You can use multivariate adaptive regression splines to tackle the same problems that you would use linear regression fo

The backward stage, a.k.a. pruning stage, goes through functions one at a time and deletes the ones that add no material performance to the model. This is done by using a generalized cross-validation (GCV) score. Note, GCV score is not actually based on cross-validation and is only an approximation of true cross-validation score, aiming to penalize model complexity.

As you can see, the MARS model added two hinge functions in the forward stage, but then it pruned h(x0–1146.33) from the model in the backward stage. Hence, the final equations for the two models are:

Looking at the graph above, we can clearly see the relationship between the two variables. The price of a house unit area decreases as the distance from the nearest MRT station increases.

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what we were doing those first few weeks of the pandemic. I’d argue that we still don’t really know what we’re doing, but at least now we have a bit of experience. Physicians like me have our years of training and our fount of clinical knowledge, but this virus caught us completely off guard. In the beginning of the pandemic nothing seemed to be certain except that it was unlike anything that we’d ever seen, and that it was deadly. Each day brought a slew of new casualties and case reports. We quickly learned how much of a threat Covid-19 was to health care providers and other essential workers. Especially to those with preexisting conditions like me.

Let us plot two graphs to visualize the results, one for multiple linear regression and another for multivariate adaptive regression splines. But before that, we need to generate a mesh with a range of input values and predict output values. This will give us the data for our two graphs.

However, the interaction between metrics in the real-world is often non-linear, which means that linear regression cannot give us a good approximation of outputs given the inputs. This is where MARS comes to the rescue.

Since we increased the number of dimensions, we now have two slope parameters in a linear regression model (one for each x). We also have 4 hinge functions that have been added to the MARS model using both independent variables.

If you wondered what that feature image represented at the beginning of the story, you should now be able to see that it overlays the predictions from linear regression and MARS models to help you see how the prediction outputs differ using each model.

Note the kink at x=1146.33. This is where the hinge function h(c-x) becomes zero, and the line changes its slope. The graph makes it very intuitive to understand how MARS can better fit the data using hinge functions.

Let us take ‘X3 distance to the nearest MRT station’ as our input (independent) variable and ‘Y house price of unit area’ as our output (dependent, a.k.a. target) variable.

It is easy to see the difference between the two models. Multiple linear regression creates a prediction plane that looks like a flat sheet of paper. Meanwhile, MARS takes that sheet of paper and folds it in a few places using hinge functions, enabling a better fit to the data.

Note that the py-earth package is only compatible with Python 3.6 or below at the time of writing. If you are using Python 3.7 or above, I suggest you create a virtual environment with Python v.3.6 to install py-earth.

Next, we download and ingest the data that we will use to build our MARS and linear regression models. (source: https://www.kaggle.com/quantbruce/real-estate-price-prediction?select=Real estate.csv)

It is clear from this example that linear regression would fail to give us a meaningful prediction as we would not be able to draw one straight line across the entire set of observations.

The result of combining linear hinge functions can be seen in the example below, where black dots are the observations, and the red line is a prediction given by the MARS model: