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gauss_mix.py
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gauss_mix.py
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import numpy as np
import pandas as pd
from scipy.stats import entropy, multivariate_normal
from sklearn.metrics import accuracy_score, confusion_matrix, f1_score, roc_auc_score, roc_curve
def generate_gauss_mix(
N=50000,
prior=(0.5, 0.5),
p=1,
mu_class0=0,
mu_class0_0=0,
mu_class0_1=5,
mu_class1=1,
mu_class1_0=0,
mu_class1_1=5,
sig_class0=1,
sig_class0_0=1,
sig_class0_1=1,
sig_class1=1,
sig_class1_0=1,
sig_class1_1=1,
split_class0=None,
split_class1=None,
):
class0_mix = True if split_class0 is not None else False
class1_mix = True if split_class1 is not None else False
prior_0, prior_1 = prior
p_class0, p_class1 = prior
n0 = int(N * prior_0) # number of samples from class 0
n1 = N - n0 # total number of samples from class 1
if class1_mix:
mixture_idx = np.random.choice(
2, N // 2, replace=True, p=split_class1
)
norm_params = [[mu_class1_0 * np.ones(p), np.identity(p) * sig_class1_0], [mu_class1_1 * np.ones(p), np.identity(p) * sig_class1_1]]
x_1 = np.fromiter(
(np.random.multivariate_normal(*(norm_params[i]), size=1) for i in mixture_idx),
dtype=np.dtype((float, p))
).reshape(N // 2, p)
else:
# p_class0, p_class1 = prior
mu_class1 = np.array([mu_class1] * p)
sig_class0 = np.identity(p) * sig_class0
sig_class1 = np.identity(p) * sig_class1
x_1 = np.random.multivariate_normal(mu_class1, sig_class1, size=n1)
if class0_mix:
mixture_idx = np.random.choice(
2, N // 2, replace=True, p=split_class0
)
norm_params = [[mu_class0_0 * np.ones(p), np.identity(p) * sig_class0_0], [mu_class0_1 * np.ones(p), np.identity(p) * sig_class0_1]]
x_0 = np.fromiter(
(np.random.multivariate_normal(*(norm_params[i]), size=1) for i in mixture_idx),
dtype=np.dtype((float, p))
).reshape(N // 2, p)
else:
mu_class0 = np.array([mu_class0] * p)
x_0 = np.random.multivariate_normal(mu_class0, np.identity(p) * sig_class0, size=n0)
x = np.vstack((x_0, x_1))
y = np.array([0] * n0 + [1] * n1).reshape(-1, 1)
# Create the probability density functions (PDFs) for the two Gaussian distributions
if class0_mix:
pdf_class0_0 = multivariate_normal(mu_class1_0, sig_class1_0)
pdf_class0_1 = multivariate_normal(mu_class1_1, sig_class1_1)
p_x_given_class0_0 = pdf_class0_0.pdf(x)
p_x_given_class0_1 = pdf_class0_1.pdf(x)
p_x_given_class0 = (
split_class1[0] * p_x_given_class0_0 + split_class0[1] * p_x_given_class0_1
)
else:
pdf_class0 = multivariate_normal(mu_class0, sig_class0)
p_x_given_class0 = pdf_class0.pdf(x)
if class1_mix:
pdf_class1_0 = multivariate_normal(mu_class1_0, sig_class1_0)
pdf_class1_1 = multivariate_normal(mu_class1_1, sig_class1_1)
p_x_given_class1_0 = pdf_class1_0.pdf(x)
p_x_given_class1_1 = pdf_class1_1.pdf(x)
p_x_given_class1 = (
split_class1[0] * p_x_given_class1_0 + split_class1[1] * p_x_given_class1_1
)
else:
pdf_class1 = multivariate_normal(mu_class1, sig_class1)
p_x_given_class1 = pdf_class1.pdf(x)
p_x = p_x_given_class0 * p_class0 + p_x_given_class1 * p_class1
pos_class0 = p_x_given_class0 * p_class0 / p_x
pos_class1 = p_x_given_class1 * (1 - p_class0) / p_x
posterior = np.hstack((pos_class0.reshape(-1, 1), pos_class1.reshape(-1, 1)))
stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))
# if class0_mix:
# prior_y_0 = np.array([p_class0_0, p_class0_1])
# else:
# prior_y_0 = np.array(p_class0)
# if class1_mix:
# prior_y_1 = np.array([p_class1_0, p_class1_1])
# else:
# prior_y_1 = np.array(p_class1)
entropy_y = entropy(prior, base=np.exp(1))
correlation = np.corrcoef(x_0.T, x_1.T)
MI = entropy_y - stats_conen
auc = roc_auc_score(y, posterior[:, 1])
pauc_90 = roc_auc_score(y, posterior[:, 1], max_fpr=0.1)
pauc_98 = roc_auc_score(y, posterior[:, 1], max_fpr=0.02)
if MI == 0.0:
# replace the posterior with random numbers ~ U(0,1) to calculate the ROC curve
posterior_ = np.random.uniform(0, 1, size=(N, 2))
fpr, tpr, thresholds = roc_curve(
y, posterior_[:, 1], pos_label=1, drop_intermediate=False
)
else:
fpr, tpr, thresholds = roc_curve(
y, posterior[:, 1], pos_label=1, drop_intermediate=False
)
tpr_s = np.max(tpr[fpr <= 0.02])
y_pred = np.argmax(posterior, axis=1)
accuracy = accuracy_score(y, y_pred)
tn, fp, fn, tp = confusion_matrix(y, y_pred).ravel()
sensitivity = tp / (tp + fn)
specificity = tn / (tn + fp)
f1 = f1_score(y, y_pred)
statistics = {
# 'Correlation': correlation[0,1],
"Accuracy": accuracy,
# "F1": f1,
"MI": MI,
"AUC": auc,
# "pAUC_90": pauc_90,
# "pAUC_98": pauc_98,
"S@98": tpr_s,
# 'Sensitivity': sensitivity,
# 'Specificity': specificity,
# 'TN': tn,
# 'FP': fp,
# 'FN': fn,
# 'TP': tp
# "tpr": tpr,
# "fpr": fpr,
}
x_min, x_max = np.min(x), np.max(x)
# print(x_min, x_max)
xs = np.linspace(x_min - 1, x_max + 1, 1000)
pdf = pd.DataFrame()
pdf["x"] = xs
if class0_mix:
pdf["pdf_class0"] = split_class0[0] * pdf_class0_0.pdf(xs) + split_class0[1] * pdf_class0_1.pdf(xs)
else:
pdf["pdf_class0"] = pdf_class0.pdf(xs)
if class1_mix:
pdf["pdf_class1"] = split_class1[0] * pdf_class1_0.pdf(xs) + split_class1[1] * pdf_class1_1.pdf(xs)
else:
pdf["pdf_class1"] = pdf_class1.pdf(xs)
return x, y, posterior[:, 1], statistics, pdf