Error Rate Measure

An Error Rate Measure is a statistical measure that quantifies the frequency or proportion of errors in a system, process, or statistical test relative to the total number of observations or decisions.

• AKA: Error Rate, Error Frequency, Mistake Rate, Failure Rate, Error Proportion.
• Context:
  • It can typically be expressed as a proportion (0 to 1) or percentage (0% to 100%).
  • It can typically serve as an inverse measure of accuracy or correctness.
  • It can typically be calculated as the number of errors divided by total opportunities for error.
  • It can typically be used to evaluate system performance, process quality, or decision accuracy.
  • It can often be decomposed into specific error types (e.g., Type I error rate, Type II error rate).
  • It can often guide quality improvement, system optimization, or decision threshold selection.
  • It can often be estimated from sample data to infer population error rates.
  • It can often be controlled through error correction methods or quality control procedures.
  • It can range from being a Binary Error Rate to being a Multi-Class Error Rate, depending on its classification complexity.
  • It can range from being a Point Error Rate to being an Interval Error Rate, depending on its estimation precision.
  • It can range from being an Empirical Error Rate to being a Theoretical Error Rate, depending on its derivation method.
  • It can range from being a Training Error Rate to being a Test Error Rate, depending on its evaluation dataset.
  • It can range from being a Marginal Error Rate to being a Conditional Error Rate, depending on its conditioning context.
  • It can range from being an Instantaneous Error Rate to being a Cumulative Error Rate, depending on its temporal scope.
  • ...
• Example(s):
  • Statistical Testing Error Rates, such as:
    • Type I Error Rate (α): probability of false positive decisions.
    • Type II Error Rate (β): probability of false negative decisions.
    • Family-Wise Error Rate: probability of any Type I error in multiple tests.
    • False Discovery Rate: expected proportion of false positives among discoveries.
  • Machine Learning Error Rates, such as:
    • Classification Error Rate: proportion of misclassified instances.
    • Training Error Rate: error on training dataset.
    • Generalization Error Rate: expected error on new data.
    • Cross-Validation Error Rate: averaged error across folds.
  • Speech Recognition Error Rates, such as:
    • Word Error Rate: proportion of incorrectly recognized words.
    • Character Error Rate: proportion of incorrect characters.
    • Sentence Error Rate: proportion of sentences with errors.
  • Data Quality Error Rates, such as:
    • Data Entry Error Rate: proportion of incorrect entries.
    • Transcription Error Rate: errors in data transcription.
    • Measurement Error Rate: frequency of measurement mistakes.
  • System Performance Error Rates, such as:
    • Bit Error Rate: proportion of incorrect bits in transmission.
    • Service Error Rate: proportion of failed service requests.
    • Production Error Rate: defect rate in manufacturing.
  • Medical Testing Error Rates, such as:
    • Diagnostic Error Rate: proportion of incorrect diagnoses.
    • Screening Test Error Rate: false positive/negative rates.
    • Laboratory Error Rate: mistakes in lab testing.
  • ...
• Counter-Example(s):
  • Accuracy Measure, which quantifies correct outcomes rather than errors.
  • Precision Measure, which focuses on positive predictive value.
  • Success Rate, which measures successful outcomes.
  • Confidence Level, which indicates certainty rather than error.
  • Effect Size, which measures magnitude rather than error frequency.
• See: Accuracy Measure, Classification Error, Type I Error, Type II Error, Family-Wise Error Rate, False Discovery Rate, Generalization Error, Statistical Hypothesis Testing Decision Error, Multiple Hypothesis Testing Framework, Quality Control, Performance Measure, Reliability Measure, Validation Metric.

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References

2023

• (James et al., 2023) ⇒ Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani. (2023). "An Introduction to Statistical Learning." Springer.
  • QUOTE: The test error rate is the average error that results from using a statistical learning method to predict the response on a new observation—one that was not used in training the method. In contrast, the training error rate is computed using the observations that were used to fit the model.

2020

• (Murphy, 2020) ⇒ Kevin P. Murphy. (2020). "Machine Learning: A Probabilistic Perspective." MIT Press.
  • QUOTE: The error rate is simply one minus the accuracy. For binary classification, the error rate equals the sum of false positive and false negative rates. This decomposition helps identify whether errors are primarily due to false alarms or missed detections.

2016

• (Hastie et al., 2016) ⇒ Trevor Hastie, Robert Tibshirani, and Jerome Friedman. (2016). "The Elements of Statistical Learning." Springer.
  • QUOTE: The expected prediction error (generalization error) can be decomposed into irreducible error (noise), squared bias, and variance. This bias-variance tradeoff is fundamental to understanding how model complexity affects error rates.

2012

• (Kohavi & Provost, 2012) ⇒ Ron Kohavi and Foster Provost. (2012). "Glossary of Terms." Machine Learning.
  • QUOTE: Error rate: The proportion of instances for which the system produces an incorrect output. For classification, this is the number of misclassified instances divided by the total number of instances. The complement of accuracy.

2006

• (Japkowicz & Shah, 2006) ⇒ Nathalie Japkowicz and Mohak Shah. (2006). "Evaluating Learning Algorithms." Cambridge University Press.
  • QUOTE: Error rate alone can be misleading, particularly with imbalanced datasets. A classifier that always predicts the majority class will have low error rate but poor performance on the minority class. Multiple metrics are needed for comprehensive evaluation.

1997

• (Efron & Tibshirani, 1997) ⇒ Bradley Efron and Robert Tibshirani. (1997). "An Introduction to the Bootstrap." Chapman & Hall.
  • QUOTE: The apparent error rate (resubstitution error) is typically over-optimistic because the same data is used for both model fitting and error estimation. Cross-validation and bootstrap methods provide more realistic error rate estimates.

1995

• (Kohavi, 1995) ⇒ Ron Kohavi. (1995). "A Study of Cross-Validation and Bootstrap for Accuracy Estimation." IJCAI.
  • QUOTE: Error estimation is crucial for model selection and assessment. The true error rate is the expected disagreement between the classifier and the target function over the entire distribution of instances.

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