Model Evaluation - Mean absolute error (MAE)

• Definition

• Calculation

• How to code

Mean absolute error (MAE) is a metric that is used to evaluate the performance of regression models. It’s defined as the average of the absolute difference between actual and predicted values. 

Note

: When there are outliers in the data, MAE is a preferred metric to assess the model's performance.

MAE is calculated using the following formula.

Mathematically we can write MAE as shown below:

When the MAE value is close to 

0

, we claim the model is at its best. This means that most of the predicted values are identical to the actual ones. 

Imagine a scenario where you’ve successfully created a regression model to predict the weight of a person based on their height, and now you want to evaluate the model. For this you gathered heights and weights of 5 people and then predicted their weights. 

Now, let’s use the regression metric MAE to evaluate the performance of the model. 

To calculate MAE we need actual (true_w) and predicted (pred_w) values.

Step-1

: Calculate the 

error 

(err) by finding the difference between the actual (true_w) and predicted weight(pred_w) values.

Step-2

: Calculate the absolute values (abs_err) for all error (err) values 

.

Let’s first understand what absolute values are:

The absolute value of a number is the non-negative value of the number. 

For example,

1. The absolute value of -15 is 15

2. The absolute value of -3.45 is 3.45

3. The absolute value of 56 is 56

We can convert a number into an absolute value in 2 ways as shown:

1. By multiplying the negative number with 

   -1

   .

2. We can use Python’s default 

   abs()

   method to calculate the absolute values.

In this lesson, we’ll calculate the absolute values using the 

abs()

method.

Step-3

: Calculate the sum of all absolute error (abs_err) values.

Step-4

: Calculate the average or mean of all absolute errors (abs_err).

As you've seen, calculating MAE from scratch is time-consuming, so let's calculate MAE using Scikit-learn, Python's machine learning library.

To calculate MAE, 

1. Import the 

   mean_absolute_error 

   function from the sklearn 

   metrics

   module. 

2. Pass the actual (true_w) and predicted (pred_w) values into the 

   mean_absolute_error

   function.

From the MAE value, we can tell that the weight prediction model is a better model, but it's not the best as the MAE value is not close to 0. This is how we utilize the MAE metric to assess regression model performance.

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