Regularization is a technique used in machine learning to prevent overfitting, which occurs when a model becomes too complex and fits noise in the training data instead of the underlying patterns. Regularization introduces a penalty term to the objective function of the model, which encourages simpler models by shrinking the weights towards zero.
L1 and L2 regularization are two common regularization techniques used in machine learning. L1 regularization, also known as Lasso regularization, penalizes the sum of the absolute values of the model’s weights. L2 regularization, also known as Ridge regularization, penalizes the sum of the squares of the model’s weights.
The primary difference between L1 and L2 regularization is the type of penalty they impose on the weights. While L1 regularization results in sparse models by setting some of the less important weights to zero, L2 regularization tends to spread the value of the weights more evenly, resulting in models that use all of the input features to some degree.
A key impact of regularization on model complexity is the trade-off between bias and variance. By adding a penalty term to the model’s objective function, regularization increases the bias of the model, resulting in a simpler, more constrained model that is less likely to fit the noise in the training data. However, the addition of the penalty also increases the model’s variance, as the model becomes more sensitive to changes in the training data, which can lead to overfitting.
In general, L1 regularization tends to work well when the dataset contains many irrelevant or redundant features, as it encourages the model to use only a small number of the most important features. L2 regularization, on the other hand, tends to work well when the dataset contains many features with similar importance, as it spreads the weight values more evenly across all of the features.
For example, let’s consider a linear regression problem with two features, x1 and x2, and the following data points:
| x1 | x2 | y |
|--------|--------|--------|
| 1 | 2 | 4 |
| 2 | 4 | 8 |
| 3 | 6 | 12 |
| 4 | 8 | 16 |
| 5 | 10 | 20 |If we apply L1 regularization to this problem, we might end up with a model that only uses x1, as x2 is less important and may have a weight of zero. On the other hand, if we apply L2 regularization, we might end up with a model that uses both x1 and x2, with smaller weights for x2 than for x1.