时间序列数据的自定义损失函数

Question

我第一次尝试编写自定义损失函数。我的模型生成一个时间序列数据，我想要一个损失函数，它会比早期的错误更多地惩罚系列中后期的错误。类似于张量索引用于确定惩罚的位置。张量具有以下结构。

y_true

y_pred

我应该怎么做才能使惩罚成为索引的函数？

 def custom_loss_function(y_true, y_pred):
   squared_difference = tf.square(y_true - y_pred) * 'sqrt(tensor_index)'  <- Desired part
   return tf.reduce_mean(squared_difference, axis=-1)

Answer 1

也许尝试使用 tf.linspace:

import tensorflow as tf

y_true = tf.random.normal((1, 48, 1))
y_pred = tf.random.normal((1, 48, 1))

def custom_loss_function(y_true, y_pred):
   penalty = tf.cast(tf.linspace(start = 1, stop = 5, num = y_pred.shape[1]), dtype=tf.float32)
   print(penalty)
   squared_difference = tf.square(y_true - y_pred) * tf.expand_dims(penalty, axis=-1)
   return tf.reduce_mean(squared_difference, axis=-1)

print(custom_loss_function(y_true, y_pred))

tf.Tensor(
[1.        1.0851064 1.1702127 1.2553191 1.3404255 1.4255319 1.5106384
 1.5957447 1.6808511 1.7659575 1.8510638 1.9361702 2.0212767 2.106383
 2.1914895 2.2765958 2.3617022 2.4468086 2.531915  2.6170213 2.7021277
 2.787234  2.8723404 2.9574468 3.0425532 3.1276596 3.212766  3.2978723
 3.3829787 3.468085  3.5531914 3.6382978 3.7234042 3.8085105 3.893617
 3.9787233 4.06383   4.1489363 4.2340426 4.319149  4.4042554 4.489362
 4.574468  4.6595745 4.744681  4.8297873 4.9148936 5.       ], shape=(48,), dtype=float32)
tf.Tensor(
[[1.3424503e+00 1.7936407e+00 9.5141016e-02 4.1933870e-01 2.9060142e-02
  1.6663458e+00 3.7182972e+00 2.3884547e-01 1.6393075e+00 9.8062935e+00
  1.4726014e+00 6.4087069e-01 1.4197667e+00 2.7730075e-01 2.6717324e+00
  1.2410884e+01 2.8422637e+00 2.2836231e+01 1.9438576e+00 7.2612977e-01
  2.9226139e+00 1.3040878e+01 5.8225789e+00 2.3456068e+00 2.8281093e+00
  4.2308202e+00 2.6682162e+00 4.0025130e-01 3.5946998e-01 8.0574770e-03
  2.7833527e-01 3.8349494e-01 7.1913116e-02 3.0325607e-03 5.8022089e+00
  4.4835452e-02 4.7429881e+00 6.4035267e-01 5.0330186e+00 2.7156603e+00
  1.2085355e-01 3.5016473e-02 7.9860941e-02 3.1455503e+01 5.3314602e+01
  3.8006527e+01 1.1620968e+01 4.1495290e+00]], shape=(1, 48), dtype=float32)

更新 1:

import tensorflow as tf

y_true = tf.random.normal((2, 48, 1))
y_pred = tf.random.normal((2, 48, 1))
def custom_loss_function(y_true, y_pred):
   penalty = tf.cast(tf.linspace(start = 1, stop = 5, num = tf.shape(y_pred)[1]), dtype=tf.float32)
   penalty = tf.expand_dims(penalty, axis=-1)
   penalty = tf.expand_dims(tf.transpose(tf.repeat(penalty, repeats=tf.shape(y_pred)[0], axis=1)), axis=-1)
   squared_difference = tf.square(y_true - y_pred) * penalty
   return tf.reduce_mean(squared_difference, axis=-1)

时间序列数据的自定义损失函数

Custom loss function for time series data

python

tensorflow

keras

loss-function