In this chapter, we started with the oldest trick in the book, ordinary least squares. It is still sometimes good enough. However, we also saw that more modern approaches that avoid overfitting can give us better results. We used Ridge, Lasso, and Elastic nets; these are the state-of-the-art methods for regression.

We once again saw the danger of relying on training error to estimate generalization: it can be an overly optimistic estimate to the point where our model has zero training error, but we can know that it is completely useless. When thinking through these issues, we were led into two-level cross-validation, an important point that many in the field still have not completely internalized. Throughout, we were able to rely on scikit-learn to support all the operations we wanted to perform, including an easy way to achieve correct cross-validation.

At the end of this chapter, we started to shift gears and look at recommendation problems. For now, we approached these problems with the tools we knew: penalized regression. In the next chapter, we will look at new, better tools for this problem. These will improve our results on this dataset.

This recommendation setting also has a disadvantage that it requires that users have rated items on a numeric scale. Only a fraction of users actually perform this operation. There is another type of information that is often easier to obtain: which items were purchased together. In the next chapter, we will also see how to leverage this information in a framework called basket analysis.