Consider a decision tree algorithm attempting to find the right feature for a node. If the first query returns a value of ${\widehat{D}}_{\chi }$ with a confidence of $\delta$ then the branching factor would be approximately $m\cdot {\widehat{I}}_{\chi }\left(\delta \right)$. This branching factor would be approximately the same for further queries required by the algorithm to make a decision about what feature to use. This results in a total multiplied choice space size of approximately ${\left[4m\cdot {\widehat{I}}_{\chi }\left(\delta \right)\right]}^F$ which can be reduced to $F$ or less using a batch query.