def setup(self):
#prepare unit test. Load data etc
print("setting up " + __name__)
self.td = atleast_2d(arange(0, 10, 1)).T
self.tw = ones(10)
self.surprise = Surprise()
self.tdt1 = ([0.], [[1.]])
self.tdt2 = ([1.], [[0.5]])
self.tdt3 = ([1.], [[2.]])
class TestSurprise(object):
def setup(self):
#prepare unit test. Load data etc
print("setting up " + __name__)
self.td = atleast_2d(arange(0, 10, 1)).T
self.tw = ones(10)
self.surprise = Surprise()
self.tdt1 = ([0.], [[1.]])
self.tdt2 = ([1.], [[0.5]])
self.tdt3 = ([1.], [[2.]])
def test_weightedLoad(self):
res = self.surprise.load(self.td, self.tw)
assert allclose(res.mean, matrix(self.td.mean(0)))
assert allclose(res.cov, matrix(cov(self.td.T)))
assert allclose(res.icov, matrix(cov(self.td.T)).I)
def test_load(self):
res = self.surprise.load(self.td, None)
assert allclose(res[0], matrix(self.td.mean(0)))
assert allclose(res[1], matrix(cov(self.td.T)))
assert allclose(res[2], matrix(cov(self.td.T)).I)
def test_getExpectedRelEnt(self):
mode = ['add', 'replace', 'partial']
D = .5 + log(2)
ere = [log(2), log(2) + 1, log(2) + .5]
S = [.5, -.5, 0]
sD = [.5, 1.5, sqrt(255.) / 16.]
lams = [.5, 1.5, 15. / 16.]
dmus = [1., 1., 15. / 16.]
# numerical values from R
p = [0.1573089, 0.4142238, 0.3173187]
for i, m in enumerate(mode):
res = self.surprise(self.tdt1,
self.tdt2,
m,
self.tdt3,
getChi2=True,
bits=False)
assert allclose(D, res[0] * 2.)
assert allclose(ere[i], res[1] * 2.)
assert allclose(S[i], res[2] * 2.)
assert allclose(sD[i], res[3] * sqrt(2.))
assert allclose(lams[i], res[5])
assert allclose(dmus[i], res[6])
if self.surprise.rpy2:
assert allclose(p[i], res[4])
else:
assert res[4] is None
def teardown(self):
#tidy up
print("tearing down " + __name__)
pass
class TestSurprise(object):
def setup(self):
#prepare unit test. Load data etc
print("setting up " + __name__)
self.td=atleast_2d(arange(0,10,1)).T
self.tw=ones(10)
self.surprise=Surprise()
self.tdt1=([0.],[[1.]])
self.tdt2=([1.],[[0.5]])
self.tdt3=([1.],[[2.]])
def test_weightedLoad(self):
res = self.surprise.load(self.td, self.tw)
assert allclose(res.mean, matrix(self.td.mean(0)))
assert allclose(res.cov, matrix(cov(self.td.T)))
assert allclose(res.icov, matrix(cov(self.td.T)).I)
def test_load(self):
res = self.surprise.load(self.td, None)
assert allclose(res[0], matrix(self.td.mean(0)))
assert allclose(res[1], matrix(cov(self.td.T)))
assert allclose(res[2], matrix(cov(self.td.T)).I)
def test_getExpectedRelEnt(self):
mode = ['add', 'replace', 'partial']
D = .5 + log(2)
ere = [log(2), log(2) + 1, log(2) + .5]
S = [.5, -.5, 0]
sD = [.5, 1.5, sqrt(255.)/16.]
lams = [.5, 1.5, 15./16.]
dmus = [1., 1., 15./16.]
# numerical values from R
p = [0.1573089, 0.4142238, 0.3173187]
for i, m in enumerate(mode):
res = self.surprise(self.tdt1, self.tdt2, m, self.tdt3,
getChi2 = True, bits = False)
assert allclose(D, res[0]*2.)
assert allclose(ere[i], res[1]*2.)
assert allclose(S[i], res[2]*2.)
assert allclose(sD[i], res[3]*sqrt(2.))
assert allclose(lams[i], res[5])
assert allclose(dmus[i], res[6])
if self.surprise.rpy2:
assert allclose(p[i], res[4])
else:
assert res[4] is None
def teardown(self):
#tidy up
print("tearing down " + __name__)
pass
def setup(self):
#prepare unit test. Load data etc
print("setting up " + __name__)
self.td=atleast_2d(arange(0,10,1)).T
self.tw=ones(10)
self.surprise=Surprise()
self.tdt1=([0.],[[1.]])
self.tdt2=([1.],[[0.5]])
self.tdt3=([1.],[[2.]])
from player import Player
import Certificates
from dice import Dice
import board
import numpy as np
from colorama import init, Fore, Back, Style
import sys
import time
import datetime
ROLLING = "-- You rolled a %s --"
START = "--- Welcome to The Package Arrived game.--- \nYou are positioned at (%s,%s)"
### Game Objects ###
board_game = board.Board().transition_dict
surprise_generator = Surprise()
def print_plan(plan, logs):
"""
Prints the plan to the screen and to the log file
:param plan: the plan
:param logs: the log file
"""
for a in plan:
if type(a) != str:
a = a.name
print(a)
write_to_log(a, logs)
#!/usr/bin/env python
"""
Uses surprise on a toy example.
"""
from surprise import Surprise
from numpy.random.mtrand import randn, randint
from matplotlib.mlab import entropy
sc = Surprise()
# Create two samples from a standard normal distribution
# Reshape into (# of samples, # of dimensions) array
n = 100
sample1 = randn(n).reshape(-1, 1)
sample2 = randn(n).reshape(-1, 1)
# Mode is 'replace', i.e. we are assuming that the two distributions
# are separately analysed posteriors.
mode = 'replace'
# Calculate entropy numbers with surprise
rel_ent, exp_rel_ent, S, sD, p = sc(sample1, sample2, mode=mode)
print('Entropy estimates for two standard normal distributions.')
print('Relative entropy D: %f' % rel_ent)
print('Expected relative entropy <D>: %f' % exp_rel_ent)
print('Surprise S: %f' % S)
print('Expected fluctuations of relative entropy sigma(D): %f' % sD)
print('p-value of Surprise: %f' % p)
def IterativeEntropy(pri_data, post_data, iterations, mode='add'):
"""
Algorithm used to iteratively compute the relative entropy based on
gaussianisation of both the prior and the posterior distribution.
Args:
pri_data (ndarray): Data array of shape (n, m) where n is #variats and
m is #observations
post_data (ndarray): Data array of shape (n, m) where n is #variats
and m is #observations
iterations (int): Number of iterations
mode (str): relation between dist1 and dist2; either
* 'add' if dist1 is the prior of dist2
* 'replace' if dist1 and dist2 are independently derived
posteriors and the prior is much wider than the constraints
Default: 'add'
Returns:
prior (ndarray): Resulting data from iterative Box-Cox transformation
posterior (ndarray): Resulting data from iterative Box-Cox transformation
cach_rel_ent (list): Entropy computed after each Box-Cox transformation
cach_exp_ent (list): Expected Entropy computed after each Box-Cox transformation
cach_S (list): Surprise computed after each Box-Cox transformation
cach_sD (list): Standard deviation computed after each Box-Cox transformation
BoxCoxError (bool): True if Box-Cox failed
"""
if not isinstance(mode, str) and mode in ["add", "replace"]:
raise Exception(
"Invalid kind value %s. Allowed format:"
"'add' or 'replace'", mode)
sc = Surprise()
cach_rel_ent = []
cach_exp_ent = []
cach_S = []
cach_sD = []
BoxCoxError = False
for steps in range(iterations):
if steps == 0:
prior, posterior, dim = standardise_data(pri_data.T,
post_data.T,
return_dim=True)
prior = prior.T
posterior = posterior.T
# Transform to positive parameter values
for k in range(dim):
prior_a = np.amin(prior[k, :])
post_a = np.amin(posterior[k, :])
if prior_a < post_a and prior_a < 0:
prior[k, :] -= prior_a
posterior[k, :] -= prior_a
elif post_a < 0:
prior[k, :] -= post_a
posterior[k, :] -= post_a
prior_a = np.amin(prior[k, :])
post_a = np.amin(posterior[k, :])
while prior_a <= 0 or post_a <= 0:
prior[k, :] += 5.0E-6
posterior[k, :] += 5.0E-6
prior_a = np.amin(prior[k, :])
post_a = np.amin(posterior[k, :])
# Find optimal one-parameter Box_Cox transformation
try:
lmbda = boxcox_normmax(prior[k, :],
brack=(-1.9, 2.0),
method='mle')
box_cox_prior = boxcox(prior[k, :], lmbda=lmbda)
prior[k, :] = box_cox_prior
box_cox_post = boxcox(posterior[k, :], lmbda=lmbda)
posterior[k, :] = box_cox_post
except RuntimeWarning:
logger.warning(
f"Box Cox transformation failed during step {steps}")
BoxCoxError = True
break
if BoxCoxError:
break
prior_mu = np.mean(prior, axis=1)
prior_std = np.std(prior, axis=1)
# Standardize data
prior = ((prior.T - prior_mu) / prior_std).T
posterior = ((posterior.T - prior_mu) / prior_std).T
if dim > 1:
# Rotate data into eigenbasis of the covar matrix
pri_cov = np.cov(prior)
# Compute eigenvalues
eVa, eVe = np.linalg.eig(pri_cov)
# Compute transformation matrix from eigen decomposition
R, S = eVe, np.diag(np.sqrt(eVa))
T = np.matmul(R, S).T
# Transform data with inverse transformation matrix T^-1
try:
inv_T = np.linalg.inv(T)
prior = np.matmul(prior.T, inv_T).T
posterior = np.matmul(posterior.T, inv_T).T
except np.linalg.LinAlgError:
logger.warning(
f"Singular matrix, inversion failed! Setting all output values for step {steps} to None"
)
cach_rel_ent.append(None)
cach_exp_ent.append(None)
cach_S.append(None)
cach_sD.append(None)
break
# Compute D, <D>, S and sigma(D)
try:
rel_ent, exp_rel_ent, S, sD, p = sc(prior.T,
posterior.T,
mode=mode)
except:
logger.warning(
f"Suprise() failed to compute the entropy values. Setting all output values for step {steps} to None"
)
rel_ent = None
exp_rel_ent = None
S = None
sD = None
cach_rel_ent.append(rel_ent)
cach_exp_ent.append(exp_rel_ent)
cach_S.append(S)
cach_sD.append(sD)
convergence_flag = 0
"""
Very empirical convergence criterions. Idee is, that the true entropy value of the probe is either found after
very vew transformations 1-3. First few transformations do not alter the computed entropy value by much, later
on the transformations push the computed entropy away from the true value. Or the probe gets truly gaussianised
by the transformation and the computed entropy value slowly converges to the true value i.e after 10+
transformations.
"""
if 6 > steps >= 1 and not None in cach_rel_ent[-2:]:
if cach_rel_ent[-1] > cach_rel_ent[-2] and abs(
cach_rel_ent[-1] -
cach_rel_ent[-2]) / cach_rel_ent[-1] < 0.035:
convergence_flag = 2
elif steps == 2 and not None in cach_rel_ent[-2:]:
if abs(cach_rel_ent[-1] -
cach_rel_ent[-2]) / cach_rel_ent[-1] < 0.001:
convergence_flag += 1
if abs(cach_rel_ent[-2] -
cach_rel_ent[-3]) / cach_rel_ent[-1] < 0.001:
convergence_flag += 1
elif steps == 3 and not None in cach_rel_ent[-3:]:
if abs(cach_rel_ent[-1] -
cach_rel_ent[-2]) / cach_rel_ent[-1] < 0.002:
convergence_flag += 1
if abs(cach_rel_ent[-1] -
cach_rel_ent[-3]) / cach_rel_ent[-1] < 0.008:
convergence_flag += 1
if steps > 3 and not None in cach_rel_ent[-4:]:
if abs(cach_rel_ent[-1] -
cach_rel_ent[-2]) / cach_rel_ent[-1] < 0.0002:
convergence_flag += 1
if abs(cach_rel_ent[-1] -
cach_rel_ent[-3]) / cach_rel_ent[-1] < 0.0005:
convergence_flag += 1
if abs(cach_rel_ent[-1] -
cach_rel_ent[-4]) / cach_rel_ent[-1] < 0.0008:
convergence_flag += 1
if convergence_flag >= 2:
logger.info(f"Convergence reached at step {steps}")
break
return prior, posterior, cach_rel_ent[-1], cach_exp_ent[-1], cach_S[
-1], cach_sD[-1], BoxCoxError
