Estimation
There are many situations where cross-entropy needs to be measured but the distribution of is unknown. An example is language modeling, where a model is created based on a training set, and then its cross-entropy is measured on a test set to assess how accurate the model is in predicting the test data. In this example, is the true distribution of words in any corpus, and is the distribution of words as predicted by the model. Since the true distribution is unknown, cross-entropy cannot be directly calculated. In these cases, an estimate of cross-entropy is calculated using the following formula:
where is the size of the test set, and is the probability of event estimated from the training set. The sum is calculated over . This is a Monte Carlo estimate of the true cross entropy, where the training set is treated as samples from .
Read more about this topic: Cross Entropy
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