文章目錄

• • 原理
  • 實現
  • • init
    • Keras
    • Tensorflow
    • numpy

原理

$logloss=\frac{1}{n}\sum [?ylog\hat{y}?(1?y)log(1?\hat{y})]$

實現

init

import tensorflow as tf import numpy as np from tensorlfow import keras from tensorflow.keras import Sequential, Model from tensorflow.keras.layers import Dense, Input, LSTMtf.random.set_seed(1)rows = 10 columns = 3epsilon = 1e-7 # sklearn keras 源碼都有epsilon，why？防止log(0)出現learning_rate = 0.01train_x = np.ones(shape=(rows, columns), dtype="float32") # 這里一定要dtype一致，否則numpy與keras計算結果會有差異，我這里統一使用float32 train_y = np.vstack([np.ones(shape=(int(rows/2), 1), dtype="float32"), np.zeros(shape=(int(rows/2),1), dtype="float32")])w = tf.random.normal(shape=(columns, 1), dtype=tf.float32) b = tf.zeros(shape=(1,), dtype=tf.float32)def w_init(shape, dtype=tf.float32):return tf.convert_to_tensor(w, dtype=tf.float32)def b_init(shape, dtype=tf.float32):return tf.convert_to_tensor(b, dtype=tf.float32)

Keras

model1 = Sequential() model1.add(Input(shape=(columns, ))) model1.add(Dense(units=1, kernel_initializer=w_init, bias_initializer=b_init, activation="sigmoid"))h1 = model1.predict(train_x)model1.compile(loss="binary_crossentropy", optimizer=tf.keras.optimizers.SGD(learning_rate=learning_rate), metrics=["accuracy"])model1.fit(train_x, train_y, epochs=1, batch_size=rows)w1, b1 = model1.layers[0].weights

Tensorflow

x = tf.Variable(train_x, dtype=tf.float32) y = tf.Variable(train_y, dtype=tf.float32) with tf.GradientTape(persistent=True) as tape:tape.watch([w, b])y_pred = tf.sigmoid(tf.matmul(x, w) + b)loss = -1*train_y*tf.math.log(y_pred+epsilon) - (1-train_y)*tf.math.log(1-y_pred+epsilon)dw2 = tape.gradient(target=loss, sources=w) db2 = tape.gradient(target=loss, sources=b)w2 = w - dw2*learning_rate b2 = b - db2*learning_rate

numpy

epochs = 1def sigmoid(x):return 1/(1+np.exp(-x))w3 = w b3 = b h3 = None for epoch in range(epochs):h3 = sigmoid(np.dot(train_x, w3)+b3)loss = -1*np.sum(train_y*np.log(h3) + (1-train_y)*np.log(1-h3))/rowsprint(f"loss: {loss}")dw3 = np.dot(train_x.T, h3-train_y)db3 = np.dot(np.ones(shape=(1, rows), dtype="float32"), h3-train_y)w3 = w3 - dw3*learning_rateb3 = b3 - db3*learning_ratew3 b3 epochs = 1def sigmoid(x):return 1/(1+np.exp(-x))w4 = w b4 = b h4 = None for epoch in range(epochs):h4 = sigmoid(np.dot(train_x, w4)+b4)loss = -1*np.sum(train_y*np.log(h4) + (1-train_y)*np.log(1-h4))/rowsprint(f"loss: {loss}")dw4 = np.dot(train_x.T, (h4-train_y-2*train_y*epsilon+epsilon)/(h4+epsilon)/(1-h4+epsilon))dw4 = np.dot(train_x.T, -1*train_y/(h4+epsilon)+(1-train_y)/(1-h4+epsilon))db4 = np.dot(np.ones(shape=(1, rows), dtype="float32"), h4-train_y)w4 = w4 - dw4*learning_rateb4 = b4 - db4*learning_ratew4 b4

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