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Multi-class Loss Functions
hard

In a multi-class classification problem, given a model that outputs the probabilities of each class using softmax, how is the cross-entropy loss calculated when using one-hot encoding for the true labels, and how does this relate to precision and recall in evaluating the model's performance?

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A

Cross-entropy loss measures the difference between predicted probabilities and actual classes, where one-hot encoding assigns a probability of 1 to the true class and 0 to others. Precision and recall are metrics used to evaluate binary classification only.

B

Cross-entropy loss is calculated by averaging the log probabilities of the predicted classes corresponding to one-hot encoded labels, and it directly influences precision and recall as they indicate the true positive rate and the accuracy of positive predictions.

C

Cross-entropy loss is irrelevant in multi-class settings as precision and recall are solely based on the confusion matrix, which ignores the predicted probabilities.

D

Cross-entropy loss provides no insight into model performance; precision and recall are sufficient to measure the model's effectiveness in a multi-class scenario.

Understanding the Answer

Let's break down why this is correct

Cross‑entropy looks at the log of the predicted probability for the true class. Other options are incorrect because The idea that precision and recall only work for binary problems is wrong; Cross‑entropy is not irrelevant; it is the objective that drives the model during training.

Key Concepts

Cross-entropy loss
One-hot encoding
Precision and recall
Topic

Multi-class Loss Functions

Difficulty

hard level question

Cognitive Level

understand

Deep Dive: Multi-class Loss Functions

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Definition
Definition

Multi-class loss functions are designed to evaluate the performance of multi-class classification models by penalizing incorrect predictions. They include Neyman-Pearson loss, hinge loss, and logistic loss, each serving different optimization and evaluation purposes.

Topic Definition

Multi-class loss functions are designed to evaluate the performance of multi-class classification models by penalizing incorrect predictions. They include Neyman-Pearson loss, hinge loss, and logistic loss, each serving different optimization and evaluation purposes.

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