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Ridge Regression (RR) is regularization technique used in statistical modeling & ML to handle the problem of multicollinearity (high correlation) among predictor variables 
It is an extension of linear regression ( LR) that adds a penalty term to the least squares objective function, resulting in a more stable and robust model.
In LR objective is find coefficient thatโฌ๏ธ sum of squared residual btwn predicted value & actual value of dependent variable. However when there r correlated predictor in dataset the estimated coefficient can become highly sensitive to small change in data leading to overfitting
RR addresses issue by introducing penalty term that shrinks coefficient estimates towards 0.
The penalty term is determined by tuning parameter called lambda (ฮป) which control amount of regularization applied. larger value of ฮป result in greater shrinkage of the coefficients
The penalty term is determined by tuning parameter called lambda (ฮป) which control amount of regularization applied. larger value of ฮป result in greater shrinkage of the coefficients
Mathematically RR modifies OLS objective function by adding penalty term based on the L2-norm (Euclidean norm) of the coefficient vector
The objective function can be written as:
Minimize: (sum of squared residuals) + ฮป * (sum of squared coefficients)
The objective function can be written as:
Minimize: (sum of squared residuals) + ฮป * (sum of squared coefficients)
The addition of the penalty term encourages the model to find a balance between minimizing the residuals and minimizing the magnitude of the coefficients.
This helps to reduce the impact of multicollinearity and stabilize the model's performance.
This helps to reduce the impact of multicollinearity and stabilize the model's performance.
RR can solve using optimization algorithm such GD or closed-form solution
The optimal value of regularization parameter ฮป is typically determined through techniques like CV where data divided into training & validation set to evaluate model performance for different values of ฮป
The optimal value of regularization parameter ฮป is typically determined through techniques like CV where data divided into training & validation set to evaluate model performance for different values of ฮป
Ridge regression is a useful technique for managing multicollinearity and improving the generalization ability of a linear regression model
By controlling the complexity of the model, it helps to prevent overfitting and provides more reliable estimates of the coefficients
By controlling the complexity of the model, it helps to prevent overfitting and provides more reliable estimates of the coefficients
We got an idea that ridge regression is a linear regression with a penalty. Learned that no equation could find the best value of lambda.
vitalflux.com/ridge-regressiโฆ
vitalflux.com/ridge-regressiโฆ
Ridge regression is a powerful tool used in statistics and machine learning. It can be intimidating to learn at first, but with a few examples, it becomes much more manageable
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