logistic regression with tensorflow
作者：互联网
二分类模型做了3个实现
1. tensorflow lower API 实现逻辑回归二分类
2. tensorflow senior API 实现二分类(sigmod函数由API内部默认实现)
3. sklearn 的逻辑回归包用于比较输出
需要注意的是 tensorflow 中对于函数输出 nan 与 inf 的处理
由于数据生成时值域较大[-35, 85], 在线性部完成计算后,
exp(x)输出超过浮点精度上边界会返回 inf
此时如果对于 y = exp(x) 做 tf.clip_by_value(y, 1e-10, 1e10) 的操作
(或者采用 tf.where 等等裁剪函数)
在 tfdbg 下依然会报 has_inf_or_nan 的错误, 并且参数估计输出始终为 nan
关键在于 tensorflow 中不能只是简单粗暴的裁剪函数输出值
而是要保证 exp(x) 中 x 的值域合理
也就是需要裁剪 “Wx+B” 线性多项式的输出
但是如此裁剪 容易导致多项式 Wx + B 参数估计产生偏倚
可选的解决方法之一是基于样本stdev做正规化(z-score)
在不改变样本分布的情况下缩小值域
import numpy as NP
import tensorflow as TF
import random
import matplotlib.pyplot as PLT
from tensorflow.python import debug as tf_debug
def rotation_mat(n_degree):
theta = n_degree / 180 * NP.pi
m = NP.mat(
[[NP.cos(theta), -NP.sin(theta)],
[NP.sin(theta), NP.cos(theta)]]
)
return m
#以两个中心点为基础生成二类样本
centra0 = NP.mat([0, 0])
centra1 = NP.mat([50, 50])
points_data = NP.zeros((720, 2))
labels_data = NP.zeros((720, 1))
for i in range(points_data.shape[0]):
rd = random.randint(0, 360)
rmat = rotation_mat(rd)
rxy = NP.mat([random.randint(0, 35), random.randint(0, 35)])
if i % 2 == 0:
centra_p = centra0
label_p = 0
else:
centra_p = centra1
label_p = 1
point = rxy * rmat + centra_p
points_data[i] = point[0]
labels_data[i] = label_p
#===========================================================
#===========================================================
#为了防止出现exp值域溢出,基于标准差正规化数据
x_mul = 1
y_mul = 1
train_data = points_data.copy()
if 1:
x_mul = points_data[:,0].std()
y_mul = points_data[:,1].std()
train_data[:,0] /= x_mul
train_data[:,1] /= y_mul
#tensorflow
X = TF.placeholder(TF.float32, [None, 2], name="X")
Y = TF.placeholder(TF.float32, [None, 1], name="Y")
W = TF.Variable(TF.zeros([2, 1]), name="W")
B = TF.Variable(TF.zeros([1, 1]), name="B")
#多项式
linear_mod = TF.matmul(X, W) + B
#将多项式函数输出值用S函数(这里选用logit), 映射到值域(0, 1)
logic_mod = 1 / (1 + TF.exp(-linear_mod))
#最大似然对数损失
#loss = -TF.reduce_mean(Y * TF.log(logic_mod) + (1 - Y) * TF.log(1 - logic_mod))
#化简形式
loss_p0 = Y * -linear_mod
loss_p1 = TF.log(1 + TF.exp(-linear_mod))
loss = TF.reduce_mean(loss_p1 - loss_p0)
#学习率
learning_rate = 0.01
#使用梯度下降优化
gdop = TF.train.GradientDescentOptimizer(learning_rate)
#正则化梯度下降率
gdop = TF.contrib.estimator.clip_gradients_by_norm(gdop, 2.0)
gdop = gdop.minimize(loss)
sess = TF.Session()
sess.run(TF.global_variables_initializer())
#sess = tf_debug.LocalCLIDebugWrapperSession(sess)
for s in range(10000):
sess.run(gdop, {X:train_data, Y:labels_data})
print(">>>>> with tensorflow")
esti_W = sess.run(W)
esti_B = sess.run(B)
x_coef = -esti_W[0][0] / esti_W[1]
bias_b = -esti_B[0][0] / esti_W[1]
print("y = %.2fx + %.2f" % (x_coef*y_mul/x_mul, bias_b*y_mul))
if 1:
fig = PLT.figure()
ax1 = fig.add_subplot(111)
for i in range(points_data.shape[0]):
x, y = points_data[i]
if labels_data[i] == 1:
ax1.plot(x, y, 'ro')
else:
ax1.plot(x, y, 'go')
#empirical estimate
# x + y - 50 = 0
x_range = [x[0] for x in points_data]
esti_y = [(x_coef * x[0] / x_mul + bias_b)*y_mul for x in points_data]
ax1.plot(x_range, esti_y, 'k-')
#=======================================================
#tensorflow senior APIs
#=======================================================
TF.logging.set_verbosity(TF.logging.ERROR)
def data_feeder(xy_data, label_data):
data_dc = {"x":xy_data[:,0], "y":xy_data[:,1]}
ts = TF.data.Dataset.from_tensor_slices((data_dc, label_data.reshape([1,-1])[0]))
ts = ts.shuffle(label_data.shape[1]).repeat().batch(label_data.shape[1])
t_data, t_label = ts.make_one_shot_iterator().get_next()
return t_data, t_label
clf_feature_cols = [
TF.feature_column.numeric_column("x"),
TF.feature_column.numeric_column("y")
]
clf_opt = TF.train.GradientDescentOptimizer(0.01)
clf_opt = TF.contrib.estimator.clip_gradients_by_norm(clf_opt, 2.0)
clf_model = TF.estimator.LinearClassifier(
feature_columns=clf_feature_cols,
optimizer=clf_opt
)
#tf的高级api对于过大的输入项(如使得exp(x)超出浮点精度的x)
#处理方式应该是直接进行了裁剪, 这会导致截距项bias发生变化
#所以依然需要对输入变量做正规化
clf_model.train(
input_fn = lambda :data_feeder(train_data, labels_data),
steps=10000
)
clf_x_coef = clf_model.get_variable_value('linear/linear_model/x/weights')[0][0]
clf_y_coef = clf_model.get_variable_value('linear/linear_model/y/weights')[0][0]
clf_b_bias = clf_model.get_variable_value('linear/linear_model/bias_weights')[0]
print(">>>>> with tensorflow senior APIs")
print("y = %.2fx + %.2f" %
(-clf_x_coef/clf_y_coef*y_mul/x_mul, -clf_b_bias/clf_y_coef*y_mul)
)
#=======================================================
#sklearn
#=======================================================
print(">>>> with sklearn")
from sklearn.linear_model import LogisticRegression
lr = LogisticRegression()
lr.fit(points_data, labels_data)
skl_x_coef = lr.coef_[0][0] / -lr.coef_[0][1]
skl_b_bias = lr.intercept_[0] / -lr.coef_[0][1]
print("y = %.2fx + %.2f" % (skl_x_coef, skl_b_bias))
标签：coef,clf,NP,logistic,mul,TF,tensorflow,data,regression 来源： https://www.cnblogs.com/tpoy/p/14402357.html