Matthews Correlation Coefficient (MCC)

Background

MCC is a single balanced scalar for binary classification quality. Unlike accuracy or F1, it works for any class ratio and gives a clean $[-1, 1]$ interpretation (1 perfect, 0 random, -1 anti-correlated). Production-grade for imbalanced fraud / medical screening.

Problem statement

Implement mcc(y_true, y_pred):

$$\text{MCC} \;=\; \frac{TP\cdot TN - FP\cdot FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}$$

Input

• y_true, y_pred - sequences of $\{0, 1\}$, same length.

Output

• float in $[-1, 1]$. Returns $0$ if any factor in the denominator is $0$ (a degenerate case).

Examples

Input: y_true=[1,1,0,0], y_pred=[1,1,0,0]
Output: 1.0

Constraints

• Same length, ValueError otherwise.
• Both inputs binary in $\{0, 1\}$.

Notes

• vs F1. F1 weights precision and recall, but ignores TN. MCC uses all four cells of the confusion matrix and is therefore symmetric under label flip.