Based on decision trees, it is efficient to handle tabular data. Conventional decision tree growth methods often result in suboptimal trees because of their greedy nature. Their inherent structure limits the options of hardware to implement decision trees in parallel. Here is a compact representation of binary decision trees to overcome these deficiencies. We explicitly formulate the dependence of prediction on binary tests for binary decision trees and construct a function to guide the input sample from the root to the appropriate leaf node. And based on this formulation we introduce a new interpretation of binary decision trees. Then we approximate this formulation via continuous functions. Finally, we interpret the decision tree as a model combination method. And we propose the selection-prediction scheme to unify a few learning methods.

These concerns have been present whenever we make important decisions. What's new is the much, much larger scale at which we now rely on algorithms to help us decide. Human errors that may have once been idiosyncratic may now become systematic. "Artificial intelligence is the pursuit of machines that are able to act purposefully to make decisions towards the pursuit of goals," wrote Harvard University Professor David Parkes in "A Responsibility to Judge Carefully in the Era of Decision Machines," an essay recently published as part of Harvard's Digital Initiative. "Machines need to be able to predict to decide, but decision making requires much more," he wrote.

But if the narrative of the present is one of "prediction machines," referencing the book of the same title by Ajay Agrawal, Joshua Gans, and Avi Goldfarb, the narrative of the future will belong to "decision machines." If the narrative of the present is one of managers who are valued for showing judgment in decision making -- don't tell me whether someone will do well on the job, or whether a new product will win in the marketplace, but tell me instead who I should hire, which products I should bet on -- then the narrative of the future will be one in which we are valued for our ability to judge and shape the decision-making capabilities of machines. Artificial intelligence (AI) is the pursuit of machines that are able to act purposefully to make decisions towards the pursuit of goals. Machines need to be able to predict to decide, but decision making requires much more. Decision making requires bringing together and reconciling multiple points of view.