L2 regularization: It tries to spread error among all the terms. L2 corresponds to a Gaussian prior.

L1 regularization: It is more binary/sparse, with many variables either being assigned a 1 or 0 in weighting. L1 corresponds to setting a Laplacean prior on the terms.

L1 and L2 regularization are techniques used in machine learning to prevent overfitting and improve the generalization of a model by adding a penalty term to the cost function. They are commonly applied in linear regression and logistic regression models.

L1 Regularization (Lasso):
- Explanation: L1 regularization adds the absolute values of the coefficients (weights) to the cost function.
- Purpose: It tends to yield sparse models, meaning it encourages some of the feature weights to be exactly zero. This can be useful for feature selection, as it effectively ignores less important features.
- Mathematically: Cost function with L1 regularization is represented as J(w) = J_0(w) + λ * Σ|w_i|, where J_0(w) is the original cost function, λ is the regularization parameter, and w_i are the individual weights.
L2 Regularization (Ridge):
- Explanation: L2 regularization adds the squared values of the coefficients to the cost function.
- Purpose: It penalizes large weights, preventing them from becoming too dominant. It leads to the distribution of weights across all features rather than assigning high importance to just a few.
- Mathematically: Cost function with L2 regularization is represented as J(w) = J_0(w) + λ * Σ(w_i^2), where J_0(w) is the original cost function, λ is the regularization parameter, and w_i are the individual weights.

Key points:

The choice between L1 and L2 regularization depends on the specific problem and the desired properties of the model.
The regularization parameter (λ) controls the strength of the regularization, and its optimal value may need to be determined through cross-validation.
L1 regularization can lead to sparsity, making it useful for feature selection, while L2 regularization tends to distribute weights more evenly.

When asked about L1 and L2 regularization in a machine learning interview, it’s important to convey a clear understanding of their mathematical formulations, purposes, and the impact they have on the model’s behavior. Additionally, discussing scenarios where one might be preferred over the other would demonstrate a deeper understanding of their practical applications.