Lasso Regression
July 30, 2023
Lasso Regression
Lasso regression, also known as L1 regularization, is another linear regression technique used to address multicollinearity and prevent overfitting in multiple regression models. Like ridge regression, lasso regression adds a regularization term to the least squares objective function. However, in lasso regression, the regularization term is the L1 norm (sum of absolute values) of the coefficients, which leads to some coefficients being exactly zero. This property makes lasso regression useful for feature selection, as it can effectively set irrelevant coefficients to zero.
Lasso Regression Objective Function: Objective = Σ(Yᵢ - Ŷᵢ)² + λ * Σ|βⱼ|
where the variables have the same meanings as in ridge regression.
The first term in the objective function represents the residual sum of squares (RSS), measuring the discrepancy between the actual and predicted dependent variable values. The second term is the L1 regularization term, which penalizes large coefficients. The use of the absolute values in the L1 norm makes some coefficients exactly zero, leading to a sparse model with fewer relevant features.
The lasso regression coefficients are obtained by minimizing the objective function. The formula for calculating the lasso regression coefficients β is given by
Lasso Regression Coefficients: β = argmin { Σ(Yᵢ - Ŷᵢ)² + λ * Σ|βⱼ| }
Where:
- Ŷᵢ is the predicted dependent variable using the lasso regression model.
- Yᵢ is the actual dependent variable (observed data).
- p is the number of independent variables (features).
- βⱼ is the coefficient for the j-th independent variable.
- λ is the regularization parameter (hyperparameter) controlling the penalty.
In practice, the lasso regression coefficients are usually estimated using numerical optimization algorithms since there is no closed-form solution.
Lasso regression's ability to perform feature selection by setting some coefficients to exactly zero makes it particularly useful when dealing with high-dimensional datasets or when there is a suspicion that some independent variables are irrelevant to the model.
Interview Questions :
1. What is Lasso regression?
2. What is Lasso Regression Objective Function?
3. How to calculate Lasso Regression Coefficients?
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