# Binary Classification Metrics

date

Jul 4, 2023

slug

bin-classification-metrics

status

Published

tags

Machine Learning

summary

The 3 dimensional equation that formulates 8 different metrics of binary classification

type

Post

It's magical how many metrics exist to evaluate a problem that outputs only two possibilities - 0 or 1. Here we will derive a formulated way of understanding the relationships between all these methods of evaluation.

Reviewing the confusion matrix, we see that supervised binary classification leads to one of four possible outcomes:
True Negative, False Positive
False Negative, True Positive

Summing the matrix horizontally, we get the

**actual**number of negative and positive examples:Summing vertically, we get the

**predicted**number of negative and positive examples:There are a few different binary classification metrics we can use to asses the quality of the predicted outcomes.

A 3-dimensional question we can use to derive any of the metrics is:

**When x y, how often is it z?**

Then, the 3 dimensions of a binary classification metric are:

- x - the actual label is / the model predicts

- y - 1 / 0

- z - Correct / Incorrect

From these 3 different dimensions, we can derive 8 different metrics for evaluating a binary classification problem.

The first 4 metrics focus on the correct predictions - the numerator focuses on what the model got right (the True Positives and True Negatives):

1:

**True Positive Rate (TPR) / Recall / Sensitivity**- When the actual label is 1, how often are we correct?2:

**Precision**- When the model predicts 1, how often are we correct?3:

**True Negative Rate (TNR) / Specificity**- When the actual label is 0, how often are we correct?4:

**Unnamed**- When the model predicts 0, how often are we correct?The next 4 metrics focus on the incorrect predictions - the numerator focuses on what the model got wrong (the False Negatives and False Positives):

5:

**False Negative Rate (FNR)**- When the actual label is 1, how often are we incorrect?6:

**Unnamed**- When the model predicts 1, how often are we incorrect?7:

**False Positive Rate (FPR)**- When the actual label is 0, how often are we incorrect?8:

**Unnamed**- When the model predicts 0, how often are we incorrect?And there we have it, the 8 key metrics fundamental for evaluating a binary classification problem fixing a threshold. However, note that more metrics exist that help combine these foundational metrics to evaluate a model across multiple thresholds (F1 score, AUC for ROC curve, AUC for Precision Recall curve, etc…).

I hope this post gave you a better foundation for understanding the relationships between the different metrics for evaluating binary classification problems.

Please don't hesitate to reach out to me on **LinkedIn****Twitter**if you have any questions or comments!

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