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cross entropy is a widely used loss function in machine learning, particularly in classification problems. it measures the performance of a classification model whose output is a probability value between 0 and 1. in this tutorial, we'll delve into the concept of cross entropy and demonstrate how to implement it in python with a simple example.
cross entropy is a mathematical formula that quantifies the difference between the predicted probability distribution and the actual probability distribution. in the context of classification problems, the predicted distribution is the output of your model, while the actual distribution is the true distribution of the labels.
for a binary classification problem, the cross entropy loss between the true distribution (y) and the predicted distribution (ŷ) is defined as:
h(y,
y
^
)=−
n
1
∑
i=1
n
[y
i
⋅log(
y
^
i
)+(1−y
i
)⋅log(1−
y
^
i
)]
for multi-class classification, the formula is slightly different:
h(y,
y
^
)=−
n
1
∑
i=1
n
∑
j=1
m
y
ij
⋅log(
y
^
ij
)
where:
let's implement the cross entropy loss function in python using numpy. for simplicity, we'll focus on binary classification.
in this example:
the binary_cross_entropy function calculates the binary cross entropy loss between y_true and y_pred.
cross entropy is a fundamental concept in machine learning, especially in classification tasks. understanding and implementing the cross entropy loss function in python is essential for evaluating and optimizing classification models. this tutorial provides a simple example for binary classification, and you can extend it for multi-class scenarios by modifying the formula accordingly.
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