Why not MCE for all cases?
A natural question that comes to mind when studying the cross-entropy loss is why we don’t use cross entropy loss for all cases. This is because of the way the outputs are stored for these two tasks.
In binary classification, the output layer utilizes the sigmoid activation function, resulting in the neural network producing a single probability score (p) ranging between 0 and 1 for the two classes.
The unique approach in binary classification involves not encoding binary predicted values as different for class 0 and class 1. Instead, they are stored as single values, which efficiently saves model parameters. This decision is motivated by the notion that, for a binary problem, knowing one probability implies knowledge of the other. For instance, consider a prediction of (0.8, 0.2); it suffices to store the 0.8 value, as the complementary probability is inherently 1 – 0.8 = 0.2. On the other hand, in multiclass classification, the softmax activation is employed in the output layer to obtain a vector of predicted probabilities (p).
Consequently, the standard definition of cross-entropy cannot be directly applied to binary classification problems where computed and correct probabilities are stored as singular values.
What Is Cross-Entropy Loss Function?
Cross-entropy loss also known as log loss is a metric used in machine learning to measure the performance of a classification model. Its value ranges from 0 to 1 with lower being better. An ideal value would be 0. The goal of an optimizer tasked with training a classification model with cross-entropy loss would be to get the model as close to 0 as possible. In this article, we will delve into binary and multiclass cross-entropy losses and how to interpret
the cross-entropy loss function.
Table of Content
- What is Cross Entropy Loss?
- Why not MCE for all cases?
- How to interpret Cross Entropy Loss?
- Key features of Cross Entropy loss
- Comparison with Hinge loss
- Implementation
- Conclusion