Privacy in Multi-Agent Learning: Securely Inducing a Multi-Agent Decision Tree

In this paper we study the problem of how multiple distributed agents can jointly induce a decision tree, such that each of them preserves privacy over its own data and item set and each of them holds a part of the learned tree. Our work is original in the following ways: First of all, we consider agents to maintain data sites and jointly induce a decision tree. This merely reflects reality, as this is unlikely to be done by humans. Secondly, we formalize what is meant by data which is horizontally or vertically distributed in the literature. Thirdly, we show significance of this problem to real world applications by means of a motivating example. Fourthly, we generalize the state of the art to a situation in which we consider data which is as well vertically as horizontally distributed, which we call grid distributed data. We discuss two different evaluation methods for preserving privacy ID3, namely, first merging data horizontally and developing vertically or first merging data vertically and next developing horizontally. Finally, the main contribution of this paper is that we show, by means of a complexity analysis, that the former evaluation method is the more efficient.