted_gumbel = ss.gumbel_l(*params) # get two points for plotting x = sample.min(), sample.max() y = -np.log(-fitted_gumbel.logsf(x)) # plot this shit plt.plot(x, y)
for tail in [tailmax, tailmin]:
plt.figure()
title('TEST TITLE')
plt.subplot(221)
plt.hist(tail)
gumbel = best_fit(tail)
loc, scale = gumbel.fit(tail)
mygl = gumbel(loc=loc, scale=scale)
plt.subplot(222)
stats.probplot(tail,dist=mygl,plot=plt)
title('bets fit gumbel')
loc, scale = stats.gumbel_l.fit(tail)
mygl = stats.gumbel_l(loc=loc, scale=scale)
plt.subplot(223)
stats.probplot(tail,dist=mygl,plot=plt)
title('gumbel l')
loc, scale = stats.gumbel_r.fit(tail)
mygr = stats.gumbel_r(loc=loc, scale=scale)
plt.subplot(224)
stats.probplot(tail,dist=mygr,plot=plt)
title('gumbel r')
#import pandas
#
##list with the path to various results files from repeated lowering analyses
#with open('list_results.txt', 'r') as pf:
# list_results = pf.readlines()
# %%
Dx = 3.0
x = np.linspace(-4, 4, 100)
norm1 = scstats.norm()
norm2 = scstats.norm(loc = Dx)
fig, ax = plt.subplots(1, 1, figsize = (7, 5))
ax.plot(x, norm1.pdf(x), label = 'before')
ax.plot(x+Dx, norm2.pdf(x+Dx), label = 'after')
ax.set_xlim((-5, 5+Dx))
ax.set_ylim((-0.01, 1))
ax.legend()
plt.savefig("./figures/distribution_shift.png")
# %%
x = np.linspace(-4, 4, 100)
dist1 = scstats.norm()
dist2 = scstats.gumbel_l(loc = 1.5)
fig, ax = plt.subplots(1, 1, figsize = (7, 5))
ax.plot(x, dist1.pdf(x), label = 'before')
ax.plot(x, dist2.pdf(x), label = 'after')
ax.set_xlim((-5, 5))
ax.set_ylim((-0.01, 1))
ax.legend()
plt.savefig("./figures/distribution_skew.png")
# %%
import matplotlib.pyplot as plt
import scipy.stats as scstats
def Supplementary_Figure1A():
x = np.linspace(-4, 4, 100)
norm1 = scstats.norm(scale = 0.5)
norm2 = scstats.norm(scale = 1.0)
for tail in [tailmax, tailmin]:
plt.figure()
title('TEST TITLE')
plt.subplot(221)
plt.hist(tail)
gumbel = best_fit(tail)
loc, scale = gumbel.fit(tail)
mygl = gumbel(loc=loc, scale=scale)
plt.subplot(222)
stats.probplot(tail, dist=mygl, plot=plt)
title('bets fit gumbel')
loc, scale = stats.gumbel_l.fit(tail)
mygl = stats.gumbel_l(loc=loc, scale=scale)
plt.subplot(223)
stats.probplot(tail, dist=mygl, plot=plt)
title('gumbel l')
loc, scale = stats.gumbel_r.fit(tail)
mygr = stats.gumbel_r(loc=loc, scale=scale)
plt.subplot(224)
stats.probplot(tail, dist=mygr, plot=plt)
title('gumbel r')
#import pandas
#
##list with the path to various results files from repeated lowering analyses
#with open('list_results.txt', 'r') as pf:
# list_results = pf.readlines()
hist, bin_edges = np.histogram(trace, bins=bin)
a = np.argmax(hist)
print("maxlike = ", bin_edges[a], bin_edges[a + 1],
(bin_edges[a] + bin_edges[a + 1]) / 2.0)
plt.subplot(2, len(things) / 2, plot_idx)
if plot_idx == 2:
n, bins, patches = plt.hist(np.array(trace),
50,
normed=1,
facecolor='green',
alpha=0.75)
X = sp.gumbel_l.fit(np.array(trace))
print(X)
dist = sp.gumbel_l(X[0], X[1])
x = np.array(bins)
y = dist.pdf(x)
print(y)
plt.plot(x, y, 'k--', linewidth=2)
X = sp.norm.fit(np.array(trace))
print(X)
dist = sp.norm(X[0], X[1])
x = np.array(bins)
y = dist.pdf(x)
plt.plot(x, y, 'r--', linewidth=2)
X = sp.genextreme.fit(np.array(trace))
print(X)
dist = sp.genextreme(X[0], X[1], X[2])
def case1(index=CASE_1_ATTRIBUTE_INDEX, output=True, ret='accuracy'):
accuracy_in_each_turn = list()
precision_in_each_turn_spam = list()
recall_in_each_turn_spam = list()
precision_in_each_turn_ham = list()
recall_in_each_turn_ham = list()
m = np.loadtxt(open("resources/normalized_data.csv", "rb"), delimiter=',')
shuffled = np.random.permutation(m)
valid.validate_cross_validation(NUMBER_OF_ROUNDS, TRAIN_TEST_RATIO)
# equiprobable priors
prior_spam = 0.5
prior_ham = 0.5
for i in xrange(NUMBER_OF_ROUNDS):
# we're using cross-validation so each iteration we take a different
# slice of the data to serve as test set
train_set, test_set = prep.split_sets(shuffled, TRAIN_TEST_RATIO, i)
#parameter estimation
sample_mean_word_spam = nb.take_mean_spam(train_set, index,
SPAM_ATTR_INDEX)
sample_mean_word_ham = nb.take_mean_ham(train_set, index,
SPAM_ATTR_INDEX)
sample_variance_word_spam = nb.take_variance_spam(
train_set, index, SPAM_ATTR_INDEX)
sample_variance_word_ham = nb.take_variance_ham(
train_set, index, SPAM_ATTR_INDEX)
#sample standard deviations from sample variance
sample_std_dev_spam = sample_variance_word_spam**(1 / 2.0)
sample_std_dev_ham = sample_variance_word_ham**(1 / 2.0)
hits = 0.0
misses = 0.0
#number of instances corretcly evaluated as spam
correctly_is_spam = 0.0
#total number of spam instances
is_spam = 0.0
#total number of instances evaluated as spam
guessed_spam = 0.0
#number of instances correctly evaluated as ham
correctly_is_ham = 0.0
#total number of ham instances
is_ham = 0.0
#total number of instances evaluated as ham
guessed_ham = 0.0
# now we test the hypothesis against the test set
for row in test_set:
# nao precisa dividir pelo termo de normalizacao pois so queremos saber qual e o maior!
posterior_spam = prior_spam * stats.gumbel_l(
sample_mean_word_spam, sample_std_dev_spam).pdf(row[index])
posterior_ham = prior_ham * stats.gumbel_l(
sample_mean_word_ham, sample_std_dev_ham).pdf(row[index])
# whichever is greater - that will be our evaluation
if posterior_spam > posterior_ham:
guess = 1
else:
guess = 0
if (row[SPAM_ATTR_INDEX] == guess):
hits += 1
else:
misses += 1
# we'll use these to calculate metrics
if (row[SPAM_ATTR_INDEX] == 1):
is_spam += 1
if guess == 1:
guessed_spam += 1
correctly_is_spam += 1
else:
guessed_ham += 1
else:
is_ham += 1
if guess == 1:
guessed_spam += 1
else:
guessed_ham += 1
correctly_is_ham += 1
#accuracy = number of correctly evaluated instances/
# number of instances
#
#
accuracy = hits / (hits + misses)
#precision_spam = number of correctly evaluated instances as spam/
# number of spam instances
#
#
# in order to avoid divisions by zero in case nothing was found
if (is_spam == 0):
precision_spam = 0
else:
precision_spam = correctly_is_spam / is_spam
#recall_spam = number of correctly evaluated instances as spam/
# number of evaluated instances como spam
#
#
# in order to avoid divisions by zero in case nothing was found
if (guessed_spam == 0):
recall_spam = 0
else:
recall_spam = correctly_is_spam / guessed_spam
#precision_ham = number of correctly evaluated instances as ham/
# number of ham instances
#
#
# in order to avoid divisions by zero in case nothing was found
if (is_ham == 0):
precision_ham = 0
else:
precision_ham = correctly_is_ham / is_ham
#recall_ham = number of correctly evaluated instances as ham/
# number of evaluated instances como ham
#
#
# in order to avoid divisions by zero in case nothing was found
if (guessed_ham == 0):
recall_ham = 0
else:
recall_ham = correctly_is_ham / guessed_ham
accuracy_in_each_turn.append(accuracy)
precision_in_each_turn_spam.append(precision_spam)
recall_in_each_turn_spam.append(recall_spam)
precision_in_each_turn_ham.append(precision_ham)
recall_in_each_turn_ham.append(recall_ham)
# calculation of means for each metric at the end
mean_accuracy = np.mean(accuracy_in_each_turn)
std_dev_accuracy = np.std(accuracy_in_each_turn)
variance_accuracy = np.var(accuracy_in_each_turn)
mean_precision_spam = np.mean(precision_in_each_turn_spam)
std_dev_precision_spam = np.std(precision_in_each_turn_spam)
variance_precision_spam = np.var(precision_in_each_turn_spam)
mean_recall_spam = np.mean(recall_in_each_turn_spam)
std_dev_recall_spam = np.std(recall_in_each_turn_spam)
variance_recall_spam = np.var(recall_in_each_turn_spam)
mean_precision_ham = np.mean(precision_in_each_turn_ham)
std_dev_precision_ham = np.std(precision_in_each_turn_ham)
variance_precision_ham = np.var(precision_in_each_turn_ham)
mean_recall_ham = np.mean(recall_in_each_turn_ham)
std_dev_recall_ham = np.std(recall_in_each_turn_ham)
variance_recall_ham = np.var(recall_in_each_turn_ham)
if output:
print "\033[1;32m"
print '============================================='
print 'CASE 1 - ONE ATTRIBUTE - USING GUMBEL LEFT MODEL'
print '============================================='
print "\033[00m"
print 'MEAN ACCURACY: ' + str(round(mean_accuracy, 5))
print 'STD. DEV. OF ACCURACY: ' + str(round(std_dev_accuracy, 5))
print 'VARIANCE OF ACCURACY: ' + str(round(variance_accuracy, 8))
print ''
print 'MEAN PRECISION FOR SPAM: ' + str(round(mean_precision_spam, 5))
print 'STD. DEV. OF PRECISION FOR SPAM: ' + str(
round(std_dev_precision_spam, 5))
print 'VARIANCE OF PRECISION FOR SPAM: ' + str(
round(variance_precision_spam, 8))
print ''
print 'MEAN RECALL FOR SPAM: ' + str(round(mean_recall_spam, 5))
print 'STD. DEV. OF RECALL FOR SPAM: ' + str(
round(std_dev_recall_spam, 5))
print 'VARIANCE OF RECALL FOR SPAM: ' + str(
round(variance_recall_spam, 8))
print ''
print 'MEAN PRECISION FOR HAM: ' + str(round(mean_precision_ham, 5))
print 'STD. DEV. OF PRECISION FOR HAM: ' + str(
round(std_dev_precision_ham, 5))
print 'VARIANCE OF PRECISION FOR HAM: ' + str(
round(variance_precision_ham, 8))
print ''
print 'MEAN RECALL FOR HAM: ' + str(round(mean_recall_ham, 5))
print 'STD. DEV. OF RECALL FOR HAM: ' + str(
round(std_dev_recall_ham, 5))
print 'VARIANCE OF RECALL FOR HAM: ' + str(
round(variance_recall_ham, 8))
# we'll only use these return values to compute rankings
# for example in script which_attribute_case_1
if ret == 'utility':
return mean_accuracy * mean_precision_ham
elif ret == 'accuracy':
return mean_accuracy
else:
print 'UNKNOWN METRIC: ' + ret
sys.exit()
conf_target = 0.9 # confidence level of non-failure
load_loc = 100 # location parameter for the load distribution
load_scale = 5 # scale parameter for the load distribution
res_scale = 3.5 # scale parameter for the resistance distribution
eps = 1e-8 # domain = pdf > eps, for load and resistance
# frozen load distribution
load_distro = ss.gumbel_r(loc=load_loc, scale=load_scale)
# finds the location parameter for the resistance distribution that
# gives the required conf_target
res_loc = sp.optimize.bisect(optimize_loc, load_loc,
load_distro.ppf(1-eps),
args=(res_scale, load_distro,
conf_target, eps))
# frozen resistance distribution
res_distro = ss.gumbel_l(loc=res_loc, scale=res_scale)
# recalculates the domain and the confidence level
x, dx = np.linspace(min(load_distro.ppf(eps), res_distro.ppf(eps)),
max(load_distro.ppf(1-eps), res_distro.ppf(1-eps)),
200, retstep=True)
confidence = 1.0 - pfail(load_distro.pdf, res_distro.cdf, x, dx)
# %% plotting
plt.plot(x, load_distro.pdf(x), label='load pdf')
plt.plot(x, res_distro.pdf(x), label='resistance pdf')
plt.grid()
plt.legend(loc='best')
plt.show()
print('Confidence %.3f%%' % (100*confidence))
pfailure = pfail_dblchk(load_distro.pdf, res_distro.pdf, x)
print('Dbl check %.3f%%' % (100*(1-pfailure)))
def get_y(params, x, tail):
if tail == 'upper':
return -np.log(-ss.gumbel_r(*params).logcdf(x))
else:
return -np.log(-ss.gumbel_l(*params).logsf(x))
# -*- coding: utf-8 -*- """ Created on Thu Oct 5 20:20:31 2017 @author: raf """ import numpy as np from scipy import stats as ss from matplotlib import pyplot as plt import quantilelib as ql n = 50 sample = ss.gumbel_l.rvs(size=n, loc=100, random_state=1234) sample.sort() y = ql.llsurvivals(n) plt.plot(sample, y, 'o') # fit that shit params = ss.gumbel_l.fit(sample) fitted_gumbel = ss.gumbel_l(*params) # get two points for plotting x = sample.min(), sample.max() y = -np.log(-fitted_gumbel.logsf(x)) # plot this shit plt.plot(x, y)
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
plt.plot(bad_sample,
-log(-log(linspace(1/len(bad_sample), (len(bad_sample)-1)/len(bad_sample),
len(bad_sample)))), '*')
##
## Using Kolmogorov-Smirnov test
## The D statistic is the absolute max distance (supremum) between the CDFs of the two samples.
## The closer this number is to 0 the more likely it is that the two samples were drawn from the
## same distribution.
## The p-value returned by the k-s test has the same interpretation as other p-values. You reject
## the null hypothesis that the two samples were drawn from the same distribution if the p-value
## is less than your significance level. You can find tables online for the conversion of the
## D statistic into a p-value if you are interested in the procedure.
##
##
stats, pvalue = ss.kstest(rvs=good_sample, cdf=ss.gumbel_l(*ss.gumbel_l.fit(good_sample)).cdf)
print('The maximumdistance between CDFs is %.2f.' % stats, end='')
print('The sample is Gumbel distributed for a significance level of %.2f' % pvalue)
stats, pvalue = ss.kstest(rvs=bad_sample, cdf=ss.gumbel_l(*ss.gumbel_l.fit(bad_sample)).cdf)
print('The maximumdistance between CDFs is %.2f.' % stats, end='')
print('The sample is Gumbel distributed for a significance level of %.2f' % pvalue)
##
## Using Anderson-Darling test
## The assumption regarding the distribution of the sample is rejected if the output value
## is larger than the critical values for the required significance level.
## For gumbel distributions, the critical values and significance levels are:
## [0.456, 0.612, 0.728, 0.843, 0.998]
## [25.0, 10.0, 5.0, 2.5, 1.0]
## I.e, for a sample to be assumed Gumbel distributed with a significant level of 25%,
Ahora usaremos lo que aprendimos arriba para "uniformizar" las marginales.
Este diagrama conjunto suele ser cómo se visualizan las cópulas.
'''
norm = stats.norm()
x_unif = norm.cdf(x)
h = sns.jointplot(x_unif[:, 0], x_unif[:, 1], kind='hex', stat_func=None)
h.set_axis_labels('Y1', 'Y2', fontsize=16)
#%%
'''
Ahora solo transformamos los marginales nuevamente a lo que queremos
(Gumbel y Beta):
'''
m1 = stats.gumbel_l()
m2 = stats.beta(a=10, b=2)
x1_trans = m1.ppf(x_unif[:, 0])
x2_trans = m2.ppf(x_unif[:, 1])
h = sns.jointplot(x1_trans,
x2_trans,
kind='kde',
xlim=(-6, 2),
ylim=(.6, 1.0),
stat_func=None)
h.set_axis_labels('Maximum river level', 'Probablity of flooding', fontsize=16)
#%%
'''
def case2(indexes=CASE_2_ATTRIBUTE_INDEXES,output=True):
accuracy_in_each_turn = list()
precision_in_each_turn_spam = list()
recall_in_each_turn_spam = list()
precision_in_each_turn_ham = list()
recall_in_each_turn_ham = list()
m = np.loadtxt(open("resources/normalized_data.csv","rb"),delimiter=',')
shuffled = np.random.permutation(m)
valid.validate_cross_validation(NUMBER_OF_ROUNDS,TRAIN_TEST_RATIO)
# equiprobable priors
prior_spam = 0.5
prior_ham = 0.5
for i in xrange(NUMBER_OF_ROUNDS):
# we're using cross-validation so each iteration we take a different
# slice of the data to serve as test set
train_set,test_set = prep.split_sets(shuffled,TRAIN_TEST_RATIO,i)
#parameter estimation
#but now we take 10 attributes into consideration
sample_means_word_spam = list()
sample_means_word_ham = list()
sample_variances_word_spam = list()
sample_variances_word_ham = list()
for attr_index in indexes:
sample_means_word_spam.append(nb.take_mean_spam(train_set,attr_index,SPAM_ATTR_INDEX))
sample_means_word_ham.append(nb.take_mean_ham(train_set,attr_index,SPAM_ATTR_INDEX))
sample_variances_word_spam.append(nb.take_variance_spam(train_set,attr_index,SPAM_ATTR_INDEX))
sample_variances_word_ham.append(nb.take_variance_ham(train_set,attr_index,SPAM_ATTR_INDEX))
#sample standard deviations from sample variances
sample_std_devs_spam = map(lambda x: x ** (1/2.0), sample_variances_word_spam)
sample_std_devs_ham = map(lambda x: x ** (1/2.0), sample_variances_word_ham)
hits = 0.0
misses = 0.0
#number of instances correctly evaluated as spam
correctly_is_spam = 0.0
#total number of spam instances
is_spam = 0.0
#total number of instances evaluated as spam
guessed_spam = 0.0
#number of instances correctly evaluated as ham
correctly_is_ham = 0.0
#total number of ham instances
is_ham = 0.0
#total number of instances evaluated as ham
guessed_ham = 0.0
# now we test the hypothesis against the test set
for row in test_set:
# ou seja, o produto de todas as prob. condicionais das palavras dada a classe
# eu sei que ta meio confuso, mas se olhar com cuidado eh bonito fazer isso tudo numa linha soh! =)
product_of_all_conditional_probs_spam = reduce(lambda acc,cur: acc * stats.gumbel_l(sample_means_word_spam[cur], sample_std_devs_spam[cur]).pdf(row[indexes[cur]]) , xrange(10), 1)
# nao precisa dividir pelo termo de normalizacao pois so queremos saber qual e o maior!
posterior_spam = prior_spam * product_of_all_conditional_probs_spam
product_of_all_conditional_probs_ham = reduce(lambda acc,cur: acc * stats.gumbel_l(sample_means_word_ham[cur], sample_std_devs_ham[cur]).pdf(row[indexes[cur]]) , xrange(10), 1)
posterior_ham = prior_ham * product_of_all_conditional_probs_ham
# whichever is greater - that will be our prediction
if posterior_spam > posterior_ham:
guess = 1
else:
guess = 0
if(row[SPAM_ATTR_INDEX] == guess):
hits += 1
else:
misses += 1
# we'll use these to calculate metrics
if (row[SPAM_ATTR_INDEX] == 1 ):
is_spam += 1
if guess == 1:
guessed_spam += 1
correctly_is_spam += 1
else:
guessed_ham += 1
else:
is_ham += 1
if guess == 1:
guessed_spam += 1
else:
guessed_ham += 1
correctly_is_ham += 1
#accuracy = number of correctly evaluated instances/
# number of instances
#
#
accuracy = hits/(hits+misses)
#precision_spam = number of correctly evaluated instances as spam/
# number of spam instances
#
#
# in order to avoid divisions by zero in case nothing was found
if(is_spam == 0):
precision_spam = 0
else:
precision_spam = correctly_is_spam/is_spam
#recall_spam = number of correctly evaluated instances as spam/
# number of evaluated instances como spam
#
#
# in order to avoid divisions by zero in case nothing was found
if(guessed_spam == 0):
recall_spam = 0
else:
recall_spam = correctly_is_spam/guessed_spam
#precision_ham = number of correctly evaluated instances as ham/
# number of ham instances
#
#
# in order to avoid divisions by zero in case nothing was found
if(is_ham == 0):
precision_ham = 0
else:
precision_ham = correctly_is_ham/is_ham
#recall_ham = number of correctly evaluated instances as ham/
# number of evaluated instances como ham
#
#
# in order to avoid divisions by zero in case nothing was found
if(guessed_ham == 0):
recall_ham = 0
else:
recall_ham = correctly_is_ham/guessed_ham
accuracy_in_each_turn.append(accuracy)
precision_in_each_turn_spam.append(precision_spam)
recall_in_each_turn_spam.append(recall_spam)
precision_in_each_turn_ham.append(precision_ham)
recall_in_each_turn_ham.append(recall_ham)
# calculation of means for each metric at the end
mean_accuracy = np.mean(accuracy_in_each_turn)
std_dev_accuracy = np.std(accuracy_in_each_turn)
variance_accuracy = np.var(accuracy_in_each_turn)
mean_precision_spam = np.mean(precision_in_each_turn_spam)
std_dev_precision_spam = np.std(precision_in_each_turn_spam)
variance_precision_spam = np.var(precision_in_each_turn_spam)
mean_recall_spam = np.mean(recall_in_each_turn_spam)
std_dev_recall_spam = np.std(recall_in_each_turn_spam)
variance_recall_spam = np.var(recall_in_each_turn_spam)
mean_precision_ham = np.mean(precision_in_each_turn_ham)
std_dev_precision_ham = np.std(precision_in_each_turn_ham)
variance_precision_ham = np.var(precision_in_each_turn_ham)
mean_recall_ham = np.mean(recall_in_each_turn_ham)
std_dev_recall_ham = np.std(recall_in_each_turn_ham)
variance_recall_ham = np.var(recall_in_each_turn_ham)
if output:
print "\033[1;32m"
print '============================================='
print 'CASE 2 - TEN ATTRIBUTES - USING GUMBEL LEFT MODEL'
print '============================================='
print "\033[00m"
print 'MEAN ACCURACY: '+str(round(mean_accuracy,5))
print 'STD. DEV. OF ACCURACY: '+str(round(std_dev_accuracy,5))
print 'VARIANCE OF ACCURACY: '+str(round(variance_accuracy,8))
print ''
print 'MEAN PRECISION FOR SPAM: '+str(round(mean_precision_spam,5))
print 'STD. DEV. OF PRECISION FOR SPAM: '+str(round(std_dev_precision_spam,5))
print 'VARIANCE OF PRECISION FOR SPAM: '+str(round(variance_precision_spam,8))
print ''
print 'MEAN RECALL FOR SPAM: '+str(round(mean_recall_spam,5))
print 'STD. DEV. OF RECALL FOR SPAM: '+str(round(std_dev_recall_spam,5))
print 'VARIANCE OF RECALL FOR SPAM: '+str(round(variance_recall_spam,8))
print ''
print 'MEAN PRECISION FOR HAM: '+str(round(mean_precision_ham,5))
print 'STD. DEV. OF PRECISION FOR HAM: '+str(round(std_dev_precision_ham,5))
print 'VARIANCE OF PRECISION FOR HAM: '+str(round(variance_precision_ham,8))
print ''
print 'MEAN RECALL FOR HAM: '+str(round(mean_recall_ham,5))
print 'STD. DEV. OF RECALL FOR HAM: '+str(round(std_dev_recall_ham,5))
print 'VARIANCE OF RECALL FOR HAM: '+str(round(variance_recall_ham,8))
def get_y(params, x, tail):
if tail == 'upper':
return -np.log(-ss.gumbel_r(*params).logcdf(x))
else:
return -np.log(-ss.gumbel_l(*params).logsf(x))