Ridge Regression for Beginners
In this article, we will cover the basics of Ridge regression. The main advantage of Ridge regression is to avoid overfitting. The ultimate goal is to obtain a regression model that can generalize patterns and perform well on both the training and testing data. We want to avoid a model that overfits the data, meaning it performs well during training but poorly during testing.
Understanding Overfitting
Overfitting occurs when the trained model performs well during training but poorly during testing. To illustrate this, let’s assume we have a set of data points represented by red dots. We have an independent variable X and a dependent variable Y. We can have two models: one that fits the data points perfectly but fails to generalize (overfitting), and another that is more balanced and general.
Regularization to Reduce Variance
The overall idea of regularization is to reduce the variance or variability between the training and testing data sets by increasing the bias slightly. This means that the model may perform slightly worse during training but will become more general and perform well on both the training and testing data sets.
Practical Example
Let’s consider a practical example with three green data points as the training data. Using the least sum of squares, we can draw a line that passes perfectly through these points. The sum of squared residuals is equal to 0, indicating a perfect fit during training. However, when we consider the entire data set, including the red testing data points, the sum of residuals is large. This indicates that the line has high variance and performs poorly on the testing data set. This is an example of overfitting.
Introducing Ridge Regression
Ridge regression aims to improve the generalization capability of the model by introducing a slight shift or tilt to the line. This introduces additional error during training but allows the model to perform better during testing. The slope of the line is changed to reduce sensitivity to changes in the independent variable.
Mathematics of Ridge Regression
Ridge regression adds a penalty term to the sum of squared residuals. The penalty term is alpha times the slope squared. By changing the value of alpha, we can adjust the effects of regularization and impact the slope of the line.
Impact of Alpha
As alpha increases, the slope of the regression line is reduced, making it more horizontal or flat. This means that the model becomes less sensitive to variations in the independent variable. Small changes in the independent variable will have a smaller impact on the dependent variable.
Conclusion
Ridge regression is a technique used to avoid overfitting in regression models. By introducing a penalty term and adjusting the slope of the line, the model becomes more general and performs well on both the training and testing data sets. In the next lecture, we will cover Lasso regression, which is similar to Ridge regression. Stay tuned for more information on applying Ridge and Lasso regression in practice.