【Python机器学习】实验03 逻辑回归2-阿里云开发者社区

1.7 试试用Sklearn来解决

from sklearn.linear_model import LogisticRegression
clf = LogisticRegression().fit(X, y)
clf.score(X,y)

0.89

clf.predict(X)

array([0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1,
       0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1,
       0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1], dtype=int64)

np.array([1 if item>0.5 else 0 for item in h(X,w)])

array([0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1,
       0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1,
       0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1])

np.argmax(clf.predict_proba(X),axis=1)

array([0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1,
       0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1,
       0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1], dtype=int64)

X.shape,y.shape

((100, 3), (100,))

from sklearn.datasets import load_iris
from sklearn.linear_model import LogisticRegression
y
clf = LogisticRegression().fit(X, y)
clf.predict(X)

array([0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1,
       0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1,
       0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,
       1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1], dtype=int64)

clf.predict(X).shape

(100,)

y.shape

(100,)

np.sum(clf.predict(X)==y.ravel())/np.sum(X.shape[0])

0.89

#所以分类问题中的score用的是准确率
clf.score(X,y)

0.89

我们的逻辑回归分类器预测正确，如果一个学生被录取或没有录取，达到89%的精确度。不坏！记住，这是训练集的准确性。我们没有保持住了设置或使用交叉验证得到的真实逼近，所以这个数字有可能高于其真实值（这个话题将在以后说明）。

2.1 准备数据(试试第二个例子)

在训练的第二部分，我们将要通过加入正则项提升逻辑回归算。简而言之，正则化是成本函数中的一个术语，它使算法更倾向于“更简单”的模型（在这种情况下，模型将更小的系数）。这个理论助于减少过拟合，提高模型的泛化能力。

设想你是工厂的生产主管，你有一些芯片在两次测试中的测试结果。对于这两次测试，你想决定是否芯片要被接受或抛弃。为了帮助你做出艰难的决定，你拥有过去芯片的测试数据集，从其中你可以构建一个逻辑回归模型。

和第一部分很像，从数据可视化开始吧！

#读取文件'ex2data2.txt'的数据
path="ex2data2.txt"
data2=pd.read_csv(path,header=None,names=["Test1","Test2","Accepted"])
data2.head()

	Test1	Test2	Accepted
0	0.051267	0.69956	1
1	-0.092742	0.68494	1
2	-0.213710	0.69225	1
3	-0.375000	0.50219	1
4	-0.513250	0.46564	1

#可视化数据
positive_index=data2["Accepted"]==1
negative_index=data2["Accepted"]==0
plt.scatter(data2[positive_index]["Test1"],data2[positive_index]["Test2"],color="r",marker="^")
plt.scatter(data2[negative_index]["Test1"],data2[negative_index]["Test2"],color="b",marker="o")
plt.legend(["Accpted","Not accepted"])
plt.show()

X2=data2.iloc[:,:2]
y2=data2.iloc[:,2]
X2.insert(0,"ones",1)
X2.shape,y2.shape

((118, 3), (118,))

X2=X2.values
y2=y2.values

2.2 假设函数与前h相同

2.3 代价函数与前相同

2.4 梯度下降算法与前相同

iter_num,alpha=600000,0.0005
w,cost_lst=grandient(X2,y2,iter_num,alpha)

#绘制误差曲线
plt.plot(range(iter_num),cost_lst,"b-o")

[<matplotlib.lines.Line2D at 0x1422d45e970>]

#看看准确率有多少
y_pred=[1 if item>=0.5 else 0  for item in sigmoid(X2@w).ravel()]
y_pred=np.array(y_pred)
y_pred.shape

(118,)

y2.shape

(118,)

np.sum(y_pred==y2)

np.sum(y_pred==y2)/y2.shape[0]

0.5508474576271186

y_pred=[1 if item>=0.5 else 0  for item in sigmoid(X2@w).ravel()]
y_pred=np.array(y_pred)
np.sum(y_pred==y2)/y2.shape[0]

0.5508474576271186

2.5 欠拟合的了（模型过于简单，增加一些多项式特征）

path="ex2data2.txt"
data2=pd.read_csv(path,header=None,names=["Test1","Test2","Accepted"])
data2.head()

	Test1	Test2	Accepted
0	0.051267	0.69956	1
1	-0.092742	0.68494	1
2	-0.213710	0.69225	1
3	-0.375000	0.50219	1
4	-0.513250	0.46564	1

#为数据框增加多列多项式特征
def poly_feature(data2,degree):
    x1=data2["Test1"]
    x2=data2["Test2"]
    items=[]
    for i in range(degree+1):
        for j in range(degree-i+1):
            data2["F"+str(i)+str(j)]=np.power(x1,i)*np.power(x2,j)
            items.append("(x1**{})*(x2**{})".format(i,j))
    data2=data2.drop(["Test1","Test2"],axis=1)
    return data2,items
data2,items=poly_feature(data2,4)

data2.shape

(118, 16)

data2.head(5)

	Accepted	F00	F01	F02	F03	F04	F10	F11	F12	F13	F20	F21	F22	F30	F31	F40
0	1	1.0	0.69956	0.489384	0.342354	0.239497	0.051267	0.035864	0.025089	0.017551	0.002628	0.001839	0.001286	0.000135	0.000094	0.000007
1	1	1.0	0.68494	0.469143	0.321335	0.220095	-0.092742	-0.063523	-0.043509	-0.029801	0.008601	0.005891	0.004035	-0.000798	-0.000546	0.000074
2	1	1.0	0.69225	0.479210	0.331733	0.229642	-0.213710	-0.147941	-0.102412	-0.070895	0.045672	0.031616	0.021886	-0.009761	-0.006757	0.002086
3	1	1.0	0.50219	0.252195	0.126650	0.063602	-0.375000	-0.188321	-0.094573	-0.047494	0.140625	0.070620	0.035465	-0.052734	-0.026483	0.019775
4	1	1.0	0.46564	0.216821	0.100960	0.047011	-0.513250	-0.238990	-0.111283	-0.051818	0.263426	0.122661	0.057116	-0.135203	-0.062956	0.069393

X2=data2.iloc[:,1:data2.shape[1]-1]
y2=data2.iloc[:,0]
X2.shape,y.shape

((118, 14), (100,))

X2

F00	F01	F02	F03	F04	F10	F11	F12	F13	F20	F21	F22	F30	F31
0	1.0	0.699560	0.489384	0.342354	2.394969e-01	0.051267	0.035864	0.025089	0.017551	0.002628	0.001839	0.001286	1.347453e-04	9.426244e-05
1	1.0	0.684940	0.469143	0.321335	2.200950e-01	-0.092742	-0.063523	-0.043509	-0.029801	0.008601	0.005891	0.004035	-7.976812e-04	-5.463638e-04
2	1.0	0.692250	0.479210	0.331733	2.296423e-01	-0.213710	-0.147941	-0.102412	-0.070895	0.045672	0.031616	0.021886	-9.760555e-03	-6.756745e-03
3	1.0	0.502190	0.252195	0.126650	6.360222e-02	-0.375000	-0.188321	-0.094573	-0.047494	0.140625	0.070620	0.035465	-5.273438e-02	-2.648268e-02
4	1.0	0.465640	0.216821	0.100960	4.701118e-02	-0.513250	-0.238990	-0.111283	-0.051818	0.263426	0.122661	0.057116	-1.352032e-01	-6.295600e-02
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
113	1.0	0.538740	0.290241	0.156364	8.423971e-02	-0.720620	-0.388227	-0.209153	-0.112679	0.519293	0.279764	0.150720	-3.742131e-01	-2.016035e-01
114	1.0	0.494880	0.244906	0.121199	5.997905e-02	-0.593890	-0.293904	-0.145447	-0.071979	0.352705	0.174547	0.086380	-2.094682e-01	-1.036616e-01
115	1.0	0.999270	0.998541	0.997812	9.970832e-01	-0.484450	-0.484096	-0.483743	-0.483390	0.234692	0.234520	0.234349	-1.136964e-01	-1.136134e-01
116	1.0	0.999270	0.998541	0.997812	9.970832e-01	-0.006336	-0.006332	-0.006327	-0.006323	0.000040	0.000040	0.000040	-2.544062e-07	-2.542205e-07
117	1.0	-0.030612	0.000937	-0.000029	8.781462e-07	0.632650	-0.019367	0.000593	-0.000018	0.400246	-0.012252	0.000375	2.532156e-01	-7.751437e-03

118 rows × 14 columns

y2

0      1
1      1
2      1
3      1
4      1
      ..
113    0
114    0
115    0
116    0
117    0
Name: Accepted, Length: 118, dtype: int64

X2=X2.values
y2=y2.values

X2.shape,y2.shape

((118, 14), (118,))

#虽然加了多项式特征，但是其他地方不需要改变
iter_num,alpha=600000,0.001
w,cost_lst=grandient(X2,y2,iter_num,alpha)
w,cost_lst

(array([[ 3.03503577],
        [ 3.20158942],
        [-4.0495866 ],
        [-1.04983379],
        [-3.95636068],
        [ 2.0490215 ],
        [-3.40302089],
        [-0.79821365],
        [-1.23393575],
        [-7.32541507],
        [-1.41115593],
        [-1.80717912],
        [-0.54355034],
        [ 0.11775491]]),
 [0.6931399371004173,
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  0.6870847238036913,
  0.68707862377725,
  0.6870725247213932,
  0.6870664266356225,
  0.6870603295194394,
  0.6870542333723462,
  0.6870481381938451,
  0.6870420439834392,
  0.6870359507406308,
  0.687029858464924,
  0.6870237671558223,
  0.6870176768128294,
  0.6870115874354497,
  0.6870054990231881,
  0.6869994115755486,
  0.6869933250920375,
  0.6869872395721597,
  0.6869811550154208,
  0.6869750714213273,
  0.6869689887893855,
  0.6869629071191022,
  0.6869568264099849,
  0.6869507466615399,
  0.6869446678732757,
  0.6869385900446999,
  0.6869325131753212,
  0.6869264372646477,
  0.6869203623121884,
  0.6869142883174523,
  0.6869082152799498,
  0.6869021431991895,
  0.6868960720746824,
  0.6868900019059384,
  0.6868839326924686,
  0.6868778644337838,
  0.6868717971293953,
  0.686865730778815,
  0.6868596653815545,
  0.6868536009371263,
  0.6868475374450429,
  0.6868414749048171,
  0.6868354133159618,
  0.6868293526779911,
  0.6868232929904182,
  0.6868172342527574,
  0.6868111764645234,
  0.68680511962523,
  0.6867990637343928,
  0.6867930087915272,
  0.6867869547961485,
  0.6867809017477724,
  0.6867748496459155,
  0.686768798490094,
  0.6867627482798252,
  0.6867566990146253,
  0.6867506506940125,
  0.6867446033175041,
  0.686738556884618,
  0.6867325113948729,
  0.686726466847787,
  0.6867204232428794,
  0.6867143805796693,
  0.6867083388576762,
  0.6867022980764199,
  0.6866962582354202,
  0.6866902193341977,
  0.6866841813722733,
  0.6866781443491677,
  0.6866721082644022,
  0.6866660731174986,
  0.6866600389079782,
  0.686654005635364,
  0.6866479732991783,
  0.6866419418989436,
  0.6866359114341828,
  0.6866298819044195,
  0.6866238533091775,
  0.686617825647981,
  0.6866117989203535,
  0.6866057731258198,
  0.6865997482639055,
  0.686593724334135,
  0.6865877013360339,
  0.686581679269128,
  0.6865756581329433,
  0.686569637927006,
  ...])

w.shape

(14, 1)

cost_lst[iter_num-1]

0.365635134439536

#绘制误差曲线
plt.plot(range(iter_num),cost_lst,"b-o")

[<matplotlib.lines.Line2D at 0x1422d44cdc0>]

这时要重新绘图了

items

X2

array([[ 1.00000000e+00,  6.99560000e-01,  4.89384194e-01, ...,
         1.28625106e-03,  1.34745327e-04,  9.42624411e-05],
       [ 1.00000000e+00,  6.84940000e-01,  4.69142804e-01, ...,
         4.03513411e-03, -7.97681228e-04, -5.46363780e-04],
       [ 1.00000000e+00,  6.92250000e-01,  4.79210063e-01, ...,
         2.18864648e-02, -9.76055545e-03, -6.75674451e-03],
       ...,
       [ 1.00000000e+00,  9.99270000e-01,  9.98540533e-01, ...,
         2.34349278e-01, -1.13696444e-01, -1.13613445e-01],
       [ 1.00000000e+00,  9.99270000e-01,  9.98540533e-01, ...,
         4.00913674e-05, -2.54406238e-07, -2.54220521e-07],
       [ 1.00000000e+00, -3.06120000e-02,  9.37094544e-04, ...,
         3.75068364e-04,  2.53215646e-01, -7.75143736e-03]])

X2.shape,w.shape

((118, 14), (14, 1))

y_pred=[1 if item>=0.5 else 0  for item in sigmoid(X2@w).ravel()]
y_pred=np.array(y_pred)
np.sum(y_pred==y2)/y2.shape[0]

0.8305084745762712

2.6 定义正则化项的代价函数

regularized cost（正则化代价函数）

w[:,0]

array([ 3.03503577,  3.20158942, -4.0495866 , -1.04983379, -3.95636068,
        2.0490215 , -3.40302089, -0.79821365, -1.23393575, -7.32541507,
       -1.41115593, -1.80717912, -0.54355034,  0.11775491])

#代价函数构造
def cost_reg(X,w,y,lambd):
    #当X(m,n+1),y(m,),w(n+1,1)
    y_hat=sigmoid(X@w)
    right1=np.multiply(y.ravel(),np.log(y_hat).ravel())+np.multiply((1-y).ravel(),np.log(1-y_hat).ravel())
    right2=(lambd/(2*X.shape[0]))*np.sum(np.power(w[1:,0],2))
    cost=-np.sum(right1)/X.shape[0]+right2
    return cost

cost(X2,w,y2)

0.365635134439536

lambd=2
cost_reg(X2,w,y2,lambd)

1.3874260376493517

【Python机器学习】实验03 逻辑回归2

1.7 试试用Sklearn来解决

2.1 准备数据(试试第二个例子)

2.2 假设函数与前h相同

2.3 代价函数与前相同

2.4 梯度下降算法与前相同

2.5 欠拟合的了（模型过于简单，增加一些多项式特征）

2.6 定义正则化项的代价函数

regularized cost（正则化代价函数）

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插件

【Python机器学习】实验03 逻辑回归2

1.7 试试用Sklearn来解决

2.1 准备数据(试试第二个例子)

2.2 假设函数与前h相同

2.3 代价函数与前相同

2.4 梯度下降算法与前相同

2.5 欠拟合的了（模型过于简单，增加一些多项式特征）

2.6 定义正则化项的代价函数

regularized cost（正则化代价函数）

热门文章

最新文章

相关课程

相关电子书

相关实验场景

推荐镜像