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@Leguark
Leguark committed May 1, 2018
2 parents 77bd28a + af1cf68 commit 3b2c99d
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292 changes: 279 additions & 13 deletions gempy/decision_making.py
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"""

import numpy as np
import scipy.optimize as sop
from matplotlib import pyplot as plt

def loss_abs(estimate_s, true_s, u=1,o=1,u_f=1,o_f=1, r=1):
"""Absolute-error loss function.
Args:
estimate_s (int, float or np.array): Score estimate.
true_s (int, float or np.array): True score value.
estimate_s (int or float): Value estimate.
true_s (int, float or np.array): True value.
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int, float or np.array, optional): Risk-affinity re-weighting factor.
r (int or float, optional): Risk-affinity re-weighting factor.
Returns:
Loss incurred for an estimate of the score given a true score.
Based on absolute-error, i.e. the absolute distance of the estimate
Loss incurred for an estimate given a true value.
Based on absolute-error loss, i.e. the absolute distance of the estimate
from the true value.
true_s can be either a single value or an array of possible true values,
the output will be a single determined absolute loss value or an array of determined
loss values, accordingly.
estimate_s has to be one single value.
"""
true_s = np.array(true_s).astype(float)
loss_s = np.zeros_like(true_s)
underest = (estimate_s < true_s)
underest_fatal = (estimate_s == 0) & (true_s > 0)
overest = (estimate_s > true_s)
overest_fatal = (estimate_s > 0) & (true_s == 0)
loss_s[underest] = (true_s[underest] - estimate_s) * (u * r)
loss_s[underest_fatal] = (true_s[underest_fatal] - estimate_s) * (u_f * (r ** -0.5))
loss_s[underest] = (true_s[underest] - estimate_s) * (u * (r ** -0.5))
loss_s[overest] = (estimate_s - true_s[overest]) * (o * r)
loss_s[overest_fatal] = np.abs((true_s[overest_fatal] - estimate_s)) * (o_f * r)
if u_f != 1:
underest_fatal = (estimate_s <= 0) & (true_s > 0)
loss_s[underest_fatal] = (true_s[underest_fatal] - estimate_s) * (u_f * (r ** -0.5))
if o_f != 1:
overest_fatal = (estimate_s > 0) & (true_s <= 0)
loss_s[overest_fatal] = np.abs((true_s[overest_fatal] - estimate_s)) * (o_f * r)
return loss_s

def loss_abs_given_values(estimate_s, true_s, u=1,o=1,u_f=1,o_f=1, r=1):
"""Absolute-error loss function for the exclusive use with a single
given true value.
Args:
estimate_s (int or float): Value estimate.
true_s (int, float): True value.
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int or float, optional): Risk-affinity re-weighting factor.
Returns:
Loss incurred for an estimate given one determined true value.
Based on absolute-error loss, i.e. the absolute distance of the estimate
from the true value.
"""
if estimate_s < true_s:
if estimate_s <= 0 and true_s > 0:
loss_s = (true_s - estimate_s) * (u_f * (r ** -0.5)) # bad case of underestimation
else:
loss_s = (true_s - estimate_s) * (u * (r ** -0.5)) # normal underestimation
elif estimate_s > true_s:
if estimate_s > 0 and true_s <= 0:
loss_s = (estimate_s - true_s) * (o_f) # bad case of overestimation
else:
loss_s = (estimate_s - true_s) * (o * r) # normal overestimation
else:
loss_s = 0
return loss_s

def expected_loss(function='absolute', estimate_s, true_s, u=1,o=1,u_f=1,o_f=1, r=1):
def loss_sqr(estimate_s, true_s, u=1,o=1,u_f=1,o_f=1, r=1):
"""Squared-error loss function.
Args:
estimate_s (int or float): Value estimate.
true_s (int, float or np.array): True value.
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int or float, optional): Risk-affinity re-weighting factor.
Returns:
Loss incurred for an estimate of the value given a true value.
Based on squared-error loss, i.e. the absolute distance of the estimate
from the true value squared.
true_s can be either a single value or an array of possible true values,
the output will be a single determined absolute loss value or an array of determined
loss values, accordingly.
estimate_s has to be one single value.
"""
return np.square(loss_abs(estimate_s, true_s, u,o,u_f,o_f, r))

def loss_sqr_given_values(estimate_s, true_s, u=1,o=1,u_f=1,o_f=1, r=1):
"""Squared-error loss function for the exclusive use with a single
given true value.
Args:
estimate_s (int or float): Value estimate.
true_s (int, float): True value.
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int or float, optional): Risk-affinity re-weighting factor.
Returns:
Loss incurred for an estimate given one determined true value.
Based on squared-error loss, i.e. the absolute distance of the estimate
from the true value squared.
"""
return loss_abs_given_values(estimate_s, true_s, u,o,u_f,o_f, r)**2

def expected_loss_for_estimate(estimate_s, true_s, function='absolute', u=1,o=1,u_f=1,o_f=1, r=1):
"""Function to attain expected loss for an estimate
given a range of possible true values by taking the mean of all
possible loss realizations.
Args:
estimate_s (int or float): Value estimate.
true_s (int, float or np.array): True value.
function ('absolute'(default) or 'squared'): Use of absolute-error or
squared-error loss function.
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int or float, optional): Risk-affinity re-weighting factor.
Returns:
Expected loss for a single estimate given a range of possible true values.
Note: If only one possible true value is passed, the expected loss equals
the actually incurred loss.
"""

if function == 'absolute':
return loss_abs(estimate_s, true_s, u,o,u_f,o_f, r).mean()
elif function == 'squared':
return loss_sqr(estimate_s, true_s, u, o, u_f, o_f, r).mean()
else:
print('Error: Type of loss function not recognized. '
'Use "absolute" or "squared".)
'Use "absolute" or "squared".')

def expected_loss_for_range(estimate_range, true_s, function='absolute', u=1,o=1,u_f=1,o_f=1, r=1):
"""Function to attain expected loss and Bayes action based on an absolute-error or
squared error-loss function for a defined range of estimates.
Args:
estimate_range (np.array): Range of value estimates.
true_s (np.array): Array of possible true value occurrences (from a probability distribution)
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int, float or np.array, optional): Risk-affinity re-weighting factor.
Returns:
[0]: Expected loss for the range of estimates.
[1]: Bayes action (estimate with minimal expected loss)
[2]: Expected loss of Bayes action.
"""
expected_loss_s = lambda estimate_s, r: expected_loss_for_estimate(estimate_s, true_s, function, u, o, u_f, o_f, r)
loss_e = [expected_loss_s(e, r) for e in estimate_range]
bayes_action = sop.fmin(expected_loss_s, -40, args=(r,), disp=False)
bayes_action_loss_e = expected_loss_s(bayes_action, r)
return loss_e, bayes_action, bayes_action_loss_e

def expected_loss_plot(estimate_range, true_s, risk_range=1, function='absolute', u=1,o=1,u_f=1,o_f=1,
verbose=False):
"""Function to plot expected losses and the Bayes action for a range of estimates
relative to a distribution of possible true values.
It is possible to plot this for several risk factors at once.
Args:
estimate_range (np.array): Range of value estimates.
true_s (np.array): Array of possible true value occurrences (from a probability distribution)
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int, float or np.array, optional): Risk-affinity re-weighting factor.
Returns:
Plot of expected losses for risk neutrality
or several risk factors.
"""
ax = plt.subplot(111)
if isinstance(risk_range, (int,float)):
r_range=[risk_range]
else:
r_range=risk_range
for r in r_range:
loss_e, bayes_a, bayes_a_loss_e = expected_loss_for_range(estimate_range, true_s, function, u,o,u_f,o_f, r)
_color = next(ax._get_lines.prop_cycler)
plt.plot(estimate_range, loss_e, label="r =" + str(r), color=_color['color'])
plt.scatter(bayes_a, bayes_a_loss_e, s=70,
color=_color['color']) # , label = "Bayes action r "+str(r))
plt.vlines(bayes_a, 0, 10 * np.max(loss_e), color=_color['color'], linestyles="--")
if verbose == True:
print("Bayes action (minimum) at risk r %.2f: %.2f --- expected loss: %.2f"\
% (r, bayes_a, bayes_a_loss_e))
plt.legend(loc="upper left", scatterpoints=1, title="Legend")
plt.xlabel("Estimate")
plt.ylabel("Expected loss")
plt.xlim(estimate_range[0], estimate_range[-1])
plt.ylim(0, 1.1 * np.max(loss_e))
plt.grid()
plt.show()

def loss_for_estimate(estimate_s, true_s, function='absolute', u=1,o=1,u_f=1,o_f=1, r=1):
"""Function to attain actually incurred loss for an estimate
given a single true value.
Args:
estimate_s (int or float): Value estimate.
true_s (int or float): True value.
function ('absolute'(default) or 'squared'): Use of absolute-error or
squared-error loss function.
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int or float, optional): Risk-affinity re-weighting factor.
Returns:
Loss for a single estimate given a single determined true value.
"""
if function == 'absolute':
return loss_abs_given_values(estimate_s, true_s, u,o,u_f,o_f, r)
elif function == 'squared':
return loss_sqr_given_values(estimate_s, true_s, u, o, u_f, o_f, r)
else:
print('Error: Type of loss function not recognized. '
'Use "absolute" or "squared".')

#def sqr_loss()
def loss_for_range(estimate_range, true_s, function='absolute', u=1,o=1,u_f=1,o_f=1, r=1):
"""Function to attain loss and Bayes action based on an absolute-error or
squared error-loss function for a defined range of estimates
given one single true value.
Args:
estimate_range (np.array): Range of value estimates.
true_value (int or float): Array of possible true value occurrences (from a probability distribution)
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int, float or np.array, optional): Risk-affinity re-weighting factor.
Returns:
[0]: Loss for the range of estimates.
[1]: Bayes action (estimate with minimal expected loss)
[2]: Expected loss of Bayes action.
Note: Since the is only one possible true value,
the Bayes action will always equal this value.
"""
incurred_loss = lambda estimate_s, r: loss_for_estimate(estimate_s, true_s, function, u, o, u_f, o_f, r)
loss_i = [incurred_loss(e, r) for e in estimate_range]
bayes_action = sop.fmin(incurred_loss, -40, args=(r,), disp=False)
bayes_action_loss = incurred_loss(bayes_action, r)
return loss_i, bayes_action, bayes_action_loss

def loss_plot(estimate_range, true_s, risk_range=1, function='absolute', u=1,o=1,u_f=1,o_f=1,
verbose=False):
"""Function to plot losses for a range of estimates
relative to a single given true value.
It is possible to plot this for several risk factors at once.
Args:
estimate_range (np.array): Range of value estimates.
true_s (int or float): Array of possible true value occurrences (from a probability distribution)
u (int or float, optional): Underestimation re-weighting factor.
o (int or float, optional): Overestimation re-weighting factor.
u_f (int or float, optional): Fatal underestimation re-weighting factor.
o_f (int or float, optional): Fatal overestimation re-weighting factor.
r (int, float or np.array, optional): Risk-affinity re-weighting factor.
Returns:
Plot of losses for risk neutrality
or several risk factors given a single determined true value.
"""
ax = plt.subplot(111)
if isinstance(risk_range, (int,float)):
r_range=[risk_range]
else:
r_range=risk_range
for r in r_range:
loss_i, bayes_a, bayes_a_loss = loss_for_range(estimate_range, true_s, function, u,o,u_f,o_f, r)
_color = next(ax._get_lines.prop_cycler)
plt.plot(estimate_range, loss_i, label="r =" + str(r), color=_color['color'])
plt.scatter(bayes_a, bayes_a_loss, s=70,
color=_color['color']) # , label = "Bayes action r "+str(r))
plt.vlines(bayes_a, 0, 10 * np.max(loss_i), color=_color['color'], linestyles="--")
if verbose == True:
print("Bayes action (minimum) at risk r %.2f: %.2f --- expected loss: %.2f"\
% (r, bayes_a, bayes_a_loss))
plt.legend(loc="upper left", scatterpoints=1, title="Legend")
plt.xlabel("Estimate")
plt.ylabel("Expected loss")
plt.xlim(estimate_range[0], estimate_range[-1])
plt.ylim(0, 1.1 * np.max(loss_i))
plt.grid()
plt.show()

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