- 损失函数
- 损失函数定义了拟合结果和真实结果之间的差异，作为优化的目标直接关系模型训练的好坏
- 三大类：均方误差，自定义，交叉熵
- 问题背景
预测酸奶日销量y。x1，x2是影响日销量的因素。
建模前，应预先采集的数据有：每日x1，x2和销量y_（即已知答案，最佳情况：产量=销量）
拟造数据集X，Y_: y_=x1+x2 噪声：-0.05~++0.05 拟合可以预测销量的函数
- 代码 opt4_1.py,opt4_2.py,opt4_3.py
#coding:utf-8
#版本信息：ubuntu18.04 python3.6.8 tensorflow1.14.0
#作者：九除以三还是三哦 如有错误，欢迎评论指正！！
#0导入模块，生成模拟数据集。
import tensorflow as tf
import numpy as np
BATCH_SIZE=8
SEED=23455
#COST=1
#PORFIT=9
rdm=np.random.RandomState(SEED)
X=rdm.rand(32,2)
Y_=[[x1+x2+(rdm.rand()/10.0-0.05)]for (x1,x2)in X]#判断如果两个坐标的平方和小于2，给Y赋值1，其余赋值0
#1定义神经网络的输入、参数和输出，定义前向传播过程。
x=tf.compat.v1.placeholder(tf.float32,shape=(None,2))
y_=tf.compat.v1.placeholder(tf.float32,shape=(None,1))
w1=tf.Variable(tf.random.normal([2,1],stddev=1,seed=1))
y=tf.matmul(x,w1)
#2定义损失函数及反向传播方法。
#定义损失函数为MSE,反向传播方法为梯度下降。
loss_mse=tf.reduce_mean(tf.square(y_-y))
#loss_mse=tf.reduce_sum(tf.where(tf.greater(y,y_),(y-y_)*COST,(y_-y)*PROFIT)) #自定义损失函数
train_step=tf.compat.v1.train.GradientDescentOptimizer(0.001).minimize(loss_mse)
#3生成会话，训练STEPS轮
with tf.compat.v1.Session() as sess:
init_op=tf.compat.v1.global_variables_initializer()
sess.run(init_op)
STEPS=20000
for i in range(STEPS):
start=(i*BATCH_SIZE)%32
end=(i*BATCH_SIZE)%32+BATCH_SIZE
sess.run(train_step,feed_dict={x:X[start:end],y_:Y_[start:end]})
if i%500==0:
print("After %d training steps,w1 is:"%(i))
print(sess.run(w1),"\n")
print("Final w1:\n",sess.run(w1))
- 运行结果
还是同样的警告，运行结果没有问题，基本符合1*x1+ 1 *x2
After 0 training steps,w1 is:
[[-0.80974597]
[ 1.4852903 ]]
After 500 training steps,w1 is:
[[-0.46074435]
[ 1.641878 ]]
After 1000 training steps,w1 is:
[[-0.21939856]
[ 1.6984766 ]]
After 1500 training steps,w1 is:
[[-0.04415595]
[ 1.7003176 ]]
After 2000 training steps,w1 is:
[[0.08942621]
[1.673328 ]]
After 2500 training steps,w1 is:
[[0.19583555]
[1.6322677 ]]
After 3000 training steps,w1 is:
[[0.28375748]
[1.5854434 ]]
After 3500 training steps,w1 is:
[[0.35848638]
[1.5374472 ]]
After 4000 training steps,w1 is:
[[0.42332518]
[1.4907393 ]]
After 4500 training steps,w1 is:
[[0.48040026]
[1.4465574 ]]
After 5000 training steps,w1 is:
[[0.53113604]
[1.4054536 ]]
After 5500 training steps,w1 is:
[[0.5765325]
[1.3675941]]
After 6000 training steps,w1 is:
[[0.61732584]
[1.3329403 ]]
After 6500 training steps,w1 is:
[[0.6540846]
[1.3013426]]
After 7000 training steps,w1 is:
[[0.6872685]
[1.272602 ]]
After 7500 training steps,w1 is:
[[0.71725976]
[1.2465005 ]]
After 8000 training steps,w1 is:
[[0.7443861]
[1.2228197]]
After 8500 training steps,w1 is:
[[0.7689324]
[1.2013483]]
After 9000 training steps,w1 is:
[[0.79115134]
[1.1818889 ]]
After 9500 training steps,w1 is:
[[0.811267 ]
[1.1642567]]
After 10000 training steps,w1 is:
[[0.8294814]
[1.1482829]]
After 10500 training steps,w1 is:
[[0.84597576]
[1.1338125 ]]
After 11000 training steps,w1 is:
[[0.8609128]
[1.1207061]]
After 11500 training steps,w1 is:
[[0.87444043]
[1.1088346 ]]
After 12000 training steps,w1 is:
[[0.88669145]
[1.0980824 ]]
After 12500 training steps,w1 is:
[[0.8977863]
[1.0883439]]
After 13000 training steps,w1 is:
[[0.9078348]
[1.0795243]]
After 13500 training steps,w1 is:
[[0.91693527]
[1.0715363 ]]
After 14000 training steps,w1 is:
[[0.92517716]
[1.0643018 ]]
After 14500 training steps,w1 is:
[[0.93264157]
[1.0577497 ]]
After 15000 training steps,w1 is:
[[0.9394023]
[1.0518153]]
After 15500 training steps,w1 is:
[[0.9455251]
[1.0464406]]
After 16000 training steps,w1 is:
[[0.95107025]
[1.0415728 ]]
After 16500 training steps,w1 is:
[[0.9560928]
[1.037164 ]]
After 17000 training steps,w1 is:
[[0.96064115]
[1.0331714 ]]
After 17500 training steps,w1 is:
[[0.96476096]
[1.0295546 ]]
After 18000 training steps,w1 is:
[[0.9684917]
[1.0262802]]
After 18500 training steps,w1 is:
[[0.9718707]
[1.0233142]]
After 19000 training steps,w1 is:
[[0.974931 ]
[1.0206276]]
After 19500 training steps,w1 is:
[[0.9777026]
[1.0181949]]
Final w1:
[[0.98019385]
[1.0159807 ]]
-
拓展
可以看到不同的损失函数对应的预测的结果也不一样
opt4_1.png
默认本金和利润一样时，预测结果趋近1，1
opt4_2.png
本金小于利润时，趋近1，1，但是会偏大于1，往多了预测
opt4_3.png
本金大于利润时，趋近1，1，但是会偏小于1，往小了预测
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