Other regression techniques
A brief introduction to following regression techniques comes next, and why you may prefer to use them in comparison to least squares. In this section, we'll cover:
- Ridge regression, with a practical example in scikit-learn
- Lasso and logistic regression
- Polynomial regression with examples
- Isotonic regression
One of the most common problems with linear regression is the ill-conditioning that causes instabilities in the solution. Ridge regression has been introduced to overcome this problem.
Ridge Regression
A very common problem in regression models arises as a result of the structure of XTX. We have previously shown that the presence of multi-collinearities forces , and this implies that the inversion becomes extremely problematic. A simple way to check the presence of multi-collinearities is based on the computation of the condition number of XTX (with normalized columns with a length equal to 1), defined as:
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