-
Notifications
You must be signed in to change notification settings - Fork 1
/
STAR_outliers_polishing_library.py
127 lines (111 loc) · 4.82 KB
/
STAR_outliers_polishing_library.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
import numpy as np
import os
import pdb
from copy import deepcopy as COPY
from matplotlib import pyplot as plt
from scipy.stats import norm
from scipy.stats import pearsonr
from scipy.stats import gaussian_kde as smooth
from scipy.stats import expon
from scipy.stats import norm
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# SECTION 2: Removes spikes from the data.
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
def remove_spikes(x, x_spiked, name, prefix, count, spikes, decreases):
x_unique, x_counts = np.unique(x, return_counts = True)
if np.max(x_counts)/np.sum(x_counts) < 0.5 or count == 3:
return(x, spikes, decreases)
decreases.append(1 - np.max(x_counts)/np.sum(x_counts))
new_spike = x_unique[np.argmax(x_counts)]
spikes.append(new_spike)
x = x[x != new_spike]
count += 1
return(remove_spikes(x, x_spiked, name, prefix,
count, spikes, decreases))
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# SECTION 2: code that corrects for various continuity violations.
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
def adjust_median_values(x, Q_vec):
dists_sub50, dists_sup50 = x - Q_vec[2], x - Q_vec[2]
dists_sub50[dists_sub50 >= 0] = -np.inf
dists_sup50[dists_sup50 <= 0] = np.inf
x_sub50 = x[np.argmax(dists_sub50)]
x_sup50 = x[np.argmin(dists_sup50)]
n_sub50 = np.sum(x == x_sub50)
n_sup50 = np.sum(x == x_sup50)
p_sup50 = n_sup50/(n_sup50 + n_sub50)
x2 = COPY(x)
n_50 = np.sum(x == Q_vec[2])
choices = [x_sub50, x_sup50]
p_vec = [1 - p_sup50, p_sup50]
x2[x == Q_vec[2]] = np.random.choice(choices, n_50, True, p_vec)
return(x2)
def get_fitted_quantiles(percentiles, fitted_cdf, range0,
qstart, qend, good_cdf_tails):
Q_vec = np.zeros(5)
if good_cdf_tails == True:
try:
Q_vec[0] = range0[np.where(fitted_cdf >= percentiles[0]/100)[0][0]]
except:
return(Q_vec)
else:
Q_vec[0] = qstart
Q_vec[1] = range0[np.where(fitted_cdf >= 0.25)[0][0]]
Q_vec[2] = range0[np.where(fitted_cdf >= 0.5)[0][0]]
Q_vec[3] = range0[np.where(fitted_cdf >= 0.75)[0][0]]
if good_cdf_tails == True:
Q_vec[4] = range0[np.where(fitted_cdf >= percentiles[4]/100)[0][0]]
else:
Q_vec[4] = qend
return(Q_vec)
def approximate_quantiles(x, percentiles):
"""
Purpose
-------
to smoothly approximate discrete distributions for
the purpose of computing quantiles when necessary.
Parameters
----------
x: numeric input numpy array
percentiles: list of percentiles at which quantiles are computed
from the x distribution's smooth approximation
bw_coef: smoothing parameter value that usually works well
Returns
-------
Q_vec: list of quantiles that were computed from the
x distribution's smooth approximation. Extreme
quantiles are taken from x when possible.
"""
q1, q5, q35, q65, q95, q99 = np.percentile(x, [0.5, 5, 35, 65, 95, 99.5])
qstart = np.percentile(x, percentiles[0])
spacer = (q99 - q1)/2.75
qend = np.percentile(x, percentiles[-1])
range1 = np.linspace(q1 - spacer, q35, 200)
range2 = np.linspace(q35, q65, 200)
range3 = np.linspace(q65, q99 + spacer, 200)
range0 = np.concatenate([range1[:-1], range2[:-1], range3])
x_bounded = x[np.logical_and(x >= q1, x <= q99)]
smooth_x = smooth(x_bounded, bw_method = 'silverman')(range0)
mid_x = (smooth_x[:-1] + smooth_x[1:])/2
integrand1 = (mid_x*(range0[1:] - range0[:-1]))
cdf1 = np.cumsum(integrand1)
good_bounds = np.abs(np.min(cdf1) - 0) + np.abs(np.max(cdf1) - 1) < 0.1
Q_vec = get_fitted_quantiles(percentiles, cdf1, range0, qstart, qend, True)
if good_bounds and len(np.unique(Q_vec)) == 5:
return(Q_vec)
for i in [0.01, 0.05, 0.1, 0.5, 1, 5, 10]:
smooth_x = smooth(x_bounded, bw_method = i)(range0)
mid_x = (smooth_x[:-1] + smooth_x[1:])/2
integrand1 = (mid_x*(range0[1:] - range0[:-1]))
cdf1 = np.cumsum(integrand1)
good_bounds = np.abs(np.min(cdf1) - 0) + np.abs(np.max(cdf1) - 1) < 0.1
Q_vec = get_fitted_quantiles(percentiles, cdf1, range0, qstart, qend, True)
if good_bounds and len(np.unique(Q_vec)) == 5:
return(Q_vec)
mu = np.mean(x)
sig = np.std(x)
return(norm(mu, sig).ppf(np.array(percentiles)/100))