On the Gini-impurity Preservation For Privacy Random Forests

Random forests have been one successful ensemble algorithms in machine learning. Various techniques have been utilized to preserve the privacy of random forests from anonymization, differential privacy, homomorphic encryption, etc., whereas it rarely takes into account some crucial ingredients of learning algorithm. This work presents a new encryption to preserve data's Gini impurity, which plays a crucial role during the construction of random forests. Our basic idea is to modify the structure of binary search tree to store several examples in each node, and encrypt data features by incorporating label and order information. Theoretically, we prove that our scheme preserves the minimum Gini impurity in ciphertexts without decrypting, and present the security guarantee for encryption. For random forests, we encrypt data features based on our Gini-impurity-preserving scheme, and take the homomorphic encryption scheme CKKS to encrypt data labels due to their importance and privacy. We conduct extensive experiments to show the effectiveness, efficiency and security of our proposed method.