Feature Selection for Classification with QAOA

TL;DR

This paper explores using the Quantum Approximate Optimization Algorithm (QAOA) to perform feature selection in machine learning, demonstrating its feasibility on real datasets and current quantum hardware.

Contribution

It introduces a QUBO formulation for feature selection and applies QAOA on both simulators and quantum hardware, showing potential for quantum-assisted feature selection.

Findings

QAOA can be used for feature selection in real datasets.

Current quantum devices can effectively implement QAOA for small problems.

Selected features improve classification accuracy.

Abstract

Feature selection is of great importance in Machine Learning, where it can be used to reduce the dimensionality of classification, ranking and prediction problems. The removal of redundant and noisy features can improve both the accuracy and scalability of the trained models. However, feature selection is a computationally expensive task with a solution space that grows combinatorically. In this work, we consider in particular a quadratic feature selection problem that can be tackled with the Quantum Approximate Optimization Algorithm (QAOA), already employed in combinatorial optimization. First we represent the feature selection problem with the QUBO formulation, which is then mapped to an Ising spin Hamiltonian. Then we apply QAOA with the goal of finding the ground state of this Hamiltonian, which corresponds to the optimal selection of features. In our experiments, we consider seven different real-world datasets with dimensionality up to 21 and run QAOA on both a quantum simulator and, for small datasets, the 7-qubit IBM (ibm-perth) quantum computer. We use the set of selected features to train a classification model and evaluate its accuracy. Our analysis shows that it is possible to tackle the feature selection problem with QAOA and that currently available quantum devices can be used effectively. Future studies could test a wider range of classification models as well as improve the effectiveness of QAOA by exploring better performing optimizers for its classical step.