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Calculate N-Gram Precision with Repeated Words

Reviewed by Calculator Editorial Team

N-gram precision measures how accurately a system predicts sequences of words, especially when words can repeat. This metric is crucial in natural language processing, machine translation, and information retrieval systems.

What is N-gram Precision?

N-gram precision evaluates how often predicted word sequences match the actual sequences in a reference text. When words can repeat, the calculation becomes more nuanced because the same word can appear multiple times in both the prediction and reference.

Precision is calculated by comparing the number of correctly predicted n-grams to the total number of predicted n-grams. The formula accounts for repeated words by considering their frequency in both the prediction and reference.

Formula

The precision of n-grams with repeated words is calculated using the following formula:

Precision = (Number of matching n-grams) / (Total number of predicted n-grams)

Where:

  • Number of matching n-grams - Count of n-gram sequences that appear in both the predicted and reference text
  • Total number of predicted n-grams - Count of all n-gram sequences in the predicted text

When words can repeat, the same n-gram sequence can appear multiple times in both texts, so we count all occurrences.

How to Calculate N-gram Precision with Repeated Words

  1. Identify all n-gram sequences in the predicted text, including repeated sequences.
  2. Identify all n-gram sequences in the reference text, including repeated sequences.
  3. Count how many times each n-gram sequence appears in both texts.
  4. Sum the counts of matching n-grams across all sequences.
  5. Count the total number of n-grams in the predicted text.
  6. Divide the sum of matching n-grams by the total number of predicted n-grams to get precision.

For best results, ensure your n-gram size (n) matches the context of your text. Common values are 2 (bigrams) or 3 (trigrams).

Example Calculation

Let's calculate precision for the following predicted and reference texts with n=2 (bigrams):

Predicted text: "the cat sat on the mat the cat sat"

Reference text: "the cat sat on the mat the dog sat"

  1. Predicted bigrams: ["the cat", "cat sat", "sat on", "on the", "the mat", "mat the", "the cat", "cat sat"]
  2. Reference bigrams: ["the cat", "cat sat", "sat on", "on the", "the mat", "mat the", "the dog", "dog sat"]
  3. Matching bigrams: "the cat", "cat sat", "sat on", "on the", "the mat", "mat the" (6 matches)
  4. Total predicted bigrams: 8
  5. Precision = 6 / 8 = 0.75 or 75%

The precision is 75%, meaning the system correctly predicted 75% of the bigrams in the reference text.

FAQ

What is the difference between n-gram precision and recall?

Precision measures how many of the predicted n-grams were correct, while recall measures how many of the actual n-grams were predicted. Both are important for evaluating system performance.

How does n-gram size affect precision?

Larger n-grams (like trigrams) capture more context but may have lower counts, while smaller n-grams (like bigrams) are more common but may lack context. Choose n based on your specific application.

Can n-gram precision be higher than 100%?

No, precision is a ratio that can range from 0 to 1 (or 0% to 100%). A value higher than 100% would indicate an error in the calculation.