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kliep.py
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kliep.py
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import matplotlib.pylab as plt
import numpy as np
import sys
# @editor: kang Liu
# email: [email protected]
class KLIEP():
def __init__(self, verbose=False):
self.verbose = verbose
pass
def fit(self, x_de, x_nu, x_re=None, sigma_chosen=0, b=100, fold=5):
"""
Kullback-Leiblar importance estimation procedure (with cross validation)估计概率密度比
:param x_de: d by n_de sample matrix corresponding to `denominator' (iid from density p_de)
:param x_nu: d by n_nu sample matrix corresponding to `numerator' (iid from density p_nu)
:param x_re: (OPTIONAL) d by n_re reference input matrix（参考输入矩阵）
:param sigma_chosen: (OPTIONAL) positive scalar representing Gaussian kernel width;
if omitted (or zero), it is automatically chosen by cross validation
:param b: (OPTINLAL) positive integer representing the number of kernels (default: 100);
:param fold:
:return: wh_x_de: estimates of density ratio w=p_nu/p_de at x_de
wh_x_re: estimates of density ratio w=p_nu/p_de at x_re (if x_re is provided)
"""
if len(np.shape(x_de)) == 1:
d = 1
n_de = np.shape(x_de)[0]
else:
d = np.shape(x_de)[0]
n_de = np.shape(x_de)[1]
if len(np.shape(x_nu)) == 1:
d_nu = 1
n_nu = np.shape(x_nu)[0]
else:
d_nu = np.shape(x_nu)[0]
n_nu = np.shape(x_nu)[1]
if d != d_nu:
sys.stderr.write('x_de and x_nu must have the same dimension')
if sigma_chosen < 0:
sys.stderr.write('Gaussian width must be positive')
if self.verbose == True:
print('Run KLIEP')
# Choosing Gaussian kernel center 'x_ce'
rand_index = np.random.permutation(n_nu)
# rand_index = np.loadtxt("D://rand_index.txt", delimiter=',', dtype=np.int32) - 1
# 返回从1：N随机排列的一维向量，这里取nu数据集的索引，随机排列
b = np.min([b, n_nu]) # 说明kernel数不会超过高斯核中心的数目
x_ce = x_nu[:, rand_index[:b]]
# 取rand_index指定的b列数据作为数据中心点
# sigma_chosen:选择高斯核宽度
if sigma_chosen == 0:
# 判断用户是否设置了sigma，为0表示没选
sigma = 10 # 如果用户没有定义sigma,那么默认为10
score = float("-inf")
for epsilon in np.arange(np.log10(sigma) - 1, -5, -1):
for iteration in range(1, 9 + 1): # matlabの for c=a:b はpythonの for c in range(a,b+1)
sigma_new = sigma - np.power(10, epsilon)
cv_index = np.random.permutation(n_nu)
# cv_index = np.loadtxt('D://cv_index.txt', delimiter=',', dtype=np.int32) - 1
cv_split = np.floor(np.arange(0, n_nu) * fold / n_nu) + 1
score_new = 0
X_de = self.kernel_Gaussian(x_de, x_ce, sigma_new)
X_nu = self.kernel_Gaussian(x_nu, x_ce, sigma_new)
mean_X_de = np.mean(X_de, axis=0).T
for i in range(1, fold + 1):
alpha_cv, _ = self.KLIEP_learning(mean_X_de, X_nu[cv_index[cv_split != i], :])
wh_cv = np.dot(X_nu[cv_index[cv_split == i], :], alpha_cv)
score_new = score_new + np.mean(np.log(wh_cv)) / fold
if score_new - score < 0:
break
score = score_new
sigma = sigma_new
if self.verbose == True:
print("score = {}, sigma = {}".format(score, sigma))
sigma_chosen = sigma
if self.verbose == True:
print("sigma = {}".format(sigma_chosen))
# 3. Computing the final solution `wh_x_de'
X_de = self.kernel_Gaussian(x_de, x_ce, sigma_chosen)
X_nu = self.kernel_Gaussian(x_nu, x_ce, sigma_chosen)
mean_X_de = np.mean(X_de, axis=0).T
import time
# t1 = time.time()
alphah, _ = self.KLIEP_learning(mean_X_de, X_nu)
# t2 = time.time()
# print("当前alphah所用时间：",t2-t1)
wh_x_de = np.dot(X_de, alphah).T
wh_x_de = wh_x_de.reshape(-1, )
if x_re is None:
wh_x_re = float('nan')
else:
X_Re = self.kernel_Gaussian(x_re.reshape(1, -1), x_ce.reshape(1, -1), sigma_chosen)
wh_x_re = np.dot(X_Re, alphah).T
return wh_x_de, wh_x_re
def kernel_Gaussian(self, x, c, sigma):
if len(np.shape(x)) == 1:
d = 1
nx = np.shape(x)[0]
else:
d = np.shape(x)[0]
nx = np.shape(x)[1]
if len(np.shape(c)) == 1:
d = 1
nc = np.shape(c)[0]
else:
d = np.shape(c)[0]
nc = np.shape(c)[1]
x2 = np.sum(np.power(x, 2), axis=0).reshape(1, -1)
c2 = np.sum(np.power(c, 2), axis=0).reshape(1, -1)
distance2 = np.tile(c2, [nx, 1]) + np.tile(x2.T, [1, nc]) - 2.0 * np.dot(x.T, c)
return np.exp(-distance2 / (2.0 * np.power(sigma, 2.0)))
def KLIEP_learning(self, mean_X_de, X_nu):
"""
利用KLIEP_projection返回值，更新alpha、score值
:param mean_X_de: 计算train高斯核函数值，基于中心点取均值，再进行转置得到的nc维列向量
:param X_nu: 分子test计算高斯核函数值后得到的nu * nc维的矩阵
:return: alpha、score
"""
if len(np.shape(X_nu)) == 1:
n_nu = 1
nc = np.shape(X_nu)[0]
else:
n_nu = np.shape(X_nu)[0]
nc = np.shape(X_nu)[1]
max_iteration = 100
epsilon_list = np.power(10.0, np.arange(3, -4, -1))
c = np.sum(np.power(mean_X_de, 2)) # 作为projection函数的输入
alpha = np.ones((nc, 1))
[alpha, X_nu_alpha, score] = self.KLIEP_projection(alpha, X_nu, mean_X_de, c)
for epsilon in epsilon_list:
for iteration in range(1, max_iteration + 1):
# 对alpha进行梯度更新
alpha_tmp = alpha + np.dot(np.dot(epsilon, X_nu.T), (1 / X_nu_alpha))
# 对alpha进行投影梯度更新
[alpha_new, X_nu_alpha_new, score_new] = self.KLIEP_projection(alpha_tmp, X_nu, mean_X_de, c)
if score_new - score <= 0: # 对score进行更新，取score较大的值
break
score = score_new
alpha = alpha_new
X_nu_alpha = X_nu_alpha_new
return alpha, score
def KLIEP_projection(self, alpha, Xte, b, c):
"""
对alpha进行投影梯度更新，进行归一化后，返回w(x)及J的值
:param alpha:nc维列向量,初始值
:param Xte:测试集->X_nu，计算过高斯核函数值的矩阵，根据test计算得到的
:param b:mean_X_de,nc维列向量，b根据train计算得到的
:param c:mean_X_de取平方再求和,bT*b
:return:alpha,Xte_alpha：Xte_alpha=Xte*alpha，其实就是w(x), score:J的值
"""
alpha = alpha + np.dot(np.dot(b, (1 - np.sum(b * alpha.reshape(-1)))).reshape(-1, 1),
np.linalg.pinv(c.reshape(1, -1), rcond=1e-20))
# 同型的矩阵X，并且满足：AXA=A,XAX=X.此时，
# 称矩阵X为矩阵A的伪逆，也称为广义逆矩阵。
alpha[alpha < 0] = 0
alpha = np.dot(alpha, np.linalg.pinv(np.sum(b * alpha.reshape(-1)).reshape(1, -1), rcond=1e-20))
Xte_alpha = np.dot(Xte, alpha)
score = np.mean(np.log(Xte_alpha))
return alpha, Xte_alpha, score
def pdf_Gaussian(self, x, mu, sigma):
if len(np.shape(x)) == 1:
d = 1
nx = np.shape(x)[0]
else:
d = np.shape(x)[0]
nx = np.shape(x)[1]
tmp = (x - np.tile(mu, [1, nx])) / np.tile(sigma, [1, nx]) / np.sqrt(2)
return (np.power((2 * np.pi), (-d / 2.0)) / np.prod(sigma)) * np.exp(-np.sum(np.power(tmp, 2), axis=0))
def demo(self):
'''
データ生成
'''
d = 1
# データ量
n_de = 100
n_nu = 100
# μ
mu_de = 1
mu_nu = 1
# σ
sigma_de = 1 / 2.0
sigma_nu = 1 / 8.0
x_de = mu_de+sigma_de*np.random.randn(d, n_de)
x_nu = mu_nu+sigma_nu*np.random.randn(d, n_nu)
# x_de = np.loadtxt('D://x_de.txt', delimiter=',').reshape(1, -1)
# x_nu = np.loadtxt('D://x_nu.txt', delimiter=',').reshape(1, -1)
xdisp = np.linspace(-0.5, 3, 100)
p_de_xdisp = self.pdf_Gaussian(xdisp, mu_de, sigma_de)
p_nu_xdisp = self.pdf_Gaussian(xdisp, mu_nu, sigma_nu)
w_xdisp = p_nu_xdisp / p_de_xdisp
p_de_x_de = self.pdf_Gaussian(x_de, mu_de, sigma_de)
p_nu_x_de = self.pdf_Gaussian(x_de, mu_nu, sigma_nu)
w_x_de = p_nu_x_de / p_de_x_de
[wh_x_de, wh_xdisp] = self.fit(x_de, x_nu, xdisp, sigma_chosen=1)
# plot
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xdisp, p_de_xdisp, 'b-', label='$p_{de}$(x)')
ax.plot(xdisp, p_nu_xdisp, 'k-', label='$p_{nu}$(x)')
ax.legend(loc="upper right")
ax.set_xlabel('x')
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xdisp, w_xdisp, 'r-', label='w(x)')
ax.plot(xdisp, wh_xdisp.reshape(-1), 'g-', label='w-hat(x)')
ax.plot(x_de.reshape(-1), wh_x_de.reshape(-1), 'b.', label='w-hat($x^{de}$)')
ax.legend(loc="upper right")
ax.set_xlabel('x')
plt.show()
return wh_x_de