Des-q: a quantum algorithm to provably speedup retraining of decision trees

TL;DR

Des-q is a quantum algorithm designed to exponentially speed up the retraining process of decision trees for regression and classification, especially effective with incremental data updates, while maintaining competitive accuracy.

Contribution

The paper introduces Des-q, a quantum algorithm that achieves logarithmic complexity in retraining decision trees, a significant improvement over classical polynomial-time methods.

Findings

Des-q matches classical decision tree performance on benchmark datasets.

Des-q significantly reduces retraining time with incremental data updates.

Quantum-supervised clustering enhances split determination in decision trees.

Abstract

Decision trees are widely adopted machine learning models due to their simplicity and explainability. However, as training data size grows, standard methods become increasingly slow, scaling polynomially with the number of training examples. In this work, we introduce Des-q, a novel quantum algorithm to construct and retrain decision trees for regression and binary classification tasks. Assuming the data stream produces small, periodic increments of new training examples, Des-q significantly reduces the tree retraining time. Des-q achieves a logarithmic complexity in the combined total number of old and new examples, even accounting for the time needed to load the new samples into quantum-accessible memory. Our approach to grow the tree from any given node involves performing piecewise linear splits to generate multiple hyperplanes, thus partitioning the input feature space into distinct regions. To determine the suitable anchor points for these splits, we develop an efficient quantum-supervised clustering method, building upon the q-means algorithm introduced by Kerenidis et al. We benchmark the simulated version of Des-q against the state-of-the-art classical methods on multiple data sets and observe that our algorithm exhibits similar performance to the state-of-the-art decision trees while significantly speeding up the periodic tree retraining.