NormalNN/sigmoid_norm.py at master · A4Vision/NormalNN · GitHub

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
127
128
129
130
131
132
133
134
135
136
137
138
139
140
import time

import itertools

print time.time()

import cPickle
import numpy as np
import scipy.stats
import matplotlib.pyplot as plt
import funcs
from sklearn import linear_model
import utils


def get_samples(sigmas, mus, N):
    coefs = []
    for sigma in sigmas:
        averages = []

        for mu in mus:
            averages.append(funcs.logit_norm_moments(mu, sigma)[0])

        averages = np.array(averages)
        logit_values = funcs.logit(averages)
        X = np.array([mus, np.ones_like(mus)]).T
        Y = logit_values
        regr = linear_model.LinearRegression(fit_intercept=False)
        regr.fit(X, Y)
        coefs.append(regr.coef_[0])
        print "score={} s={} coef={}".format(regr.score(X, Y), sigma, regr.coef_.tolist())
        # plt.plot(mus, logit_values, '>')
        # plt.plot(mus, mus * regr.coef_[0], '-*')
        # plt.show()
    return coefs


def find_expectation_of_sigmoid(mus, sigmas, N):
    coefs = get_samples(sigmas, mus, N)
    variances = sigmas ** 2
    X = np.stack([variances ** i for i in xrange(5)]).T
    Y = coefs
    regr = linear_model.LinearRegression(fit_intercept=False)
    regr.fit(X, Y)

    print "score={} coef={}".format(regr.score(X, Y), regr.coef_.tolist())
    Y2 = np.array((np.matrix(regr.coef_) * np.matrix(X).T))[0]
    plt.plot(sigmas, Y2, '-')
    plt.plot(sigmas, Y, '*')
    plt.show()


def calc_errors(mu, sigma, N):
    global good, bad
    x = np.random.normal(mu, sigma, size=N)
    z = funcs.sigmoid(x)
    avg = np.average(z)
    expected = [funcs.expectation_of_sigmoid_norm(mu, sigma, i) for i in xrange(len(funcs.l))]
    return [np.abs(e - avg) / (np.abs(e) + np.abs(avg)) for e in expected]


def main_verify_expectancy(mus, sigmas, N):
    print time.time()
    pairs = list(itertools.product(mus, sigmas))
    mus_flat = np.array([x[0] for x in pairs])
    sigmas_flat = np.array([x[1] for x in pairs])
    estimated_averages = funcs.expectation_of_sigmoid_norm(mus_flat, sigmas_flat)
    actual_averages = np.array([funcs.logit_norm_moments(mu, sigma)[0] for mu, sigma in pairs])
    utils.plot_3d(mus_flat, sigmas_flat, estimated_averages, actual_averages)
    utils.plot_3d(mus_flat, sigmas_flat, np.abs(estimated_averages - actual_averages) / (estimated_averages + actual_averages), None)


def calc_error(real, wanted):
    error = np.abs(real - wanted) / np.abs(wanted)
    return error


def main_verify_variance(points):
    # Note: When exceeding the interpolation range, (mu < -4 for instance)
    #       then the error is significant.
    errors_points = []
    for mu, variance, actual in points:
        estimate = funcs.variance_of_sigmoid_norm(mu, variance ** 0.5)
        error = calc_error(actual, estimate)
        errors_points.append((mu, variance, error, actual, estimate))
    x, y, relative_error, actual, estimate = np.array(errors_points).T
    utils.plot_3d(x, y, relative_error, None)
    utils.plot_3d(x, y, np.abs(actual - estimate), None)


def main_expectancy():
    mus = np.arange(-6, 6, 0.2)
    sigmas = np.sort(np.arange(0.01, 5., 0.03))
    funcs.precalc_logit_moments(mus, sigmas)
    find_expectation_of_sigmoid(mus, sigmas, 2 ** 16)
    main_verify_expectancy(mus, sigmas, 2 ** 17)


def variance_points(mus, sigmas):
    return [(x, y ** 2, w) for x, y, z, w in gen_points(mus, sigmas)]


def main_variance():
    mus = np.arange(-6, 6, 0.1)
    sigmas = np.sort(np.concatenate((np.arange(0.05, 0.2, 0.05), np.arange(0.01, 4., 0.1))))
    funcs.precalc_logit_moments(mus, sigmas)
    points = variance_points(mus, sigmas)
    # coefs = interpolate(points, 5, 5, True)
    # print 'coefs'
    # print coefs.tolist()
    main_verify_variance(points)


def interpolate(points, degree_x, degree_y, plot=False):
    x, y, z = np.array(points).T
    x_powers = [x ** i for i in xrange(degree_x)]
    y_powers = [y ** i for i in xrange(degree_y)]
    inputs = [x_powers[i] * y_powers[j] for i, j in itertools.product(range(degree_x), range(degree_y))]
    regr = linear_model.LinearRegression(fit_intercept=False, n_jobs=2)
    regr.fit(np.array(inputs).T, z)
    coefs = regr.coef_
    z_predicted = np.dot(coefs, np.array(inputs))
    if plot:
        utils.plot_3d(x, y, z, z_predicted)
        utils.plot_3d(x, y, z - z_predicted, None)
    return coefs


def gen_points(mus, sigmas):
    points = []
    for mu in mus:
        for sigma in sigmas:
            z = tuple(funcs.logit_norm_moments(mu, sigma))
            points.append((mu, sigma) + z)
    return points


if __name__ == '__main__':
    # main_expectancy()
    main_variance()