文章目錄

• • 基礎理論
  • • 交叉熵
  • tensorFlow中的損失函數
  • • BinaryCrosstropy
    • CategoricalCrossentropy
    • CosineSimilarity
    • Hinge
    • Huber
    • KLDivergence
    • LogCosh
    • MeanAbsoluteError
    • MeanAbsolutePercentageError
    • MeanSquaredError
    • MeanSquaredLogarithmicError
    • Poisson
    • SquaredHinge

基礎理論

交叉熵

參考：https://zhuanlan.zhihu.com/p/35709485
常用于分類問題，但是也可以用于回歸問題

tensorFlow中的損失函數

BinaryCrosstropy

計算真實標簽和預測標簽之間的交叉熵損失。
當只有兩個標簽類別（假定為0和1）時，請使用此交叉熵損失。對于每個示例，每個預測應該有一個浮點值。

tf.keras.losses.BinaryCrossentropy(from_logits=False, label_smoothing=0, reduction=losses_utils.ReductionV2.AUTO,name='binary_crossentropy' ) y_true = [[0., 1.], [0., 0.]] y_pred = [[0.6, 0.4], [0.4, 0.6]] # Using 'auto'/'sum_over_batch_size' reduction type. bce = tf.keras.losses.BinaryCrossentropy() bce(y_true, y_pred).numpy()

CategoricalCrossentropy

計算標簽和預測之間的交叉熵損失。
當有兩個或多個標簽類別時，請使用此交叉熵損失函數。我們希望標簽以one_hot表示形式提供。如果要以整數形式提供標簽，請使用SparseCategoricalCrossentropy損失。

tf.keras.losses.CategoricalCrossentropy(from_logits=False, label_smoothing=0, reduction=losses_utils.ReductionV2.AUTO,name='categorical_crossentropy' ) y_true = [[0, 1, 0], [0, 0, 1]] y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]] # Using 'auto'/'sum_over_batch_size' reduction type. cce = tf.keras.losses.CategoricalCrossentropy() cce(y_true, y_pred).numpy()

CosineSimilarity

直接計算l2范數的差別
loss = -sum(l2_norm(y_true) * l2_norm(y_pred))

y_true = [[0., 1.], [1., 1.]] y_pred = [[1., 0.], [1., 1.]] # Using 'auto'/'sum_over_batch_size' reduction type. cosine_loss = tf.keras.losses.CosineSimilarity(axis=1) # l2_norm(y_true) = [[0., 1.], [1./1.414], 1./1.414]]] # l2_norm(y_pred) = [[1., 0.], [1./1.414], 1./1.414]]] # l2_norm(y_true) . l2_norm(y_pred) = [[0., 0.], [0.5, 0.5]] # loss = mean(sum(l2_norm(y_true) . l2_norm(y_pred), axis=1)) # = -((0. + 0.) + (0.5 + 0.5)) / 2 cosine_loss(y_true, y_pred).numpy()

Hinge

loss = maximum(1 - y_true * y_pred, 0)

y_true = [[0., 1.], [0., 0.]] y_pred = [[0.6, 0.4], [0.4, 0.6]] # Using 'auto'/'sum_over_batch_size' reduction type. h = tf.keras.losses.Hinge() h(y_true, y_pred).numpy()

Huber

結合了均方誤差和平均絕對值誤差

tf.keras.losses.Huber(delta=1.0, reduction=losses_utils.ReductionV2.AUTO, name='huber_loss' ) y_true = [[0, 1], [0, 0]] y_pred = [[0.6, 0.4], [0.4, 0.6]] # Using 'auto'/'sum_over_batch_size' reduction type. h = tf.keras.losses.Huber() h(y_true, y_pred).numpy()

KLDivergence

相對熵

y_true = [[0, 1], [0, 0]] y_pred = [[0.6, 0.4], [0.4, 0.6]] # Using 'auto'/'sum_over_batch_size' reduction type. kl = tf.keras.losses.KLDivergence() kl(y_true, y_pred).numpy()

LogCosh

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [0., 0.]] # Using 'auto'/'sum_over_batch_size' reduction type. l = tf.keras.losses.LogCosh() l(y_true, y_pred).numpy()

MeanAbsoluteError

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [1., 0.]] # Using 'auto'/'sum_over_batch_size' reduction type. mae = tf.keras.losses.MeanAbsoluteError() mae(y_true, y_pred).numpy()

MeanAbsolutePercentageError

y_true = [[2., 1.], [2., 3.]] y_pred = [[1., 1.], [1., 0.]] # Using 'auto'/'sum_over_batch_size' reduction type. mape = tf.keras.losses.MeanAbsolutePercentageError() mape(y_true, y_pred).numpy()

MeanSquaredError

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [1., 0.]] # Using 'auto'/'sum_over_batch_size' reduction type. mse = tf.keras.losses.MeanSquaredError() mse(y_true, y_pred).numpy()

MeanSquaredLogarithmicError

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [1., 0.]] # Using 'auto'/'sum_over_batch_size' reduction type. msle = tf.keras.losses.MeanSquaredLogarithmicError() msle(y_true, y_pred).numpy()

Poisson

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [0., 0.]] # Using 'auto'/'sum_over_batch_size' reduction type. p = tf.keras.losses.Poisson() p(y_true, y_pred).numpy()

SquaredHinge

y_true = [[0., 1.], [0., 0.]] y_pred = [[0.6, 0.4], [0.4, 0.6]] # Using 'auto'/'sum_over_batch_size' reduction type. h = tf.keras.losses.SquaredHinge() h(y_true, y_pred).numpy()

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