# What is Accuracy, Precision, Recall & F1 Score?

## The Most Important Classification Metrics in AppNava

# 1. How to evaluate the performance of a machine learning model?

Let us consider a task to classify whether a player is a **purchaser** or **not**. If the player completes an in-app purchase on store **purchase status **is positive (+ve ). When don't complete the in-app purchase, the status** **is negative (-ve), then the person is **not the purchaser**.

Now consider the above classification ( **purchaser** or **not purchaser**) carried out by a machine learning algorithm. The output of the machine learning algorithm can be mapped to one of the following categories.

1.1 A person who is actually a **purchaser **(positive) and classified as a purchaser (positive). This is called **TRUE POSITIVE ( TP).**

Figure 1: True Positive.

1.2. A person who is actually not **purchaser** (negative) and classified as **not** **purchaser **(negative). This is called **TRUE NEGATIVE ( TN).**

Figure 2: True Negative.

1.3. A person who is actually **not purchaser** (negative) and classified as **purchaser **(positive). This is called **FALSE POSITIVE ( FP).**

1.4. A person who is actually a **purchaser **(positive) and classified as not a **purchaser **(negative). This is called **FALSE NEGATIVE ( FN).**

What we desire is **TRUE POSITIVE** and **TRUE NEGATIVE** but due to the misclassifications, we may also end up in **FALSE POSITIVE** and **FALSE NEGATIVE. **So there is confusion in classifying whether a player is a **purchaser **or **not**. This is because no machine learning algorithm is perfect. Soon we will describe this confusion in classifying the data in a matrix called confusion matrix.

Now, we select 100 players which include the **purchaser**, **non-purchaser. **Let us assume out of this 100 players 40 are **purchasers **and the remaining 60 players include non-**purchaser. **We now use a machine-learning algorithm to predict the outcome. The predicted outcome (**purchaser**+ve or -ve) using a machine learning algorithm is termed as the ** predicted label** and the true outcome is termed as the

**.**

*true label*Now we will introduce the ** confusion matrix** which is required to compute the

**of the machine learning algorithm in classifying the data into its corresponding labels.**

*accuracy*The following diagram illustrates the confusion matrix for a binary classification problem.

Figure 5: Confusion Matrix.

We will now go back to the earlier example of classifying 100 players (which includes 40 **purchasers **and the remaining 60 are **non-purchasers**) as the **purchaser **or **non-purchaser**. Out of 40 **purchaser **players 30 **purchaser **players are classified correctly and the remaining 10 are classified as **non**-**purchaser **by the machine learning algorithm. On the other hand, out of 60 players in the **not purchasers **category, 55 are classified as **non-purchaser** and the remaining 5 are classified as the **purchaser**.

In this case, ** TN** = 55,

**= 5,**

*FP***= 10,**

*FN***= 30. The confusion matrix is as follows.**

*TP*Figure 6: Confusion matrix for the **purchaser **vs **non**-**purchaser **classification.

# 2. What is the Accuracy of the AppNava Machine Learning model for classification?

Accuracy represents the number of correctly classified data instances over the total number of data instances.

In this example, Accuracy = (55 + 30)/(55 + 5 + 30 + 10 ) = 0.85 and in percentage the accuracy will be 85%.

# 3. Is Accuracy enough alone?

Accuracy may not be a good measure if the dataset is not balanced (both negative and positive classes have different numbers of data instances). We will explain this with an example.

Consider the following scenario: There are 90 players who are **non-purchaser **(negative) and 10 players who are **purchaser** (positive). Now let’s say our machine learning model perfectly classified the 90 players as **non-purchaser, **but it also classified the **purchaser **people as **non-purchaser**. What will happen in this scenario? Let us see the confusion matrix and find out the accuracy?

In this example, ** TN** = 90,

**= 0,**

*FP***= 10 and**

*FN***= 0. The confusion matrix is as follows.**

*TP*Figure 7: Confusion matrix for **purchaser **vs **non**-**purchaser** player classification.

Accuracy in this case will be (90 + 0)/(100) = 0.9 and in percentage the accuracy is 90 %.

# 4. Is there anything wrong?

The accuracy, in this case, is 90 % but this model is very poor because all the 10 players who are **purchaser **are classified as **non**-**purchaser**. By this example what we are trying to say is that accuracy is not a good metric when the data set is unbalanced. Using accuracy in such scenarios can result in a misleading interpretation of results.

Now we will find the **precision (positive predictive value)** in classifying the data instances. Precision is defined as follows:

# 5. What does Precision mean?

** Precision** should ideally be 1 for a good classifier.

**becomes 1 only when the numerator and denominator are equal i.e**

*Precision***, this also means**

*TP = TP +FP***is zero. As**

*FP***increases the value of the denominator becomes greater than the numerator and the**

*FP***value decreases.**

*precision*So in the **purchaser **example, ** precision** = 30/(30+ 5) = 0.857

Now we will introduce another important metric called ** recall**.

**is also known as**

*The recall***or**

*sensitivity***and is defined as follows:**

*true positive rate*** Recall** should ideally be 1 for a good classifier.

**becomes 1 only when the numerator and denominator are equal i.e**

*Recall***, this also means**

*TP = TP +FN***is zero. As**

*FN***increases the value of the denominator becomes greater than the numerator and the**

*FN***value decreases (which we don’t want).**

*recall*So in the **purchaser **example let us see what will be the recall.

** Recall **= 30/(30+ 10) = 0.75

So ideally in a good classifier, we want both ** precision** and

**to be one which also means**

*recall***and**

*FP***are zero. Therefore we need a metric that takes into account both**

*FN***and**

*precision***.**

*recall***is a metric that takes into account both**

*F1-score***and**

*precision***and is defined as follows:**

*recall*** F1 Score** becomes 1 only when

**and**

*precision***are both 1.**

*recall***becomes high only when both**

*F1 score***and**

*precision***are high.**

*recall***is the harmonic mean of**

*F1 score***and**

*precision***and is a better measure than**

*recall***.**

*accuracy*In the **purchaser **example, ** F1 Score** = 2* ( 0.857 * 0.75)/(0.857 + 0.75) = 0.799.