Explain L1 vs L2 and ridge vs lasso

Describe the differences between:

1. L1 vs L2 regularization — how each one changes the objective, the geometric/intuitive picture, and the typical effect on learned parameters.
2. Ridge vs Lasso regression — how they relate to L2/L1, and how they affect feature selection/sparsity.

Also cover practical considerations:

• when ridge vs lasso (or elastic net) is preferred
• how correlated features behave
• why feature scaling/standardization is important

(Optional) define a likelihood and explain its relationship to loss functions such as negative log-likelihood.

Overview: This question tests understanding of regularization methods in machine learning—specifically the distinctions between L1 and L2 norms and their use in Lasso and Ridge regression—including effects on objective functions, parameter sparsity, geometric intuitions, correlated features, and the role of feature scaling.