Regularization: Taming the Wild L1 and L2 Beasts and the Mysterious Dropout

Source: https://towardsdatascience.com/regularization-in-deep-learning-l1-l2-and-dropout-377e75acc036

As data scientists, we often face the challenge of overfitting when training our models. Overfitting occurs when our model is too complex and learns patterns that are specific to the training data, but do not generalize well to new, unseen data.

One way to combat overfitting is through the use of regularization techniques. In this article, we’ll discuss two popular types of regularization: L1 and L2 regularization, as well as a lesser-known technique called dropout regularization.

L1 regularization, also known as Lasso regularization, adds a penalty to the model’s objective function equal to the absolute value of the weights of the model. This leads to a sparse model, where some weights are exactly equal to zero.

L2 regularization, also known as Ridge regularization, adds a penalty to the model’s objective function equal to the square of the weights of the model. This leads to a model with small, non-zero weights.

Both L1 and L2 regularization can be expressed as follows:

L1 regularization: loss + alpha * sum(abs(weights)) L2 regularization: loss + alpha * sum(weights²)

where alpha is a hyperparameter that controls the strength of the regularization, and weights are the model’s weights.

Dropout regularization is a bit more mysterious, as it does not add a penalty to the objective function like L1 and L2 regularization. Instead, it randomly “drops out” (sets to zero) a certain percentage of the neurons in the model during training. This forces the remaining neurons to learn more robust features and helps prevent overfitting.

To implement dropout regularization, we can define a dropout rate (e.g., 0.5 means 50% of neurons are dropped out) and use it to randomly drop out neurons during training. For example:

def dropout(x, dropout_rate):
  mask = np.random.rand(*x.shape) < (1 - dropout_rate)
  x *= mask
  return x

# During training
x = dropout(x, dropout_rate)

It’s important to note that dropout should only be used during training, and should not be used during inference (i.e., when making predictions on new, unseen data). This is because during inference, we want the model to use all of its neurons to make the most accurate predictions possible.

So how do we choose which regularization technique to use? It really depends on the specific problem and the type of model we are using. L1 regularization is often preferred for sparse models, where we want to eliminate as many unnecessary features as possible. L2 regularization is often preferred for models with many features, as it helps keep the weights small and prevent overfitting. Dropout regularization is a good choice for neural networks, as it can help prevent overfitting and improve the generalization ability of the model.

In conclusion, regularization is a powerful tool for preventing overfitting and improving the generalization ability of our models. By taming the wild L1 and L2 beasts and using the mysterious dropout technique, we can build models that are robust and perform well on new, unseen data.