Machine learning is a branch of artificial intelligence that has become increasingly popular over the years. It involves the use of algorithms and statistical models to enable artificial systems to improve their performance on a task by learning from data. One of the essential components of machine learning is loss, which is a measure of how well a model fits the data. L1 loss, also known as mean absolute error (MAE), is one type of loss function that is commonly used to train machine learning models.

What is L1 Loss?

L1 loss is a measure of the difference between the predicted values of a machine learning model and the true values of the dataset. It is calculated as the sum of the absolute differences between the predicted and the actual values. This loss function is known as L1 because it uses the absolute values of the errors, whereas L2 loss (mean squared error) calculates the square values of the errors. The formula for L1 loss is as follows:

L1 Loss = ∑|yi − ŷi|

where:

yi = actual value of the target variable

ŷi = predicted value of the target variable

Why is L1 Loss Used in Machine Learning?

The choice of loss function depends on the type of problem and the distribution of the data. L1 loss is commonly used in cases where the dataset has outliers or the cost of false positives and false negatives is the same. Additionally, L1 loss is a robust measure of the accuracy of the model as it is less sensitive to the outliers compared to other loss functions, such as L2 loss.

L1 loss is also used when the linear regression model has sparse coefficients, which means that only a few of the coefficients have a significant impact on the output. L1 loss helps in selecting a subset of important features by shrinking the least important ones to zero.

L1 vs. L2 Loss

L1 loss and L2 loss are two popular loss functions used in machine learning. The main difference between the two is the way they handle outliers. L1 loss measures the absolute difference between the predicted and actual values, whereas L2 loss measures the squared difference. The squared difference magnifies the impact of outliers and hence results in a higher loss for the model.

Another difference is that L2 loss favors small errors and is better suited for problems that require high precision such as image classification and speech recognition. On the other hand, L1 loss is better suited for regression problems where the data is likely to have outliers.

Conclusion

L1 loss is a commonly used loss function in machine learning that calculates the absolute differences between the predicted and actual values. It is a robust measure of the accuracy of the machine learning model and is less sensitive to outliers. L1 loss is better suited for cases where the data has outliers, and the cost of false positives and false negatives is the same. It is also used in problems where the linear regression model has sparse coefficients. L1 loss and L2 loss are popular loss functions, and the choice of loss function depends on the type of problem and the distribution of data.