6. The effects that can occur when different drugs are taken together can be difficult for doctors to predict. Machine learning models can be built to help predict optimal dosages of drugs so as to achieve a medical practitioner’s goals.26 The image below on the left shows a scatter plot of a dataset used to train a model to distinguish between dosages of two drugs that cause a dangerous interaction and those that cause a safe interaction. There are just two continuous features in this dataset, DOSE1 and DOSE2 (these have both been normalized to the range (−1, 1) using range normalization), and two target levels, dangerous and safe. In the scatter plot DOSE1 is shown on the horizontal axis, DOSE2 is shown on the vertical axis, and the shapes of the points represent the target level—

crosses represent dangerous interactions and triangles represent safe interactions.

The image above on the right shows a simple linear logistic regression model trained to perform this task. This model is

Plainly, this model is not performing well.

a. Would the similarity-based, information-based, or probability-based predictive modeling approaches that have already been covered in this book be likely to do a better job of learning this model than the simple linear regression model?

b. A simple approach to adapting a logistic regression model to learn this type of decision boundary is to introduce a set of basis functions that will allow a non-linear decision boundary to be learned. In this case, a set of basis functions that generate a cubic decision boundary will work well. An appropriate set of basis functions is as follows:

Training a logistic regression model using this set of basis functions leads to the following model:

Use this model to make predictions for the following query instances:

Transcribed Image Text:

Dose! 00 -10 -05 -1.0 -05 05 10 00 Dosel 0.5 10 Dose2 so 01- -1.0 -05 so 1.0 00 Dosel 0.5 10