更高维的数据
import numpy as np
from sklearn.datasets import *
import pandas as pd
import tensorflow as tf
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
from random import *
from sklearn.metrics import accuracy_score
from scipy.special import logit
Xinput, yinput = make_blobs(n_samples = 1000, centers = 2, n_features = 2)
df = pd.DataFrame(dict(x=Xinput[:,0], y = Xinput[:,1], label = yinput))
Xinput[0:5,]
yinput[0:10,]
colors = {0:'red', 1:'blue', 2:'green'}
fig, ax = plt.subplots()
plt.scatter(df[yinput==1]['x'], df[yinput==1]['y'], color = 'red')
plt.scatter(df[yinput==0]['x'], df[yinput==0]['y'], color = 'blue')
plt.tick_params(labelsize=14)
plt.xlabel('x', fontsize = 16)
plt.ylabel('y', fontsize = 16)
plt.show()
#tf.reset_default_graph()
X = tf.cast( Xinput.reshape(-1,2),tf.float32)
Y = tf.cast( yinput.reshape(-1,1),tf.float32)
def run_logistic_model(learning_r, training_epochs, train_obs, train_labels, debug = False):
optimizer = tf.optimizers.SGD(learning_r)
#optimizer= tf.keras.optimizers.Adam(learning_rate=learning_r)
cost_history = np.empty(shape=[0], dtype = float)
loss_list_train = []
loss_list_valid = []
acc_list_train = []
acc_valid_train = []
W = tf.Variable(tf.random.normal((2, 1)))
b = tf.Variable(tf.random.normal((1,)))
for epoch in range(training_epochs+1):
with tf.GradientTape() as tape:
PRED=1/(1+tf.exp(-tf.matmul(X,W)+b))
Loss=-tf.reduce_mean(Y*tf.math.log(PRED)+(1-Y)*tf.math.log(1-PRED))
gradients=tape.gradient(Loss,[W,b])
#_, summary, loss = sess.run([train_op, merged, l], feed_dict=feed_dict)
#y_logit = tf.matmul(X, W) + b
the sigmoid gives the class probability of 1
#y_one_prob = tf.sigmoid(y_logit)
Rounding P(y=1) will give the correct prediction.
#y_pred = tf.round(y_one_prob)
#entropy = tf.nn.sigmoid_cross_entropy_with_logits(logits=y_logit, labels=Y)
Sum all contributions
#l = tf.reduce_sum(entropy)
#gradients=tape.gradient(l,[W,b])
optimizer.apply_gradients(zip(gradients, [W, b]))
#Acc=tf.reduce_mean(tf.cast(tf.equal(tf.cast(tf.where(PRED.numpy()<0.5,0,1),tf.float32),Y),tf.float32))
#loss_train =loss(train_obs,train_labels,W,b).numpy()
#loss_valid =loss(valid_x,valid_y,W,B).numpy()
#acc_train=accuracy(train_obs,train_labels,W,b).numpy()
#acc_valid=accuracy(valid_x,valid_y,W,B).numpy()
loss_list_train.append(Loss)
#loss_list_valid.append(loss_valid)
#acc_list_train.append(Acc)
#acc_valid_train.append(acc_valid)
#print("epoch={:3d},train_loss={:.4f},train_acc={:.4f},val_loss={:.4f},val_acc={:.4f}".format(epoch+1,loss_train,acc_train,loss_valid,acc_valid))
if (epoch % 1000 == 0) & debug:
print("Reached epoch",epoch,"cost J =", str.format('{0:.6f}', Loss))
return loss_list_train,W,b
cost_history,W,b = run_logistic_model(learning_r = 0.01,
training_epochs = 10000,
train_obs =X,
train_labels = Y,
debug = True)
plt.rc('font', family='arial')
plt.rc('xtick', labelsize='x-small')
plt.rc('ytick', labelsize='x-small')
plt.tight_layout()
fig = plt.figure(figsize=(10,8))
ax = fig.add_subplot(1, 1, 1)
ax.plot(cost_history, ls='solid', color = 'black', label = '\\gamma = 0.01')
ax.set_xlabel('epochs', fontsize = 16)
ax.set_ylabel('Cost function J', fontsize = 16)
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0., fontsize = 16)
plt.tick_params(labelsize=16)
colors = {0:'red', 1:'blue', 2:'green'}
fig, ax = plt.subplots()
plt.scatter(df[yinput==1]['x'], df[yinput==1]['y'], color = 'red')
plt.scatter(df[yinput==0]['x'], df[yinput==0]['y'], color = 'blue')
plt.tick_params(labelsize=14)
plt.xlabel('x', fontsize = 16)
plt.ylabel('y', fontsize = 16)
plt.xlim(-10, 7.5)
plt.ylim(-10, 20)
x_left = -10
y_left = (1./W[1]) * (-b + logit(.5) - W[0]*x_left)
x_right = 7.5
y_right = (1./W[1]) * (-b + logit(.5) - W[0]*x_right)
plt.plot([x_left, x_right], [y_left, y_right], color='k')
plt.show()
#plt.savefig("logistic_pred.png")
