Which factor influences the selection of splits in decision trees for interval inputs?

The measurement scale of the inputs is a critical factor influencing the selection of splits in decision trees for interval inputs. Decision trees work fundamentally by partitioning data into subsets based on feature values. When the input variables are measured on an interval scale, it allows for a meaningful interpretation of the distances between values.

For interval inputs, the splits are chosen based on criteria that evaluate how well they can separate the data into distinct classes or predicted intervals. The algorithm typically assesses potential splits by calculating metrics such as Gini impurity or information gain, which rely on the numerical properties of the interval data. This means that the range and the precise values of the inputs play a significant role in determining the optimal points for splitting the data.

While other factors, such as the distributions of the target variable and sample size, can impact the performance of the resulting model, they do not directly influence the mechanics of selecting splits in the same fundamental way that the measurement scale does. The linear relationship of inputs is also less relevant in a decision tree context since trees do not assume linearity in the relationships between variables; they handle non-linear relationships and interactions inherently through their structure. Hence, the measurement scale is the most pertinent factor when it comes to making decisions about splits in decision