Tree-Based Machine Learning Methods in SAS Viya by Dr. Sharad Saxena

Author:Dr. Sharad Saxena [Dr. Sharad Saxena]
Language: eng
Format: epub
Publisher: SAS Institute
Published: 2022-02-21T00:00:00+00:00

Figure 5.17: Event Classification in Confusion Matrix

The counts need to be adjusted if the class proportion in the training sample (ρj) is not the same as in the population (πj). This is shown on the right side of Figure 5.17. It is common practice to try to balance the classes, particularly with rare outcomes.

A confusion matrix presupposes an allocation (decision) rule. A primitive rule allocates cases to the class with the greatest posterior probability. For binary targets, this corresponds to a 50% cutoff on the posterior probability.

Model Studio automatically adjusts assessment measures, assessment graphs, and prediction estimates for this bias. After running the pipeline, you can examine the score code. The score code contains a section titled Adjust Posterior Probabilities. This code block modifies the posterior probability by multiplying it by the ratio of the actual probability to the event-based sampling values specified above.

Tree Accuracy

The accuracy of a tree can be calculated as a weighted average of the accuracy in each leaf. The weights are the node sizes as shown in Figure 5.18.

Accuracy is obtained by multiplying the proportion of observations falling into each leaf by the proportion of those correctly classified in the leaf.

For example, to calculate training accuracy for the tree shown in Figure 5.19, 42% of the observations fall into the left branch and all are classified as a 1. Of those, 85% are classified correctly. Consequently, the accuracy in the left branch would be (0.42)(0.85). Similarly, 58% of the observations fall into the right branch and all are classified as a 0. Of those, 91% are classified correctly. The accuracy in the right branch would be (0.58)(0.91). The training accuracy of the tree would be (0.42)(0.85) + (0.58)(0.91) = 0.88. The validation accuracy is calculated in a similar manner.

Figure 5.18: Accuracy in a Decision Tree

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