Misclassification Error

TL;DR

A classification mistake where a sample is assigned to the wrong class.
Can cause harmful or costly outcomes in domains like medical diagnosis, credit scoring, and fraud detection.
Commonly measured with a confusion matrix and summary metrics such as accuracy, precision, and recall.

Definition

Misclassification error, also known as classification error or error rate, is the incorrect prediction or assignment of a sample to a class in the process of classification.

Explanation

Misclassification error occurs when a classification algorithm predicts the wrong class for a sample. It can have significant consequences depending on the application domain; for example, misdiagnosing a disease or incorrectly denying credit. Misclassification is evaluated using a confusion matrix, which reports the counts of true positive, true negative, false positive, and false negative predictions. The diagonal elements of the confusion matrix are correct predictions and the off-diagonal elements are incorrect predictions. Common performance metrics derived from the confusion matrix include accuracy, precision, and recall.

Strategies mentioned to reduce misclassification error include using a larger and more diverse training dataset, selecting more accurate or sophisticated algorithms, and carefully evaluating algorithm performance with appropriate metrics.

Examples

Medical diagnosis

A doctor uses a classification algorithm to predict whether a patient has a disease based on features such as symptoms, test results, and medical history. If the algorithm predicts that the patient does not have the disease when they actually do, this misclassification can delay or prevent needed treatment and may be harmful to the patient.

Credit scoring

A credit scoring model predicts the likelihood that a borrower will default on a loan, assigning a score based on credit history, income, and other financial factors. If the model misclassifies a reliable borrower with a low score, the borrower may be denied a loan or offered a higher interest rate despite being capable of repayment.

Use cases

Medical diagnosis
Credit scoring
Fraud detection

Notes or pitfalls

Misclassification error can lead to incorrect decisions and negative consequences in practical applications.
Minimizing misclassification requires careful model design and training, larger or more diverse data, more accurate algorithms, and thorough evaluation using metrics like accuracy, precision, and recall.

Classification (process)
Confusion matrix
Accuracy
Precision
Recall
True positive
True negative
False positive
False negative
Classification error / Error rate

Formula (from confusion matrix)

Accuracy can be computed as the sum of correct predictions divided by the total number of predictions. Using the confusion-matrix counts:

\text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN}