Fβ-Measure Score

An Fβ-Measure Score is a weighted harmonic mean measure that generalizes the F-Measure by allowing differential weighting between precision and recall.

• AKA: F-Beta Score, Fβ Score, F-Beta Measure, Weighted F-Measure, Fβ Metric.
• Context:
  • It can (typically) be calculated as (1 + β²) × (precision × recall) / ((β² × precision) + recall).
  • It can (typically) weight Recall β times as important as Precision through its beta parameter.
  • It can (typically) reduce to F1-Score when β = 1 (equal weighting).
  • It can (typically) emphasize Recall when β > 1 (e.g., β = 2 for F2-Score).
  • It can (typically) emphasize Precision when β < 1 (e.g., β = 0.5 for F0.5-Score).
  • It can (often) be used in Binary Classification Tasks and Multi-Class Classification Tasks.
  • It can (often) guide Model Selection when error types have different importance.
  • It can (often) be computed for each class in Multi-Class Problems before aggregation.
  • It can range from being an F0.5-Score to being an F10-Score, depending on its beta value.
  • It can range from being a Micro-Fβ Score to being a Macro-Fβ Score, depending on its aggregation method.
  • It can integrate with Classification Systems for performance evaluation.
  • It can integrate with Hyperparameter Optimization Frameworks for model tuning.
  • ...
• Example(s):
  • Common Fβ Scores, such as:
    • F1-Score (β = 1): Equal weight to precision and recall.
    • F2-Score (β = 2): Recall weighted twice as important as precision.
    • F0.5-Score (β = 0.5): Precision weighted twice as important as recall.
  • Domain-Specific Fβ Scores, such as:
    • Medical Diagnosis F2-Score emphasizing recall to minimize false negatives.
    • Spam Detection F0.5-Score emphasizing precision to minimize false positives.
    • Information Retrieval F-Score with task-specific beta values.
  • Aggregated Fβ Scores, such as:
    • Macro-Fβ Score: Average of per-class Fβ scores.
    • Micro-Fβ Score: Fβ computed on aggregated confusion matrix.
    • Weighted-Fβ Score: Class-frequency weighted average.
  • ...
• Counter-Example(s):
  • Arithmetic Mean, which uses simple averaging rather than harmonic mean.
  • Accuracy Measure, which treats all errors equally.
  • AUC-ROC, which is threshold-independent.
  • Log Loss, which measures probabilistic predictions.
  • Matthews Correlation Coefficient, which considers all confusion matrix cells equally.
• See: F-Measure, F1-Score, Precision, Recall, Harmonic Mean, Binary Classification Performance Measure, Multi-Class Classification Performance Measure, Information Retrieval Evaluation, Model Selection, Cost-Sensitive Learning.

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