# coding: utf-8
# In[1]:
# 数据校验
def validate(X, Y):
if len(X) != len(Y):
raise Exception("参数异常")
else:
m = len(X[0])
for l in X:
if len(l) != m:
raise Exception("参数异常")
if len(Y[0]) != 1:
raise Exception("参数异常")
# 计算差异值
def calcDiffe(x, y, a):
lx = len(x)
la = len(a)
if lx == la:
result = 0
for i in range(lx):
result += x[i] * a[i]
return y - result
elif lx + 1 == la:
result = 0
for i in range(lx):
result += x[i] * a[i]
result += 1 * a[lx] # 加上常数项
return y - result
else :
raise Exception("参数异常")
## 要求X必须是List集合，Y也必须是List集合
def fit(X, Y, alphas, threshold=1e-6, maxIter=20, addConstantItem=True):
import math
import numpy as np
## 校验
validate(X, Y)
## 开始模型构建
l = len(alphas)
m = len(Y)
n = len(X[0]) + 1 if addConstantItem else len(X[0])
B = [True for i in range(l)]
## 差异性(损失值)
J = [np.nan for i in range(l)]
# 1. 随机初始化0值(全部为0), a的最后一列为常数项
a = [[0 for j in range(n)] for i in range(l)]
# 2. 开始计算
for times in range(maxIter):
for i in range(l):
if not B[i]:
# 如果当前alpha的值已经计算到最优解了，那么不进行继续计算
continue
ta = a[i]
for j in range(n):
alpha = alphas[i]
ts = 0
for k in range(m):
if j == n - 1 and addConstantItem:
ts += alpha*calcDiffe(X[k], Y[k][0], a[i]) * 1
else:
ts += alpha*calcDiffe(X[k], Y[k][0], a[i]) * X[k][j]
t = ta[j] + ts
ta[j] = t
## 计算完一个alpha值的0的损失函数
flag = True
js = 0
for k in range(m):
js += math.pow(calcDiffe(X[k], Y[k][0], a[i]),2)
if js > J[i]:
flag = False
break;
if flag:
J[i] = js
for j in range(n):
a[i][j] = ta[j]
else:
# 标记当前alpha的值不需要再计算了
B[i] = False
## 计算完一个迭代，当目标函数/损失函数值有一个小于threshold的结束循环
r = [0 for j in J if j <= threshold]
if len(r) > 0:
break
# 如果全部alphas的值都结算到最后解了，那么不进行继续计算
r = [0 for b in B if not b]
if len(r) > 0:
break;
# 3. 获取最优的alphas的值以及对应的0值
min_a = a[0]
min_j = J[0]
min_alpha = alphas[0]
for i in range(l):
if J[i] < min_j:
min_j = J[i]
min_a = a[i]
min_alpha = alphas[i]
print "最优的alpha值为:",min_alpha
# 4. 返回最终的0值
return min_a
# 预测结果
def predict(X,a):
Y = []
n = len(a) - 1
for x in X:
result = 0
for i in range(n):
result += x[i] * a[i]
result += a[n]
Y.append(result)
return Y
# 计算实际值和预测值之间的相关性
def calcRScore(y,py):
if len(y) != len(py):
raise Exception("参数异常")
import math
import numpy as np
avgy = np.average(y)
m = len(y)
rss = 0.0
tss = 0
for i in range(m):
rss += math.pow(y[i] - py[i], 2)
tss += math.pow(y[i] - avgy, 2)
r = 1.0 - 1.0 * rss / tss
return r
# In[2]:
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import pandas as pd
import warnings
import sklearn
from sklearn.linear_model import LinearRegression,Ridge, LassoCV, RidgeCV, ElasticNetCV
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import Pipeline
from sklearn.linear_model.coordinate_descent import ConvergenceWarning
# In[3]:
## 设置字符集，防止中文乱码
mpl.rcParams['font.sans-serif']=[u'simHei']
mpl.rcParams['axes.unicode_minus']=False
# In[4]:
warnings.filterwarnings(action = 'ignore', category=ConvergenceWarning)
## 创建模拟数据
np.random.seed(0)
np.set_printoptions(linewidth=1000, suppress=True)
N = 10
x = np.linspace(0, 6, N) + np.random.randn(N)
y = 1.8*x**3 + x**2 - 14*x - 7 + np.random.randn(N)
x.shape = -1, 1
y.shape = -1, 1
# In[5]:
plt.figure(figsize=(12,6), facecolor='w')
## 模拟数据产生
x_hat = np.linspace(x.min(), x.max(), num=100)
x_hat.shape = -1,1
## 线性模型
model = LinearRegression()
model.fit(x,y)
y_hat = model.predict(x_hat)
s1 = calcRScore(y, model.predict(x))
print model.score(x,y) ## 自带R^2输出
print "模块自带实现==============="
print "参数列表:", model.coef_
print "截距:", model.intercept_
## 自模型
ma = fit(x,y,np.logspace(-4,-2,100), addConstantItem=True)
y_hat2 = predict(x_hat, ma)
s2 = calcRScore(y, predict(x,ma))
print "自定义实现模型============="
print "参数列表:", ma
## 开始画图
plt.plot(x, y, 'ro', ms=10, zorder=3)
plt.plot(x_hat, y_hat, color='#b624db', lw=2, alpha=0.75, label=u'Python模型，$R^2$:%.3f' % s1, zorder=2)
plt.plot(x_hat, y_hat2, color='#6d49b6', lw=2, alpha=0.75, label=u'自己实现模型，$R^2$:%.3f' % s2, zorder=1)
plt.legend(loc = 'upper left')
plt.grid(True)
plt.xlabel('X', fontsize=16)
plt.ylabel('Y', fontsize=16)
plt.suptitle(u'自定义的线性模型和模块中的线性模型比较', fontsize=22)
plt.show()
# In[6]:
from sklearn.ensemble import GradientBoostingRegressor#梯度下降的回归
clf = GradientBoostingRegressor()
y1 = y.ravel()
clf.fit(x,y1)
print "自带梯度下降法R方:", clf.score(x,y1)
y_hat3=clf.predict(x_hat)
s3=calcRScore(y, clf.predict(x))
## 开始画图
plt.plot(x, y, 'ro', ms=10, zorder=3)
plt.plot(x_hat, y_hat, color='#b624db', lw=2, alpha=0.75, label=u'Python模型，$R^2$:%.3f' % s1, zorder=2)
plt.plot(x_hat, y_hat2, color='#6d49b6', lw=2, alpha=0.75, label=u'自己实现模型，$R^2$:%.3f' % s2, zorder=1)
plt.plot(x_hat, y_hat3, color='#6daaba', lw=2, alpha=0.75, label=u'自带梯度下降方法，$R^2$:%.3f' % s3, zorder=1)
plt.legend(loc = 'upper left')
plt.grid(True)
plt.xlabel('X', fontsize=16)
plt.ylabel('Y', fontsize=16)
plt.suptitle(u'自定义的线性模型和模块中的线性模型比较', fontsize=22)
plt.show()
# In[ ]:
