Keras 中具有样本权重的自定义损失函数

Question

我是 Tensorflow 和 Keras 的新手。我想在自定义损失函数中使用样本权重。

如果我理解正确，这篇文章 (Custom loss function with weights in Keras) 建议将权重作为网络的输入。 还有这个： Custom weighted loss function in Keras for weighing each element

我想知道我是否遗漏了什么（我也不想将权重定义为全局变量）。我也有点惊讶没有直接使用它的方法，因为 Loss 类 _ _ call _ _ 方法接受 sample_weight 作为参数，但如果我理解正确，损失函数必须只有参数 y_true 和 y_pred。

然而，从文档 (https://keras.io/api/losses/#creating-custom-losses)：

创建自定义损失 任何带有签名 loss_fn(y_true, y_pred) 且返回损失数组（输入批次中的样本之一）的可调用函数都可以作为损失传递给 compile()。请注意，任何此类损失都会自动支持样本加权。

听起来应该可以通过 model.fit(..., sample_weight=sample_weight) 方法使用样本加权。

在这篇文章中（Should the custom loss function in Keras return a single loss value for the batch or an arrary of losses for every sample in the training batch? ) 关于损失函数的输出大小有一个冗长的讨论。

最后还提到，当创建自定义损失函数时，应该返回一组损失（单个样本损失）。它们的减少由框架处理。

在我看来，如果 custom_loss(y_true, y_pred) 返回一个大小为 (batch_size, ) 的张量，那么应该能够在 fit 方法中使用 sample_weight。我错过了什么？

非常感谢您的帮助！

代码sn-ps：

class NegLogLikMixedGaussian(Loss):
    """
    Negative Log-Likelihood of Mixed Gaussian with:
        num_components: number of components
        mu: means of the Gaussian components
        sg: standard deviations of the Gaussian components
    """

    def __init__(self, num_params=NUM_PARAMS_MG,
                 num_components=2, name='neg_log_lik_mixed_gaussian'):
        super(NegLogLikMixedGaussian, self).__init__(name=name)
        self.num_params = num_params
        self.num_components = num_components

    def call(self, y_true, p_predict):
        """
        Rem: for MDN the output of the networks are _parameters_ of the
        predicted distribution, _not_ point-estimates

        Parameters
        ----------
        y_true: (batch_size, 1)
            Observed value of the random variable
        p_predict: (batch_size, num_components)
            Output parameters of the network given some input

        Returns
        -------
        Negative log likelihood of the batch (batch_size, 1)

        """
        alpha, mu, sg = tf.split(p_predict,
                                 num_or_size_splits=self.num_params, axis=1)
        gm = tfd.MixtureSameFamily(
            mixture_distribution=tfd.Categorical(probs=alpha),
            components_distribution=tfd.Normal(loc=mu, scale=sg))
        log_likelihood = tf.transpose(gm.log_prob(tf.transpose(y_true)))
        return -tf.reduce_mean(log_likelihood, axis=-1)

我希望那时能够使用：

model.compile(optimizer=Adam(learning_rate=0.005),
                  loss=NegLogLikMixedGaussian(
                      num_components=2, num_params=3))

还有：

# For testing purposes
sample_weight = np.ones(len(y_train)) / len(dh.y_train_scaled)  # this should give same results as un-weighted

# Some non-trivial weights
sample_weights = np.zeros(len(y_train))
sample_weights[:5] = 1
# This will give me same results as above


model.fit(x_train, y_train, sample_weight=sample_weight,
                      batch_size=128, epochs=10)

Answer 1

如果我理解你想要做什么，你的代码是正确的，除了一些细节。 样本权重应该是维度（样本数），尽管损失应该是维度（batch_size）。 样本权重可以传递给 fit 方法，它似乎有效。 在您的自定义损失类中，num_components 和 num_params 已初始化，但在 call 方法中仅使用了两个参数之一。 我不确定我是否理解张量的维度（alpha、mu、sg），它是否是模型预测的维度（batch_size、3、num_components）？ 根据我对您的问题的理解，以下是根据您的代码改编的代码。

import tensorflow as tf
import numpy as np
from tensorflow.keras.losses import Loss, BinaryCrossentropy
from tensorflow.keras import Model, Input
from tensorflow.keras.layers import Dense, Concatenate

import tensorflow_probability as tfp
tfd = tfp.distributions

# parameters
num_components = 2
num_samples = 1001
num_features = 10

# synthetic data
x_train = np.random.normal(size=(num_samples, num_features))
y_train = np.random.normal(size=(num_samples, 1, num_components))

print(x_train.shape)
print(y_train.shape)

class NegLogLikMixedGaussian(Loss):
    """
    Negative Log-Likelihood of Mixed Gaussian with:
        num_components: number of components
        mu: means of the Gaussian components
        sg: standard deviations of the Gaussian components
    """

    def __init__(self, num_components=2, name='neg_log_lik_mixed_gaussian'):
        super(NegLogLikMixedGaussian, self).__init__(name=name)
        self.num_components = num_components

    def call(self, y_true, p_predict):
        """
        Rem: for MDN the output of the networks are _parameters_ of the
        predicted distribution, _not_ point-estimates

        Parameters
        ----------
        y_true: (batch_size, 1, num_components)
            Observed value of the random variable
        p_predict: (batch_size, 3, num_components)
            Output parameters of the network given some input

        Returns
        -------
        Negative log likelihood of the batch (batch_size, 1)

        """
        alpha, mu, sg = tf.split(p_predict, num_or_size_splits=3, axis=1)
        gm = tfd.MixtureSameFamily(
            mixture_distribution=tfd.Categorical(probs=alpha),
            components_distribution=tfd.Normal(loc=mu, scale=sg))
        log_likelihood = gm.log_prob(y_true)
        return -tf.reduce_mean(log_likelihood, axis=[1, 2])

# the model (simple predicting (alpha, mu, sigma))
input = Input((num_features,))
alpha = tf.expand_dims(Dense(num_components, 'relu')(input), axis=1)+0.0001
# normalization
alpha = alpha/tf.reduce_sum(alpha, axis=2, keepdims=True)
mu = tf.expand_dims(Dense(num_components)(input), axis=1)
# sg > 0
sg = tf.expand_dims(Dense(num_components, 'relu')(input), axis=1)+ 0.0001

outputs = Concatenate(axis=1)([alpha, mu, sg])

model = Model(inputs=input, outputs=outputs, name='gmm_params')
model.compile(optimizer='adam', loss=NegLogLikMixedGaussian(num_components=num_components), run_eagerly=False)

sample_weight=np.ones((num_samples, ))
sample_weight[500:] = 0.

model.fit(x_train, y_train, batch_size=16, epochs=20, sample_weight=sample_weight)