本文共 2725 字，大约阅读时间需要 9 分钟。
l o g l o s s = 1 n ∑ [ − y l o g y ^ − ( 1 − y ) l o g ( 1 − y ^ ) ] logloss=\frac{1}{n}\sum[-ylog\hat{y}-(1-y)log(1-\hat{y})] logloss=n1∑[−ylogy^−(1−y)log(1−y^)]
import tensorflow as tfimport numpy as npfrom tensorlfow import kerasfrom tensorflow.keras import Sequential, Modelfrom tensorflow.keras.layers import Dense, Input, LSTMtf.random.set_seed(1)rows = 10columns = 3epsilon = 1e-7 # sklearn keras 源码都有epsilon，why？防止log(0)出现learning_rate = 0.01train_x = np.ones(shape=(rows, columns), dtype="float32") # 这里一定要dtype一致，否则numpy与keras计算结果会有差异，我这里统一使用float32train_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)
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
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_rateb2 = b - db2*learning_rate
epochs = 1def sigmoid(x): return 1/(1+np.exp(-x))w3 = wb3 = bh3 = Nonefor 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))/rows print(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_rate b3 = b3 - db3*learning_ratew3b3 epochs = 1def sigmoid(x): return 1/(1+np.exp(-x))w4 = wb4 = bh4 = Nonefor 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))/rows print(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_rate b4 = b4 - db4*learning_ratew4b4 转载地址：http://tlugf.baihongyu.com/