Understanding Accuracy and Error Rate in Machine Learning
Accuracy is one of the most intuitive performance measures in machine learning. It is a metric that quantifies the number of correct predictions made out of all predictions made. This measure is extremely straightforward in binary and multiclass classification problems, but it’s important to understand its nuances and limitations.
Error rate, on the other hand, complements accuracy by quantifying the number of incorrect predictions. It is calculated by subtracting the accuracy from one and often expressed as a percentage. Both accuracy and error rate provide a quick snapshot of model performance, but they may not always give a complete picture, especially in cases where class distributions are imbalanced.
Formula for Accuracy
The formula for calculating accuracy is:
Mathematical definition of accuracy
Accuracy Formula Symbols Explained
| True Positives (TP) | Instances correctly predicted as positive |
| True Negatives (TN) | Instances correctly predicted as negative |
| False Positives (FP) | Instances incorrectly predicted as positive |
| False Negatives (FN) | Instances incorrectly predicted as negative |
Calculating Accuracy
To calculate accuracy, we divide the sum of true positives and true negatives by the total number of predictions. For example, if a model made 100 predictions and 90 of them were correct (either as true positives or true negatives), the accuracy would be 90%.
Error Rate
Error rate is simply one minus the accuracy. If the accuracy of a model is 90%, the error rate would be 10%. It is calculated as:
Error Rate = (FP + FN) / (TP + TN + FP + FN)
Or, more simply:
Error Rate = 1 - Accuracy
Limitations of Accuracy and Error Rate
While accuracy and error rate are useful, they have limitations, especially in datasets with imbalanced classes. For example, if a dataset contains 95% of one class and 5% of another, a model that always predicts the majority class will have a high accuracy of 95%, but it will be ineffective at identifying the minority class.
In such cases, other metrics like precision, recall, F1-score, and the area under the ROC curve (AUC-ROC) are more informative as they take into account the balance between classes and the trade-offs between different types of errors.
Accuracy and Error Rate in Practice
In practice, accuracy and error rate are often the starting point for model evaluation. However, data scientists must delve deeper into other performance metrics to fully understand a model's behavior. This is particularly important in fields like medicine or finance, where the cost of a false negative can be much higher than a false positive, or vice versa.
Conclusion
Accuracy and error rate are fundamental metrics in machine learning that provide an initial assessment of model performance. However, they should be used judiciously and supplemented with other metrics for a comprehensive evaluation, especially in cases of class imbalance or when different types of errors have different costs or implications.
References
He, H., & Garcia, E. A. (2009). Learning from imbalanced data. IEEE Transactions on knowledge and data engineering, 21(9), 1263-1284.
Provost, F., & Fawcett, T. (2013). Data Science for Business: What you need to know about data mining and data-analytic thinking. O'Reilly Media, Inc.
Witten, I. H., Frank, E., Hall, M. A., & Pal, C. J. (2016). Data Mining: Practical machine learning tools and techniques. Morgan Kaufmann.