Harmonic mean of precision and recall is called

General
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harmonic mean of precision and recall is called

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Harmonic mean of precision and recall is called

Answer:
The harmonic mean of precision and recall is called the F1 Score. It is a measure used in statistical analysis, particularly in the field of machine learning and information retrieval, to evaluate the accuracy of a binary classification system.

Understanding Precision and Recall:

  1. Precision:

    • Precision is the ratio of correctly predicted positive observations to the total predicted positives.
    • Formula:
      \text{Precision} = \frac{TP}{TP + FP}
    • Where TP is the number of true positives and FP is the number of false positives.

  2. Recall:

    • Recall (or Sensitivity) is the ratio of correctly predicted positive observations to all observations in the actual class.
    • Formula:
      \text{Recall} = \frac{TP}{TP + FN}
    • Where FN is the number of false negatives.

Combining Precision and Recall:

F1 Score:

  • The F1 Score is defined as the harmonic mean of precision and recall. It provides a single metric that balances both precision and recall.

  • The harmonic mean is used rather than the average because it punishes extreme values (i.e., a model with either very low precision or recall).

    \text{F1 Score} = 2 \times \left(\frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}\right)

Detailed Calculation Steps:

  1. Calculate Precision and Recall:

    • Obtain the true positives (TP), false positives (FP), and false negatives (FN) from your confusion matrix.
    • Compute precision:
      \text{Precision} = \frac{TP}{TP + FP}
    • Compute recall:
      \text{Recall} = \frac{TP}{TP + FN}

  2. Compute the F1 Score:

    • Substitute the calculated precision and recall values into the F1 Score formula:
      \text{F1 Score} = 2 \times \left(\frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}\right)

Example:

Assume a model has the following outcomes from its confusion matrix:

  • True Positives (TP) = 100
  • False Positives (FP) = 25
  • False Negatives (FN) = 10

  1. Calculate Precision:

    \text{Precision} = \frac{100}{100 + 25} = \frac{100}{125} = 0.8

  2. Calculate Recall:

    \text{Recall} = \frac{100}{100 + 10} = \frac{100}{110} \approx 0.909

  3. Calculate the F1 Score:

    \text{F1 Score} = 2 \times \left(\frac{0.8 \times 0.909}{0.8 + 0.909}\right) = 2 \times \left(\frac{0.7272}{1.709}\right) \approx 0.851

Final Answer:
The F1 Score, which is the harmonic mean of precision and recall, is \boxed{0.851} in this example.

By calculating the F1 Score, you can evaluate the effectiveness of your classifier by taking into account both precision and recall, ensuring a more balanced understanding of its performance.