How to Calculate Mean Absolute Error in Python?

Introduction

In statistics or machine learning, Mean Absolute Error (MAE) is used to check the model's accuracy in its prediction. It provides a way that it will check the predicted values against the actual ones in an easy manner. This article discusses the notion of Mean Absolute Error and leads you to compute it using Python programming.

Understanding Mean Absolute Error

Mean Absolute Error (MAE) can be considered as the average value of all absolute errors between the true values and predicted values. Lastly, this system is also very helpful because it helps with problems such as regression. The formula for calculating MAE is straightforward:

Mean Absolute Error = (1/n) * ∑|yi - xi|

Where,

• Σ: Greek symbol for summation
• Yi: Actual value for the ith observation
• Xi: Calculated value for the ith observation
• N: Total number of observations

Python Libraries for Mean Absolute Error Calculation:

There isn't a library for Mean Absolute Error (MAE) calculation in python. However, we can use the following formula to calculate it:

Python makes it easy to compute mean absolute error by using several different libraries. The two most popularly used libraries are NumPy and scikit-learn.

Using NumPy

When there is a need to perform numerical computations in Python, the most used library for this purpose is NumPy. It gives an efficient way to play with array data by providing advanced mathematical functions. Let's see how to calculate MAE using NumPy:

Output:

 Mean Absolute Error: 3.2 

Explanation

• The Python code largely operates in NumPy, performing all the numerical tasks from there.
• Two lists "actual_values" and "predicted_values", will be initialized, to hold the actual values from the dataset and those predicted by an algorithm.
• One can calculate the absolute difference by subtracting predicted values from actual ones and taking an np.abs of this difference.
• The function "np.mean()" is utilized to calculate the average of these differences.
• The calculated mean shows the difference between the actual and predicted values.
• The print function is implemented to display the output.
• The average absolute difference between the actual values and the predicted values is 5.6 units as shown by an example, and this compute from MAE ( mean absolute error).
• This code is designed to calculate MAE in a more efficient and easy way so you would have a better understanding of it.

Using scikit-learn

Scikit-learn is a widely used ML library in Python through which we can present, analyze, and model our data. It includes a metrics module that contains various evaluation metrics, including Mean Absolute Error:

Output:

 Mean Absolute Error: 5.6 

Explanation

• The 'mean_absolute_error' can be imported from the metrics module of scikit learn library to calculate mean absolute error.
• Two lists called 'actual_values' and 'predicted_values' are representing the values that we have predicted, respectively.
• In order to find out the Mean Absolute Error between observed and predicted values, we make use of 'mean_absolute_error' function.
• The value returned has been kept in the variable named 'mae'.
• Using the printing function, get the Mean Absolute error.
• For the given problem, Mean Absolute Error (MAE) is around 5.6 which means any predicted value will have an error of approximately 5.6 units from the true value.
• This scikit-learn facility is been using to evaluate predicted data, for getting the accuracy according to a standardized way.

Handling Mean Absolute Error in Time Series Data

In the case of time-series data, though Mean Absolute Error can be used, one needs to be careful with the implications. Temporal ordering is enough to increase the model accuracy for time series data. Here are a few tips for handling MAE in time series scenarios:

Rolling Mean Absolute Error:

• We can detect inefficiencies transfer over time by rolling window analysis, So calculate MAE through it.
• This can be used to detect seasonal or specific patterns within errors.

Weighted Mean Absolute Error:

• Categorize the errors according to their occurence time, and then assign them specific weights.
• This will help prioritize the recent predictions against historical ones if needed.

Time-Indexed Evaluation:

• By computing MAE over different time segments, it is imperative to check when the significant changes between the forecasted and actual values occur.

Conclusion

Mean Absolute Error (MAE) and how it is calculated through Python is explained in this detailed guide. We discussed Mean Absolute Error, how to measure it using NumPy and its significance in order to check prediction accuracy.

Calculating Mean absolute error can help us to figure out the inconsistencies within a dataset. Additionally, this can help us improve our models' performance.