github
import numpy as np
from sklearn.linear_model import linearregression
from sklearn.datasets import load_diabetes
from sklearn.utils import shuffle
import matplotlib.pyplot as plt
# 形狀非常重要，而且容易錯誤
deffit_normal
(x_train, y_train)
:"""根據訓練資料集x_train, y_train訓練linear regression模型"""
assert x_train.shape[0]
== y_train.shape[0]
, \ "the size of x_train must be equal to the size of y_train"
# np.vstack():在豎直方向上堆疊
# np.hstack():在水平方向上平鋪
x_b = np.hstack(
[np.ones(
(len
(x_train),1
)), x_train]
)# 為了增加常數項
theta = np.linalg.inv(x_b.t.dot(x_b)
).dot(x_b.t)
.dot(y_train)
intercept = theta[0]
coef = theta[1:
]return theta
deffit_bgd
(x_train, y_train, eta=
0.01
, n_iters=
1e5)
:"""根據訓練資料集x_train, y_train, 使用梯度下降法訓練linear regression模型"""
assert x_train.shape[0]
== y_train.shape[0]
, \ "the size of x_train must be equal to the size of y_train"
defcostfunc
(theta, x_b, y)
:# 計算損失函式
try:
return np.
sum(
(y - x_b.dot(theta))**
2)/len
(y)/
2except
:return
float
('inf'
)def
dj(theta, x_b, y)
:# 損失函式求導
return x_b.t.dot(x_b.dot(theta)
- y)
/len
(y)def
gradient_descent
(x_b, y, initial_theta, eta, n_iters=n_iters, epsilon=1e-
8): theta = initial_theta
cur_iter =
0print
('x_b.dot(theta)='
,(x_b.dot(theta)
).shape)
print
('(x_b.dot(theta) - y).shape='
,(x_b.dot(theta)
- y)
.shape)
print
('x_b.t.dot(x_b.dot(theta) - y).shape='
,x_b.t.dot(x_b.dot(theta)
- y)
.shape)
# y = np.array(data[:,1])時的維度
# y_train.shape= (97,)
# theta.shape= (2,)
# x_b.dot(theta)= (97,)
# (x_b.dot(theta) - y).shape= (97,)
# x_b.t.dot(x_b.dot(theta) - y).shape= (2,)
# y = np.c_[data[:,1]]時的維度
# y_train.shape= (97, 1)
# theta.shape= (2,)
# x_b.dot(theta)= (97,)
# (x_b.dot(theta) - y).shape= (97, 97)
# x_b.t.dot(x_b.dot(theta) - y).shape= (2, 97)
# valueerror: operands could not be broadcast together with shapes (2,) (2,97)
while cur_iter < n_iters:
gradient = dj(theta, x_b, y)
# print((x_b.dot(theta)).shape)
last_theta = theta
# print(gradient.shape)
theta = theta - eta * gradient
if(abs
(costfunc(theta, x_b, y)
- costfunc(last_theta, x_b, y)
)< epsilon)
:break
cur_iter +=
1return theta
x_b = np.hstack(
[np.ones(
(len
(x_train),1
)), x_train]
)print
('x_b.shape='
,x_b.shape)
print
('y_train.shape='
,y_train.shape)
initial_theta = np.zeros(x_b.shape[1]
)#初始化theta
print
('theta.shape='
,initial_theta.shape)
theta = gradient_descent(x_b, y_train, initial_theta, eta, n_iters)
intercept_ = theta[0]
coef_ = theta[1:
]return theta
defpredict
(x_predict,theta)
:"""給定待**資料集x_predict，返回表示x_predict的結果向量"""
x_b = np.hstack(
[np.ones(
(len
(x_predict),1
)), x_predict]
)return x_b.dot(theta)
deftest()
: data = np.loadtxt(
'linear_regression_data1.txt'
, delimiter=
',')
x = np.c_[data[:,
0]] y = np.array(data[:,
1]) y1 = np.c_[data[:,
1]]print
(fit_normal(x,y)
)print
(fit_bgd(x,y)
) regr = linearregression(
) regr.fit(x, y)
print
(regr.intercept_,regr.coef_)
deftest0425()
:# 載入資料
diabets = load_diabetes(
) data = diabets.data
target = diabets.target
# 打亂資料
x, y = shuffle(data, target, random_state=13)
# 劃分訓練集和測試集
offset =
int(x.shape[0]
*0.9
) x_train, y_train = x[
:offset]
, y[
:offset]
x_test, y_test = x[offset:
], y[offset:
] y_train = y_train.reshape((-
1,1)
) y_test = y_test.reshape((-
1,1)
)print
(x_train.shape)
print
(x_test.shape)
print
(y_train.shape)
print
(y_test.shape)
x=x_train
y=y_train
print
(fit_normal(x,y)
)print
(fit_bgd(x,y.reshape(
len(y)))
) regr = linearregression(
) regr.fit(x, y)
print
(regr.intercept_,regr.coef_)
if __name__ ==
'__main__'
: test0425(
)
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