Mean Absolute error (MAE) in Machine Learning

Mean absolute error is a common metric in Machine learning, statistics to evaluate the prediction accuracy of the regression model.

Formula

MAE = mean(|y_actual - y_pred|)

 

where:

 

1. y_actual are the actual values
2. y_pred are the predicted values
3. mean() is the average function
4. |x| is the absolute value of x

 

A lower MAE indicates that the model's predictions are closer to the actual values, whereas higher MAE indicated that the model’s predictions are far from the actual values.

 

MAE is less sensitive to outliers as compared to Root Mean Squared Error  (RMSE).

 

Following application used ‘Mean Absolute Error’ to compare the prediction accuracies of two models.

 

mae.py 

import numpy as np
import matplotlib.pyplot as plt

# Mean absolute error
def mae(actual, predicted):
    # Calculate absolute residuals
    absolute_residuals = np.abs(actual - predicted)

    # Calculate mean absolute error (MAE)
    mae = np.mean(absolute_residuals)

    return mae

# Generate some data
year = np.array([2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016, 2015])
population_in_millions = np.array([1425.776, 1417.173, 1407.564, 1396.387, 1384.332, 1371.818, 1359.003, 1346.021, 1332.993])

# Fit two different regression models to the data
model1 = np.polyfit(year, population_in_millions, 1)
model2 = np.polyfit(year, population_in_millions, 2)

# Predict the values for both models
m1 = model1[0]
c1 = model1[1]
population_pred1 =  m1 * year + c1

a1 = model2[0]
a2 = model2[1]
a3 = model2[2]
population_pred2 = a1 * year**2 + a2 * year + a3

# print(f'population_pred1 : {population_pred1}')
# print(f'population_pred2 : {population_pred2}')

# Calculate the MSE for both models
mae1 = mae(population_in_millions, population_pred1)
mae2 = mae(population_in_millions, population_pred2)

print("MAE for model1:", mae1)
print("MAE for model2:", mae2)

if mae1 > mae2:
    print('prediction2 is more accurate')
else:
    print('prediction1 is more accurate')

# Draw the plot
plt.plot(year, population_in_millions, color='red')
plt.plot(year, population_pred1, color='blue', label=f'pred1 : {m1}*x+{c1}')
plt.plot(year, population_pred2, color='green', label=f'pred2 : {a1}*x*x+{a2}*x+{a3}')

plt.legend()

plt.show()

 

Output

MAE for model1: 1.6444691358031176
MAE for model2: 0.5022695527730624
prediction2 is more accurate

 

You can confirm the same from below diagram.

 

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