使用TensorFlow v2.0实现逻辑斯谛回归

此示例使用简单方法来更好地理解训练过程背后的所有机制

MNIST数据集概览

此示例使用MNIST手写数字。该数据集包含60,000个用于训练的样本和10,000个用于测试的样本。这些数字已经过尺寸标准化并位于图像中心，图像是固定大小(28x28像素)，其值为0到255。

在此示例中，每个图像将转换为float32，归一化为[0,1]，并展平为784个特征(28 * 28)的1维数组。

from __future__ import absolute_import,division,print_functionimport tensorflow as tfimport numpy as np# MNIST 数据集参数num_classes = 10 # 数字0-9num_features = 784 # 28*28# 训练参数learning_rate = 0.01training_steps = 1000batch_size = 256display_step = 50# 准备MNIST数据from tensorflow.keras.datasets import mnist(x_train, y_train),(x_test,y_test) = mnist.load_data()# 转换为float32x_train, x_test = np.array(x_train, np.float32), np.array(x_test, np.float32)# 将图像平铺成784个特征的一维向量(28*28)x_train, x_test = x_train.reshape([-1, num_features]), x_test.reshape([-1, num_features])# 将像素值从[0,255]归一化为[0,1]x_train,x_test = x_train / 255, x_test / 255# 使用tf.data api 对数据随机分布和批处理train_data = tf.data.Dataset.from_tensor_slices((x_train, y_train))train_data = train_data.repeat().shuffle(5000).batch(batch_size).prefetch(1)# 权值矩阵形状[784,10]，28 * 28图像特征数和类别数目W = tf.Variable(tf.ones([num_features, num_classes]), name="weight")# 偏置形状[10], 类别数目b = tf.Variable(tf.zeros([num_classes]), name="bias")# 逻辑斯谛回归(Wx+b)def logistic_regression(x): #应用softmax将logits标准化为概率分布 return tf.nn.softmax(tf.matmul(x,W) + b)# 交叉熵损失函数def cross_entropy(y_pred, y_true): # 将标签编码为一个独热编码向量 y_true = tf.one_hot(y_true, depth=num_classes) # 压缩预测值以避免log(0)错误 y_pred = tf.clip_by_value(y_pred, 1e-9, 1.) # 计算交叉熵 return tf.reduce_mean(-tf.reduce_sum(y_true * tf.math.log(y_pred)))# 准确率度量def accuracy(y_pred, y_true): # 预测的类别是预测向量中最高分的索引(即argmax) correct_prediction = tf.equal(tf.argmax(y_pred, 1), tf.cast(y_true, tf.int64)) return tf.reduce_mean(tf.cast(correct_prediction, tf.float32))# 随机梯度下降优化器optimizer = tf.optimizers.SGD(learning_rate)# 优化过程def run_optimization(x, y): #将计算封装在GradientTape中以实现自动微分 with tf.GradientTape() as g: pred = logistic_regression(x) loss = cross_entropy(pred, y) # 计算梯度 gradients = g.gradient(loss, [W, b]) # 根据gradients更新 W 和 b optimizer.apply_gradients(zip(gradients, [W, b]))# 针对给定训练步骤数开始训练for step, (batch_x,batch_y) in enumerate(train_data.take(training_steps), 1): # 运行优化以更新W和b值 run_optimization(batch_x, batch_y) if step % display_step == 0: pred = logistic_regression(batch_x) loss = cross_entropy(pred, batch_y) acc = accuracy(pred, batch_y) print("step: %i, loss: %f, accuracy: %f" % (step, loss, acc))

output:

step: 50, loss: 608.584717, accuracy: 0.824219step: 100, loss: 828.206482, accuracy: 0.765625step: 150, loss: 716.329407, accuracy: 0.746094step: 200, loss: 584.887634, accuracy: 0.820312step: 250, loss: 472.098114, accuracy: 0.871094step: 300, loss: 621.834595, accuracy: 0.832031step: 350, loss: 567.288818, accuracy: 0.714844step: 400, loss: 489.062988, accuracy: 0.847656step: 450, loss: 496.466675, accuracy: 0.843750step: 500, loss: 465.342224, accuracy: 0.875000step: 550, loss: 586.347168, accuracy: 0.855469step: 600, loss: 95.233109, accuracy: 0.906250step: 650, loss: 88.136490, accuracy: 0.910156step: 700, loss: 67.170349, accuracy: 0.937500step: 750, loss: 79.673691, accuracy: 0.921875step: 800, loss: 112.844872, accuracy: 0.914062step: 850, loss: 92.789581, accuracy: 0.894531step: 900, loss: 80.116165, accuracy: 0.921875step: 950, loss: 45.706650, accuracy: 0.925781step: 1000, loss: 72.986969, accuracy: 0.925781# 在验证集上测试模型pred = logistic_regression(x_test)print("Test Accuracy: %f" % accuracy(pred, y_test))

output:

Test Accuracy: 0.901100# 可视化预测import matplotlib.pyplot as plt# 在验证集上中预测5张图片n_images = 5test_images = x_test[:n_images]predictions = logistic_regression(test_images)# 可视化图片和模型预测结果for i in range(n_images): plt.imshow(np.reshape(test_images[i],[28,28]), cmap='gray') plt.show() print("Model prediction: %i" % np.argmax(predictions.numpy()[i]))

output:

Model prediction: 7Model prediction: 2Model prediction: 1Model prediction: 0Model prediction: 4

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