Cross Entropy
Introduction
Cross Entropy is a critical concept in the fields of machine learning and deep learning, especially in classification problems. It measures the difference between two probability distributions and is often used as a loss function in neural networks.
What is Cross Entropy?
Cross Entropy originates from information theory, where it quantifies the amount of information lost or gained in transmitting a message. In machine learning, it measures the difference between the predicted probability distribution and the actual distribution.
Mathematical Definition
Mathematically, Cross Entropy can be defined as:
where p is the true distribution and q is the predicted distribution.
Why Use Cross Entropy?
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Effectiveness in Classification Problems: Cross Entropy is particularly effective in scenarios where we need to measure the performance of a model outputting probabilities.
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Sensitivity to Prediction Confidence: It penalizes incorrect predictions more severely when the model is confident about those predictions.
Implementing Cross Entropy in Machine Learning
In Neural Networks
Cross Entropy is commonly used as a loss function in neural networks for classification tasks. When paired with softmax activation function in the output layer, it becomes very effective for multi-class classification.
Example Code Snippet
import torch.nn as nn
# CrossEntropyLoss in PyTorchloss = nn.CrossEntropyLoss()