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stepwise_regression.py
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stepwise_regression.py
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import numpy as np
class Stepwise_regression:
def __init__(self, x, y):
self.x_mean = np.mean(x, axis=0)
self.x_scale = np.std(x, axis=0)
self.x_c = (x - self.x_mean) / self.x_scale
self.y_mean = np.mean(y)
self.y_c = y - self.y_mean
self.betahat = np.zeros(np.shape(x)[1])
self.intercept = self.y_mean
self.A = np.dot(np.c_[self.x_c, self.y_c].T, np.c_[self.x_c, self.y_c])
def eliminate_trans(self, m, index):
n = len(m)
m1 = m.copy()
center = m[index, index]
m1[index, index] = 1 / center
for j in range(n):
if j != index:
m1[index, j] = m[index, j] / center
m1[j, index] = - m[j, index] / center
for i in range(n):
if i != index:
for j in range(n):
if j != index:
m1[i, j] = m[i, j] - m[i, index] * m[index, j] / center
return m1
def compute_aic(self, rss, n, q):
return n * np.log(rss) + q
def search(self):
n = len(self.y_c)
p = np.shape(self.x_c)[1]
in_effect = np.zeros(p)
out_effect = np.ones(p)
aic_path = [self.compute_aic(self.A[p, p], n, 0)]
operate_path = []
best_aic = aic_path[0]
q = 0
while 1:
p_value = (self.A[0:p, p] ** 2) / np.diag(self.A)[0:p]
aic_add = best_aic + 1
aic_del = best_aic + 1
ind_add = p + 1
ind_del = p + 1
if q <= p-1:
ind_add = np.argmax(out_effect * p_value)
rss_add = self.A[p, p] - p_value[ind_add]
aic_add = self.compute_aic(rss_add, n, q + 1)
if q >= 1:
nz_ind = np.where(in_effect > 0)[0]
ind_del = nz_ind[np.argmin((in_effect * p_value)[nz_ind])]
rss_del = self.A[p, p] + p_value[ind_del]
aic_del = self.compute_aic(rss_del, n, q - 1)
aic_next = min(best_aic, aic_add, aic_del)
if aic_next == best_aic:
break
elif aic_next == aic_add:
best_aic = aic_next
q += 1
in_effect[ind_add] = 1
out_effect[ind_add] = 0
operate_path.append(ind_add)
aic_path.append(best_aic)
self.A = self.eliminate_trans(self.A, ind_add)
else:
best_aic = aic_next
q -= 1
out_effect[ind_del] = 1
in_effect[ind_del] = 0
operate_path.append(-ind_del)
aic_path.append(best_aic)
self.A = self.eliminate_trans(self.A, ind_del)
self.betahat[in_effect == 1] = self.A[0:p, p][in_effect == 1]
self.betahat = self.betahat / self.x_scale
self.intercept = self.intercept - np.sum(self.betahat * self.x_mean)
return {'selected_effect': in_effect, 'operate_path': operate_path, 'AIC_path': aic_path}
def coef(self):
return {'intercept': self.intercept, 'betahat': self.betahat}
def predict(self, x, newx=True):
if newx:
return self.intercept + np.dot(x, self.betahat)
else:
return self.intercept + np.dot((self.x_c + self.x_mean) * self.x_scale, self.betahat)
if __name__ == '__main__':
np.random.seed(0)
n=100
p=200
rho=0.5
s=5
x = np.random.randn(n, p)
snr=10
beta_type = 2
index = np.ones((p, p)) * range(p)
sigma = np.power(rho, np.abs(index - index.T))
eigen, u = np.linalg.eig(sigma)
sigma_half = u.dot(np.diag(np.sqrt(eigen))).dot(u.T)
x = x.dot(sigma_half)
s = min(s, p)
beta = np.zeros(p)
if beta_type == 1:
beta[(np.around(np.linspace(0, p - 1, num=s))).astype('int')] = 1
elif beta_type == 2:
beta[range(s)] = 1
elif beta_type == 3:
beta[range(s)] = np.linspace(0.5, 10, num=s)
elif beta_type == 4:
beta[range(s)] = 1
beta[s:p] = np.power(0.5, range(1, p - s + 1))
var = np.sum(beta * np.dot(sigma, beta))
sigma_1 = (var / snr) ** 0.5
y = np.dot(x, beta) + np.random.randn(n) * sigma_1
fit = Stepwise_regression(x, y)
path = fit.search()
print(path)
print(fit.coef())