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Interpreting Negative Log-Likelihood as Cross-Entropy
A machine learning model is trained for a multi-class classification task using a negative log-likelihood loss function. For a given training example, this loss is calculated based on the model's predicted probability for the single correct class. Explain how this specific loss calculation represents a cross-entropy between two distinct probability distributions. In your explanation, clearly identify and describe both of these distributions.
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MLM Loss Function as Negative Log-Likelihood
A neural network is trained on a 4-class classification task. For a single training example where the true class is the second class, the model outputs the probability vector
[0.1, 0.7, 0.1, 0.1]. The loss for this example is calculated as-log(0.7). This loss function can be interpreted as a measure of divergence between two probability distributions. What are these two distributions?Interpreting Negative Log-Likelihood as Cross-Entropy
A neural network is being trained for a 3-class classification task (Classes A, B, C). For a single training example, the true label is 'Class B'. The model outputs the probability distribution
P(A)=0.2, P(B)=0.5, P(C)=0.3. The loss for this example is calculated using the negative log-likelihood of the correct class, resulting in a loss of-log(0.5). This calculation is a direct application of the cross-entropy formula between the model's predicted distribution and the empirical distribution from the training data. What is the specific empirical probability distribution for this single training example?