python-tensorflow实现非线性回归（两个案例）

''' tensorflow 实现非线性回归 案例一：y = ax^2+bx+c 案例二：y = a*exp(-(x-u)**2/(x*sigma**2))+b 这个和神经网络目前来看还没有关系，好像完全就是利用模型，然后去进行反向传播，最后去计算的最优参数 ''' import tensorflow as tf import numpy as np import matplotlib.pyplot as plt '''案例一：y = ax^2+bx+c''' def demo1(): #构造数据 x = np.arange(-10,10,0.1) y = 3*x**2+2*x+1 plt.plot(x,y,'*') # plt.show() #构造模型 xx = tf.placeholder(dtype=tf.float32,shape=[x.shape[0]],name='xx') a = tf.Variable(initial_value=0.0,name='a') b = tf.Variable(initial_value=0.0,name='b') c = tf.Variable(initial_value=0.0,name='c') yy = tf.placeholder(dtype=tf.float32,shape=[y.shape[0]],name='yy') predict = a*xx**2+b*xx+c loss = tf.sqrt(tf.reduce_mean((yy-predict)**2)) Optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.0005).minimize(loss) with tf.Session() as sess: tf.global_variables_initializer().run() for i in range(7000): Optimizer.run(feed_dict={xx:x,yy:y}) print("loss:%f"%(loss.eval(feed_dict={xx:x,yy:y}))) print('a:%f,b:%f,c:%f'%(a.eval(),b.eval(),c.eval())) plt.plot(x,a.eval()*x**2+b.eval()*x+c.eval()) plt.show()

迭代了7000次后，达到了较小的损失

loss:0.500241 loss:0.500210 loss:0.500238 a:3.012125,b:2.000031,c:0.941524

输出结果

第二个案例

'''案例二：y = a*exp(-(x-u)**2/(x*sigma**2))+b''' def demo2(): #构造数据 x = np.arange(-10,10,0.1) a = 2 u = 1.0 s = 1.0 b = 2 y = a*np.exp(-(x-u)**2*s)+b plt.plot(x,y,'*') # plt.show() #构造模型 xx = tf.placeholder(dtype=tf.float32,shape=[x.shape[0]],name='xx') aa = tf.Variable(initial_value=3.5,name='aa') bb = tf.Variable(initial_value=2.2,name='bb') uu = tf.Variable(initial_value=1.5,name='uu') ss = tf.Variable(initial_value=2.0,name='sigma') yy = tf.placeholder(dtype=tf.float32,shape=[y.shape[0]],name='xx') predict = aa*tf.exp(-(xx-uu)**2*ss)+bb loss = tf.sqrt(tf.reduce_mean((yy-predict)**2)) Optimizer = tf.train.AdamOptimizer(learning_rate=0.0005).minimize(loss) with tf.Session() as sess: tf.global_variables_initializer().run() for i in range(5000): Optimizer.run(feed_dict={xx:x,yy:y}) print("loss:%f"%(loss.eval(feed_dict={xx:x,yy:y}))) print('aa:%f,uu:%f,ss:%f,bb:%f'%(aa.eval(),uu.eval(),ss.eval(),bb.eval())) plt.plot(x,aa.eval()*np.exp(-(x-uu.eval())**2*ss.eval())+bb.eval()) plt.show() # demo2()

loss:0.000044 loss:0.000041 loss:0.000031 aa:2.000023,uu:1.000000,ss:0.999975,bb:2.000025

结果图