Cost-sensitive learning in Tensorflow - machine-learning

Question

I am trying to set up a cost-sensitive binary classification learning in TensorFlow, which would put different penalties on false positives and false negatives. Does anyone know how to create a loss function from a set of penalty weights $(w_1, w_2, w_3, w_4)$ for (true positive, false positive, false negative, true negative).
I went over the standard cost functions offered, but can't figure out how to combine them to get something similar to the above.

Answer 1

Following #Cauchyzhou's answer, if you have the logits, and the sparse labels as well as a cost_matrix whose shape is [L, L], where L is the number of unique labels, you can simply use the function below to calculate the loss
def sparse_cost_sensitive_loss (logits, labels, cost_matrix):
batch_cost_matrix = tf.nn.embedding_lookup(cost_matrix, labels)
eps = 1e-6
probability = tf.clip_by_value(tf.nn.softmax(logits), eps, 1-eps)
cost_values = tf.log(1-probability)*batch_cost_matrix
loss = tf.reduce_mean(-tf.reduce_sum(cost_values, axis=1))
return loss

Answer 2

I am not aware of anyone who has built a cost sensitive neural network classifier but Alejandro Correa Bahnsen has published academic papers for cost sensitive logistic regression and cost sensitive decision trees and a very well documented python cost sensitive classification library named CostCla. CostCla is pretty easy to use if you are familiar with scikit-learn.
You should be able to use the Bayes minimum risk model in the library to minimize the cost of your neural network since it fits a cost model to output prediction probabilities of any classifier.
Note that CostCla is intended to work with potentially different costs for each sample. You give it a cost matrix for your training and test samples. However, you can just make all the rows in the cost matrix the same if that applies to your problem.
Here are a couple of additional academic papers on the subject:
The Foundations of Cost-Sensitive Learning
Optimal ROC Curve for a Combination of Classifiers

Answer 3

cost_matrix:
[[0,1,100],
[1,0,1],
[1,20,0]]
label:
[1,2]
y*:
[[0,1,0],
[0,0,1]]
y(prediction):
[[0.2,0.3,0.5],
[0.1,0.2,0.7]]
label,cost_matrix-->cost_embedding:
[[1,0,1],
[1,20,0]]
It obvious 0.3 in [0.2,0.3,0.5] refers to right lable probility of [0,1,0], so it should not contibute to loss.
0.7 in [0.1,0.2,0.7] is the same. In other words, the pos with value 1 in y* not contibute to loss.
So I have (1-y*):
[[1,0,1],
[1,1,0]]
Then the entropy is target*log(predict) + (1-target) * log(1-predict),and value 0 in y*,should use (1-target)*log(1-predict), so I use (1-predict) said (1-y)
1-y:
[[0.8,*0.7*,0.5],
[0.9,0.8,*0.3*]]
(italic num is useless)
the custom loss is
[[1,0,1], [1,20,0]] * log([[0.8,0.7,0.5],[0.9,0.8,0.3]]) *
[[1,0,1],[1,1,0]]
and you can see the (1-y*) can be drop here
so the loss is -tf.reduce_mean(cost_embedding*log(1-y))
,to make it applicable , should be:
-tf.reduce_mean(cost_embedding*log(tf.clip((1-y),1e-10)))
the demo is below
import tensorflow as tf
import numpy as np
hidden_units = 50
num_class = 3
class Model():
def __init__(self,name_scope,is_custom):
self.name_scope = name_scope
self.is_custom = is_custom
self.input_x = tf.placeholder(tf.float32,[None,hidden_units])
self.input_y = tf.placeholder(tf.int32,[None])
self.instantiate_weights()
self.logits = self.inference()
self.predictions = tf.argmax(self.logits,axis=1)
self.losses,self.train_op = self.opitmizer()
def instantiate_weights(self):
with tf.variable_scope(self.name_scope + 'FC'):
self.W = tf.get_variable('W',[hidden_units,num_class])
self.b = tf.get_variable('b',[num_class])
self.cost_matrix = tf.constant(
np.array([[0,1,100],[1,0,100],[20,5,0]]),
dtype = tf.float32
)
def inference(self):
return tf.matmul(self.input_x,self.W) + self.b
def opitmizer(self):
if not self.is_custom:
loss = tf.nn.sparse_softmax_cross_entropy_with_logits\
(labels=self.input_y,logits=self.logits)
else:
batch_cost_matrix = tf.nn.embedding_lookup(
self.cost_matrix,self.input_y
)
loss = - tf.log(1 - tf.nn.softmax(self.logits))\
* batch_cost_matrix
train_op = tf.train.AdamOptimizer().minimize(loss)
return loss,train_op
import random
batch_size = 128
norm_model = Model('norm',False)
custom_model = Model('cost',True)
split_point = int(0.9 * dataset_size)
train_set = datasets[:split_point]
test_set = datasets[split_point:]
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
for i in range(100):
batch_index = random.sample(range(split_point),batch_size)
train_batch = train_set[batch_index]
train_labels = lables[batch_index]
_,eval_predict,eval_loss = sess.run([norm_model.train_op,
norm_model.predictions,norm_model.losses],
feed_dict={
norm_model.input_x:train_batch,
norm_model.input_y:train_labels
})
_,eval_predict1,eval_loss1 = sess.run([custom_model.train_op,
custom_model.predictions,custom_model.losses],
feed_dict={
custom_model.input_x:train_batch,
custom_model.input_y:train_labels
})
# print '默认',eval_predict,'\n自定义',eval_predict1
print np.sum(((eval_predict == train_labels)==True).astype(np.int)),\
np.sum(((eval_predict1 == train_labels)==True).astype(np.int))
if i%10 == 0:
print '默认测试',sess.run(norm_model.predictions,
feed_dict={
norm_model.input_x:test_set,
norm_model.input_y:lables[split_point:]
})
print '自定义测试',sess.run(custom_model.predictions,
feed_dict={
custom_model.input_x:test_set,
custom_model.input_y:lables[split_point:]
})

Answer 4

Here is other solution where you can use any tensorflow loss and make it cost sensitive using kwarg weights ... note that unlike most cases here you need to use cost as '1' instead of '0' when you want to keep loss as it is ...
Some advantages of this approach are:
it extends tf.losses.Loss and satisfies the call api
reduction kwarg of the original loss remains functional and the behaviour is propagated to CostSensitiveLoss
you can also pass your own extra weights to new loss instances. Note that internally generated weights are used by wrapped self.loss
import numpy as np
from keras.api._v2 import keras as tk
import tensorflow as tf
from keras.utils import losses_utils
import typing as t
class CostSensitiveLoss(tk.losses.Loss):
def __init__(
self,
cost_matrix: t.List, loss: tk.losses.Loss,
):
super().__init__(reduction=loss.reduction, name=loss.name)
self.loss = loss
self.cost_matrix = cost_matrix
self._cost_matrix = tf.constant(cost_matrix, dtype=tf.float32)
#classmethod
def from_config(cls, config):
config['loss'] = tk.losses.deserialize(config['loss'])
return cls(**config)
def get_config(self):
return {
'cost_matrix': self.cost_matrix,
'loss': tk.losses.serialize(self.loss),
'reduction': self.reduction, 'name': self.name
}
def call(self, y_true, y_pred):
# if y_true is one hot encoded then get integer indices
if y_true.ndim == 1:
y_true_index = y_true
elif y_true.ndim == 2:
y_true_index = tf.argmax(y_true, axis=1)
else:
raise Exception(f"`y_true.ndim` {y_true.ndim} not supported")
# get cost for batch
cost_for_batch = tf.nn.embedding_lookup(self._cost_matrix, y_true_index)
cost_for_batch *= y_pred
cost_for_batch = tf.reduce_sum(cost_for_batch, axis=1)
# get loss
return self.loss(y_true, y_pred, cost_for_batch)
if __name__ == '__main__':
# for debug purpose I have kept 'none' you can
# safely use other options like 'sum', 'auto'
_loss = tk.losses.MeanAbsoluteError(reduction='none')
# some cost matrices the first cost matrix is the case when you are
# not using cost sensitive weights
_cs_loss_1 = CostSensitiveLoss(
cost_matrix=[[1, 1, 1], [1, 1, 1], [1, 1, 1], ],
loss=_loss
)
_cs_loss_2 = CostSensitiveLoss(
cost_matrix=[[1, 2, 2], [4, 1, 4], [8, 8, 1], ],
loss=_loss
)
_cs_loss_3 = CostSensitiveLoss(
cost_matrix=[[1, 4, 8], [2, 1, 8], [2, 4, 1], ],
loss=_loss
)
_y_true = np.asarray(
[
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
]
)
_y_pred = np.asarray(
[
[0.8, 0.1, 0.1],
[0.1, 0.8, 0.1],
[0.1, 0.1, 0.8],
[0.1, 0.8, 0.1],
[0.1, 0.1, 0.8],
[0.8, 0.1, 0.1],
[0.1, 0.1, 0.8],
[0.8, 0.1, 0.1],
[0.1, 0.8, 0.1],
]
)
print("loss ........................")
print(_loss(_y_true, _y_pred).numpy())
print("cs_loss_1 ...................")
print(_cs_loss_1(_y_true, _y_pred).numpy())
print("cs_loss_2 ...................")
print(_cs_loss_2(_y_true, _y_pred).numpy())
print("cs_loss_3 ...................")
print(_cs_loss_3(_y_true, _y_pred).numpy())