Understanding the Confusion Matrix for Model Evaluation & Monitoring

confusion matrix animal chart
Animal example of Confusion Matrix

Introduction

Anyone can build a machine learning (ML) model with a few lines of code, but building a good machine learning model is a whole other story.

What do I mean by a GOOD machine learning model? 

It depends, but generally, you’ll evaluate your machine learning model based on some predetermined metrics that you decide to use. When it comes to building classification models, you’ll most likely use a confusion matrix and related metrics to evaluate your model. Confusion matrices are not just useful in model evaluation but also model monitoring and model management!

Don’t worry, we’re not talking about linear algebra matrices here!

In this article, we’ll cover what a confusion matrix is, some key terms and metrics, an example of a 2×2 matrix, and all of the related python code.

With that said, let’s dive into it!

What is a Confusion Matrix?

A confusion matrix, also known as an error matrix, is a summarized table used to assess the performance of a classification model. The number of correct and incorrect predictions are summarized with count values and broken down by each class. 

Below is an image of the structure of a 2×2 confusion matrix. To give an example, let’s say that there were ten instances where a classification model predicted ‘Yes’ in which the actual value was ‘Yes’. Then the number ten would go in the top left corner in the True Positive quadrant. This leads us to some key terms:

confusion matrix
  • Positive (P): Observation is positive (eg. is a dog).
  • Negative (N): Observation is not positive (eg. is not a dog).
  • True Positive (TP): Outcome where the model correctly predicts the positive class.
  • True Negative (TN): Outcome where the model correctly predicts the negative class.
  • False Positive (FP): Also called a type 1 error, an outcome where the model incorrectly predicts the positive class when it is actually negative.
  • False Negative (FN): Also called a type 2 error, an outcome where the model incorrectly predicts the negative class when it is actually positive.

Confusion Matrix Metrics

Now that you understand the general structure of a confusion matrix as well as the associated key terms, we can dive into some of the main metrics that you can calculate from a confusion matrix. 

Note: this list is not exhaustive — if you want to see all of the metrics that you can calculate, check out Wikipedia’s page.

Accuracy

This is simply equal to the proportion of predictions that the model classified correctly.

accuracy formula for confusion matrix

Precision

Precision is also known as positive predictive value and is the proportion of relevant instances among the retrieved instances. In other words, it answers the question “What proportion of positive identifications was actually correct?”

precision formula for confusion matrix

Recall

Recall, also known as the sensitivity, hit rate, or the true positive rate (TPR), is the proportion of the total amount of relevant instances that were actually retrieved. It answers the question “What proportion of actual positives was identified correctly?”

recall formula for confusion matrix

To really hit it home, the diagram below is a great way to remember the difference between precision and recall (it certainly helped me!)

Specificity

Specificity, also known as the true negative rate (TNR), measures the proportion of actual negatives that are correctly identified as such. It is the opposite of recall.

F1 Score

The F1 score is a measure of a test’s accuracy — it is the harmonic mean of precision and recall. It can have a maximum score of 1 (perfect precision and recall) and a minimum of 0. Overall, it is a measure of the preciseness and robustness of your model.

Example of 2×2 Confusion Matrix

If this still isn’t making sense to you, it will after we take a look at the example below.

Imagine that we created a machine learning model that predicts whether a patient has cancer or not. The table on the left shows twelve predictions that the model made as well as the actual result of each patient. With our paired-data, you can then fill out the confusion matrix using the structure that I showed above.

Once this is filled in, we can learn a number of things about our model:

  • Our model predicted that 4/12 (red + yellow) patients had cancer when there were actually 3/12 (red + blue) patients with cancer
  • Our model has an accuracy of 9/12 or 75% ((red + green)/(total))
  • The recall of our model is equal to 2/(2+1) = 66%
Example of 2x2 Confusion Matrix

In reality, you would want the recall of a cancer detection model to be as close to 100% as possible. It’s far worse if a patient with cancer is diagnosed as cancer-free, as opposed to a cancer-free patient being diagnosed with cancer only to realize later with more testing that he/she doesn’t have it.

Python Code

Below is a summary of code that you need to calculate the metrics above: 

 # Confusion Matrix
 from sklearn.metrics import confusion_matrix
 confusion_matrix(y_true, y_pred)
 # Accuracy
 from sklearn.metrics import accuracy_score
 accuracy_score(y_true, y_pred)
 # Recall
 from sklearn.metrics import recall_score
 recall_score(y_true, y_pred, average=None)
 # Precision
 from sklearn.metrics import precision_score
 precision_score(y_true, y_pred, average=None)

There are three ways you can calculate the F1 score in Python:

# Method 1: sklearn
from sklearn.metrics import f1_score
f1_score(y_true, y_pred, average=None)
# Method 2: Manual Calculation
F1 = 2 * (precision * recall) / (precision + recall)
# Method 3: Classification report [BONUS]
from sklearn.metrics import classification_report
print(classification_report(y_true, y_pred, target_names=target_names))

Conclusion

Now that you know what a confusion matrix is as well as its associated metrics, you can effectively evaluate your classification ML models. This is also essential to understand even after you finish developing your ML model, as you’ll be leveraging these metrics in the model monitoring and model management stages of the machine learning life cycle.

Thanks for Reading!

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