  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.
