/
support_funs_sens.py
168 lines (150 loc) · 5.93 KB
/
support_funs_sens.py
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"""
THIS SCRIPT CONTAINS THE SUPPORT FUNCTIONS NEEDED TO CARRY OUT SAP
"""
# Load necessary modules
import numpy as np
import pandas as pd
from scipy import stats
from scipy.stats import norm, t
from sklearn.utils import resample
from time import time
def beta_fun(n, pt, pm, alpha):
ta = stats.norm.ppf(1-alpha)
sigma_t = np.sqrt(pt*(1-pt)/n)
sigma_m = np.sqrt(pm*(1-pm)/n)
Phi = stats.norm.cdf( (sigma_t*ta-(pm-pt))/sigma_m )
return Phi
def perf_fun(*args, **kwargs):
"""
Function to calculate the performance metric of interest
1) You must use *args and **kwargs
2) 'thresh' must be one of the kwargs
3) This function must return a scalar
"""
assert len(args) == 2
assert 'thresh' in kwargs
thresh = kwargs['thresh']
y, score = args[0], args[1]
assert np.all( (y==0) | (y==1) )
assert thresh <= score.max()
yhat = np.where(score >= thresh, 1, 0)
sens = np.mean(yhat[y == 1])
return sens
# args=(df.y.values, df.score.values);kwargs={'target':0.8}
def thresh_find(*args, **kwargs):
"""
Function to find threshold for performance of interest
1) You must use *args and **kwargs
2) 'target' must be one of the kwargs. This is the value you want to get from perf_fun
3) 'jackknife' must be an optional argument in kwargs that will return the function output by leaving one observation out
See: https://en.wikipedia.org/wiki/Jackknife_resampling
Note that many statistics have fast way to calculate the jackknife beyond brute-force
4) This function must return a scalar, or a np.array is jackknife=True
"""
# --- assign --- #
jackknife = False
ret_df = False
if 'jackknife' in kwargs:
jackknife = kwargs['jackknife']
assert 'target' in kwargs
target = kwargs['target']
assert len(args) == 2
y, score = args[0], args[1]
assert len(y) == len(score)
assert np.all((y==0) | (y==1))
# --- Find quantile --- #
s1 = np.sort(score[y == 1])
n1 = len(s1)
n0 = len(y) - n1
sidx = np.arange(n1,0,-1) / n1
sidx = np.argmax(np.where(sidx >= target)[0])
tstar = np.quantile(s1, 1-target)
if jackknife:
# Effect of dropping an observation on the choice of the sensivity threshold
tstar0 = np.repeat(tstar, n0) # Zero class has no impact
tmed = np.quantile(np.delete(s1,sidx),1-target)
thigh = np.quantile(np.delete(s1,sidx-1),1-target)
tlow = np.quantile(np.delete(s1,sidx+1),1-target)
assert tlow <= tmed <= thigh
tstar1 = np.append(np.repeat(thigh,sidx), np.array([tmed]))
tstar1 = np.append(tstar1, np.repeat(tlow,n1-sidx-1))
tstar = np.append(tstar0, tstar1)
return tstar
def draw_samp(*args, strata=None):
"""
FUNCTION DRAWS DATA WITH REPLACEMENT (WITH STRATIFICATION IF DESIRED)
"""
args = list(args)
if strata is not None:
out = resample(*args, stratify=strata)
else:
out = resample(*args)
if len(args) == 1:
out = [out]
return out
class bootstrap():
def __init__(self, nboot, func):
self.nboot = nboot
self.stat = func
def fit(self, *args, mm=100, **kwargs):
strata=None
if 'strata' in kwargs:
strata = kwargs['strata']
# Get the baseline stat
self.theta = self.stat(*args, **kwargs)
self.store_theta = np.zeros(self.nboot)
self.jn = self.stat(*args, **kwargs, jackknife=True)
self.n = len(self.jn)
stime = time()
for ii in range(self.nboot): # Fit bootstrap
if (ii+1) % mm == 0:
nleft = self.nboot - (ii+1)
rtime = time() - stime
rate = (ii+1)/rtime
eta = nleft / rate
#print('Bootstrap %i of %i (ETA=%0.1f minutes)' % (ii+1, self.nboot, eta/60))
args_til = draw_samp(*args, strata=strata)
self.store_theta[ii] = self.stat(*args_til, **kwargs)
self.se = self.store_theta.std()
def get_ci(self, alpha=0.05, symmetric=True):
assert (symmetric==True) | (symmetric=='upper') | (symmetric=='lower')
self.di_ci = {'quantile':[], 'se':[], 'bca':[]}
self.di_ci['quantile'] = self.ci_quantile(alpha, symmetric)
self.di_ci['se'] = self.ci_se(alpha, symmetric)
self.di_ci['bca'] = self.ci_bca(alpha, symmetric)
def ci_quantile(self, alpha, symmetric):
if symmetric==True:
return np.quantile(self.store_theta, [alpha/2,1-alpha/2])
elif symmetric == 'lower':
return np.quantile(self.store_theta, alpha)
else:
return np.quantile(self.store_theta, 1-alpha)
def ci_se(self, alpha, symmetric):
if symmetric==True:
qq = t(df=self.n).ppf(1-alpha/2)
return np.array([self.theta - self.se*qq, self.theta + self.se*qq])
else:
qq = t(df=self.n).ppf(1-alpha)
if symmetric == 'lower':
return self.theta - qq*self.se
else:
return self.theta + qq*self.se
def ci_bca(self, alpha, symmetric):
if symmetric==True:
ql, qu = norm.ppf(alpha/2), norm.ppf(1-alpha/2)
else:
ql, qu = norm.ppf(alpha), norm.ppf(1-alpha)
# Acceleration factor
num = np.sum((self.jn.mean() - self.jn)**3)
den = 6*np.sum((self.jn.mean() - self.jn)**2)**1.5
self.ahat = num / den
# Bias correction factor
self.zhat = norm.ppf(np.mean(self.store_theta < self.theta))
self.a1 = norm.cdf(self.zhat + (self.zhat + ql)/(1-self.ahat*(self.zhat+ql)))
self.a2 = norm.cdf(self.zhat + (self.zhat + qu)/(1-self.ahat*(self.zhat+qu)))
if symmetric==True:
return np.quantile(self.store_theta, [self.a1, self.a2])
elif symmetric=='lower':
return np.quantile(self.store_theta, self.a1)
else:
return np.quantile(self.store_theta, self.a2)