def main():
tau = pm.rdiscrete_uniform(0, 80)
print tau
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
print lambda_1, lambda_2
data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]
def plot_artificial_sms_dataset():
tau = pm.rdiscrete_uniform(0, 80)
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
data = np.r_[pm.rpoisson(lambda_1, tau),
pm.rpoisson(lambda_2, 80 - tau)]
plt.bar(np.arange(80), data, color="#348ABD")
plt.bar(tau - 1,
data[tau - 1],
color="r",
label="user behaviour changed")
plt.xlim(0, 80)
plt.title("More example of artificial datasets")
for i in range(1, 5):
plt.subplot(4, 1, i)
plot_artificial_sms_dataset()
plt.show()
def data_gen(samples_n=10, tau_start=75, tau_end=100, gamma=0.1):
alpha = 1.0 / gamma
for x in xrange(samples_n):
tau = pm.rdiscrete_uniform(tau_start, tau_end)
# lam = pm.rexponential(alpha)
lam = alpha
yield pm.rpoisson(lam, tau)
def plot_artificial_sms_dataset():
tau = pm.rdiscrete_uniform(0, 80)
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]
plt.bar(np.arange(80), data, color="#348ABD")
plt.bar(tau - 1, data[tau - 1], color="r", label="user behaviour changed")
plt.xlim(0, 80)
def plot_artificial_sms_dataset():
maxdays = 80
tau = pm.rdiscrete_uniform( 0, maxdays )
alpha = 1 / 20.
lambda_1, lambda_2 = pm.rexponential( alpha, 2 )
data = np.r_[
pm.rpoisson( lambda_1, tau ),
pm.rpoisson( lambda_2, maxdays-tau )]
plt.bar( np.arange(maxdays), data )
plt.bar( tau - 1, data[tau-1], color = 'r', label='change point' )
plt.xlim( 0, 80 )
def plot_artificail_sms_dataset():
#----------------------------------
# initialize both deterministic and stochastic variables
tau = pm.rdiscrete_uniform(0, 80)
print("tau = {0}".format(tau))
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
print("lambda_1 = {0}\nlambda_2 = {1}".format(lambda_1, lambda_2))
lambda_ = np.r_[lambda_1 * np.ones(tau), lambda_2 * np.ones(80 - tau)]
print("lambda = \n{0}".format(lambda_))
data = pm.rpoisson(lambda_)
print("data = \n{0}".format(data))
#-----------------------------------
# plot the artificial
plt.bar(np.arange(80), data, color="#348ABD")
plt.bar(tau - 1, data[tau - 1], color="r", label="user behavior changed")
plt.xlabel("Time(days)")
plt.ylabel("Text messages received")
plt.xlim(0, 80)
def plot_artifical_sms_dataset():
# specify when the user's behaviour (amount of sms received) switches by sampling from DiscreteUniform
tau = rdiscrete_uniform(0, 80)
print('τ = {}'.format(tau,))
alpha = 1. / 20.
lambda_1, lambda_2 = rexponential(alpha, 2)
print(lambda_1, lambda_2)
# for days before tau, repr. the user's received sms count by sampling from a
# Poisson(lambda_1), and for days after tau by sampling from Poisson(lambda_2)
data = np.r_[rpoisson(lambda_1, tau), rpoisson(lambda_2, 80 - tau)]
print(data)
# plot artificial data set
pyplot.bar(np.arange(80), data, color="#348ABD")
pyplot.bar(tau - 1, data[tau - 1], color="r", label="user behaviour changed")
pyplot.xlabel("time (days)")
pyplot.ylabel("count of sms received")
pyplot.xlim(0, 80)
pyplot.legend()
def data_gen_for_rnn(samples_n=1, tau_start=75, tau_end=100, gamma=0.01, var=5):
alpha = 1.0 / gamma
lam = alpha
for i in xrange(samples_n):
con = []
tau = pm.rdiscrete_uniform(tau_start, tau_end)
for j in xrange(tau):
if j == 0:
val = round(pm.rnormal(lam, var), 2)
con.append(val)
elif j == 1:
val = con[0] + pm.rnormal(0, var)
val = round(val, 2)
con.append(val)
else:
# n = len(con)
# lam_n = float(np.array(con).sum())/n
val = 0.7 * con[-1] + 0.3 * con[-2] + pm.rnormal(0, var)
val = round(val, 2)
con.append(val)
# print val, lam_n
yield con
def main():
tau = pm.rdiscrete_uniform(0, 80)
print tau
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
print lambda_1, lambda_2
data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]
def plot_artificial_sms_dataset():
tau = pm.rdiscrete_uniform(0, 80)
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]
plt.bar(np.arange(80), data, color="#348ABD")
plt.bar(tau - 1, data[tau - 1], color="r", label="user behaviour changed")
plt.xlim(0, 80)
plt.title("More example of artificial datasets")
for i in range(1, 5):
plt.subplot(4, 1, i)
plot_artificial_sms_dataset()
plt.show()
import numpy as np
import pymc as pm
from matplotlib import pyplot as plt
tau = pm.rdiscrete_uniform(0, 80)
print(tau)
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
print(lambda_1, lambda_2)
data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]
plt.bar(np.arange(80), data, color="#348ABD")
plt.bar(tau - 1, data[tau - 1], color="r", label="user behaviour changed")
plt.xlabel("Time (days)")
plt.ylabel("count of text-msgs received")
plt.title("Artificial dataset")
plt.xlim(0, 80)
plt.legend();
plt.show()
fixed_variable.value
# fix txt msg to observed data set
data = np.array( [10, 20, 15, 20, 49] )
obs = pm.Poisson( "obs", lambda_, value=data, observed=True )
obs.value
#
# Model class - analyze variables as a single unit
model = pm.Model( [obs, lambda_, lambda_1, lambda_2, taus] )
#
# Creating new datasets
#
maxdays = 80
tau = pm.rdiscrete_uniform( 0, maxdays )
alpha = 1 / 20.
lambda_1, lambda_2 = pm.rexponential( alpha, 2 )
data = np.r_[
pm.rpoisson( lambda_1, tau ),
pm.rpoisson( lambda_2, maxdays-tau )]
plt.bar( np.arange(maxdays), data )
plt.bar( tau - 1, data[tau-1], color = 'r', label='change point' )
plt.xlabel( "Time (days)" )
plt.ylabel( "count" )
plt.title( "Artificial Data" )
plt.xlim( 0, 80 )
plt.legend()
import numpy as np
import pymc as pm
from matplotlib import pyplot as plt
true_N = 500
D = pm.rdiscrete_uniform(1, true_N, size=10)
N = pm.DiscreteUniform("N", lower=D.max(), upper=10000)
observation = pm.DiscreteUniform("obs",
lower=0,
upper=N,
value=D,
observed=True)
model = pm.Model([observation, N])
mcmc = pm.MCMC(model)
mcmc.sample(40000, 10000, 1)
N_samples = mcmc.trace('N')[:]
# histogram of the samples:
plt.hist(N_samples, normed=True)
plt.show()
from IPython.core.pylabtools import figsize
from matplotlib import pyplot as plt
figsize(12.5, 4)
samples = [lambda_1.random() for i in range(20000)]
plt.hist(samples, bins=70, normed=True, histtype="stepfilled")
plt.title("Prior distribution for $\lambda_1$")
plt.xlim(0, 8);
# Take the case of the sms data in the previous chapter, knowing what we do
# about parent and child variables and taking an omniscient view on the data
# and determining a modeling procedure we can work backwards to create the
# data mimicing the expected creation of the data. i.e.
tau = pm.rdiscrete_uniform(0, 80)
print( tau )
alpha = 1. / 20.
lambda_1, lambda_2 = pm.rexponential(alpha, 2)
print( lambda_1, lambda_2)
data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]
# Plot the distribution
plt.bar(np.arange(80), data, color="#348ABD")
plt.bar(tau - 1, data[tau - 1], color="r", label="user behaviour changed")
plt.xlabel("Time (days)")
plt.ylabel("count of text-msgs received")
plt.title("Artificial dataset")
