A Quantum-Inspired Ensemble Method and Quantum-Inspired Forest Regressors

TL;DR

This paper introduces a quantum-inspired ensemble method and forest regressors that leverage quantum mechanics principles to enhance diversity and accuracy in ensemble learning, with theoretical and empirical validation.

Contribution

It presents a novel quantum-inspired ensemble regression algorithm and establishes a theoretical link between quantum interpretations and machine learning.

Findings

Quantum-Inspired Forest shows robustness across hyperparameters.

The method encourages ensemble diversity and accuracy.

Theoretical proof links quantum interpretation to ensemble regression.

Abstract

We propose a Quantum-Inspired Subspace(QIS) Ensemble Method for generating feature ensembles based on feature selections. We assign each principal component a Fraction Transition Probability as its probability weight based on Principal Component Analysis and quantum interpretations. In order to generate the feature subset for each base regressor, we select a feature subset from principal components based on Fraction Transition Probabilities. The idea originating from quantum mechanics can encourage ensemble diversity and the accuracy simultaneously. We incorporate Quantum-Inspired Subspace Method into Random Forest and propose Quantum-Inspired Forest. We theoretically prove that the quantum interpretation corresponds to the first order approximation of ensemble regression. We also evaluate the empirical performance of Quantum-Inspired Forest and Random Forest in multiple hyperparameter settings. Quantum-Inspired Forest proves the significant robustness of the default hyperparameters on most data sets. The contribution of this work is two-fold, a novel ensemble regression algorithm inspired by quantum mechanics and the theoretical connection between quantum interpretations and machine learning algorithms.