Hybrid Quantum-Classical Variational Algorithms for High-Dimensional Feature Selection

Abstract

Feature selection in high-dimensional data spaces continues to be an intrinsic challenge in machine learning algorithms, especially when the number of features regularly exceeds thousands. Traditional techniques including mutual information filters, LASSO regularization, and recursive feature elimination are limited by the computational inefficiency of brute force searching as well as poor scalability in the ultra-high-dimensional setting. In this paper, a novel technique, the Hybrid Quantum-Classical Variational Algorithm (HQCVA), that combines quantum computing and classical optimization methods in the Variational Quantum Eigensolver (VQE) approach is introduced. Specifically, the quantum part is responsible for representing the correlation structure of the input features via the Ising model. To reduce composite loss, the classical sub-system uses the Adam stochastic optimizer to update variational parameters iteratively while also balancing density between predictive accuracies, densifications and depth of quantum circuits. Using five benchmark datasets (22,000 gene data; 12,000 pixels of hyperspectral imagery; 8,500 data points of financial time series), HQCVA produces a 12-18% higher F1-score than leading, state-of-the-art classical systems while decreasing the number of selected features by 40-65%. All simulations of circuits are performed on IBM Qiskit Aer with noise added, to simulate Eagle r3 consoles. Furthermore, the results indicate that the quantum advantage scales with increasing feature dimension through this process to demonstrate that near-term quantum devices have practical applications in real-world feature selection applications.