Which property in tree algorithms allows for backup rules when main rules are not applicable due to missing values?

The property in tree algorithms that enables backup rules when main rules are not applicable due to missing values is the number of surrogate. Surrogate splitting allows a decision tree to handle missing values effectively by providing alternative rules based on the values of other features. When a primary predictor variable is missing for a particular observation, the algorithm can refer to these surrogates, which are secondary predictors that have shown some correlation with the target outcome.

This ability to use surrogate variables ensures that predictions can still be made even in the presence of incomplete data, enhancing the robustness of the model. The number of surrogate variables indicates how many alternatives are available for handling such missing values, thereby improving the decision-making process within the tree.

The other options do not serve this specific function. Data detection relates to identifying the characteristics of the dataset but does not directly deal with surrogate rules. Variance measure is used mainly in assessing how much variability exists and does not influence how trees manage missing values. Tree depth pertains to the structure of the tree and its complexity but does not relate to the issue of applying backup rules for missing data.