Describe the distinctions between L1 and L2 regression.

The question requires you to clarify the distinctions between two regression types: L1 and L2. L1 and L2 denote two different loss functions applicable to regression models, commonly known as Lasso (L1) and Ridge (L2) regression, respectively. In your response, it is essential to define what regression is, describe L1 (Lasso) and L2 (Ridge) regressions, highlight the differences in their loss functions, and discuss how these differences influence the regression models. Key points to address include: The fundamental concept of regression. A description of L1 and L2 regression. The distinctions between L1 and L2 loss functions. The consequences of these differences on the regression models.

Regression is a statistical technique employed in machine learning to forecast a continuous target variable based on a set of features. In L1 regression, commonly referred to as Lasso regression, the loss function is defined as the sum of the absolute values of the coefficients. This approach can result in some coefficients being exactly zero, effectively performing feature selection by disregarding less significant features. L1 regression is more affected by outliers since it attempts to fit these points, leading to non-zero coefficients. Conversely, L2 regression, known as Ridge regression, incorporates the square of the coefficients in its loss function. Unlike L1, all coefficients in an L2 regression model are non-zero, even those that are very small, which may result in overfitting as it considers all features. L2 regression is less impacted by outliers, as it squares the differences between predicted and actual values, causing outliers to be 'spread' out and making it more resilient.

Regression methods primarily aim to minimize a loss function, but they vary in the specific loss function they target. L1 regression, also known as Lasso regression, focuses on minimizing the sum of absolute differences (SAD), which diminishes the influence of outliers in the model and can result in some coefficients being reduced to zero. This process aids in feature selection and simplifies the model, enhancing its interpretability. In contrast, L2 regression, or Ridge regression, aims to minimize the sum of squared differences (SSE), which prevents any coefficients from equaling zero. This results in a more complex model since it retains all features; however, it offers the benefit of increased stability and is less sensitive to variations in the input data.