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Scientific Reports

A quantum computing-based approach for feature selection in regression models

Amirhossein Nourbakhshrezaei, Soroush Sheikh Gargar, Mojgan Jadidi

Published Sep 17, 2026• 0 citations
Publisher

Abstract

Feature Selection (FS) is an essential data preprocessing technique aimed at identifying the most relevant features for predictive models. However, traditional FS approaches often struggle to capture complex interactions in real-world datasets, limiting their ability to fully support high-performing Machine Learning (ML) models. This study introduces a QA-compatible QUBO-based FS formulation for regression that models both linear and non-linear feature dependencies through hybrid linear and quadratic coefficients. Using three datasets; Wine Quality, Insurance, and Bike Sharing System (BSS) we evaluate the method across multiple predictive models to assess its robustness and generalizability. Results show competitive predictive performance and, in several settings, more compact feature subsets than Mutual Information and the MI_QC baseline. This study introduces a methodological refinement over previous QUBO-based FS methods and demonstrates practical applicability through statistically robust benchmarking.

DOI
10.1038/s41598-026-71141-w

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Feature Selection (FS) is an essential data preprocessing technique aimed at identifying the most relevant features for predictive models. However, traditional FS approaches often struggle to capture complex interactions in real-world datasets, limiting their ability to fully support high-performing Machine Learning (ML) models. This study introduces a QA-compatible QUBO-based FS formulation for regression that models both linear and non-linear feature dependencies through hybrid linear and quadratic coefficients. Using three datasets; Wine Quality, Insurance, and Bike Sharing System (BSS) we evaluate the method across multiple predictive models to assess its robustness and generalizability. Results show competitive predictive performance and, in several settings, more compact feature subsets than Mutual Information and the MI_QC baseline. This study introduces a methodological refinement over previous QUBO-based FS methods and demonstrates practical applicability through statistically robust benchmarking.
Abstract In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higher-quality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer, and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark data sets. We observe competitive performance.
In this work, we tackle the feature selection problem for content-based recommender systems using Quadratic Unconstrained Binary Optimization (QUBO). Our approach, submitted as Team MALTO to the QuantumCLEF 2025 challenge, aims to improve the performance of an Item-Based K-Nearest Neighbors (Item-KNN) model by selecting a compact and informative subset of item features. We formulate a QUBO objective that combines feature relevance – estimated via Random Forest (RF) importance scores – and feature redundancy – captured through pairwise Pearson correlations. We compare our method against a collaborative-driven QUBO baseline and a random selection strategy. Experiments on the official QuantumCLEF dataset demonstrate that our relevanceaware strategy outperforms the other methods regarding recommendation quality, especially in low-dimensional feature regimes. Our results highlight the potential of combining machine learning and quantum optimization for effective feature selection in recommender systems
Within machine learning model evaluation regimes, feature selection is a technique to reduce model complexity and improve model performance in regards to generalization, model fit, and accuracy of prediction. However, the search over the space of features to find the subset of kkk optimal features is a known NP-Hard problem. In this work, we study metrics for encoding the combinatorial search as a binary quadratic model, such as Generalized Mean Information Coefficient and Pearson Correlation Coefficient in application to the underlying regression problem of price prediction. We investigate trade-offs in the form of run-times and model performance, of leveraging quantum-assisted vs. classical subroutines for the combinatorial search, using minimum redundancy maximal relevancy as the heuristic for our approach. We achieve accuracy scores of 0.9 (in the range of [0,1]) for finding optimal subsets on synthetic data using a new metric that we define. We test and cross-validate predictive models on a real-world problem of price prediction, and show a performance improvement of mean absolute error scores for our quantum-assisted method (1471.02±135.6)(1471.02 \pm{135.6})(1471.02±135.6), vs. similar methodologies such as recursive feature elimination (1678.3±143.7)(1678.3 \pm{143.7})(1678.3±143.7). Our findings show that by leveraging quantum-assisted routines we find solutions that increase the quality of predictive model output while reducing the input dimensionality to the learning algorithm on synthetic and real-world data.
Feature selection is a pivotal step in machine learning, aimed at reducing feature dimensionality and improving model performance. Conventional feature selection methods, typically framed as NP-hard problems, focus primarily on selecting non-redundant and discriminative features but neglect how these selected features influence downstream machine learning tasks. To bridge this gap, we propose a mixed-integer non-linear programming-based integrated feature selection and logistic regression (IFSLR) model that jointly optimizes feature selection and classifier parameters. To solve the proposed IFSLR model efficiently, we reformulate it into two quantum-computing-compatible quadratic unconstrained binary optimization (QUBO) models via discretization of continuous variables and Taylor expansions, and provide a theoretical approximation guarantee for the proposed QUBO models. To adaptively optimize both the discretization step length optimization sub-problems and the parameterized QUBO sub-problems, we develop a dual-level Q-learning-guided hybrid quantum-classical algorithm that dynamically selects which sub-problem to solve. At the upper level, an adaptive Q learning agent is employed to select appropriate sub-problems during the search process. At the lower level, each iteration addresses either discretization step length optimization sub-problems or parameterized QUBO sub-problems. Experiments on the German credit dataset demonstrate that our method achieves a 10.83% improvement in accuracy and a 4.54-fold enhancement in computational efficiency on average compared with state-of-the-art methods. It also achievesF1 score improvements of 2.86% on the Wisconsin diagnostic breast cancer dataset and 7.65% on the Portuguese bank marketing dataset. The improvements further validate the effectiveness and generalizability of the proposed model and algorithm.
Abstract Feature selection is a technique used to reduce complexity and improve performance in regards to generalization, fit, and accuracy of prediction for machine learning models. A central challenge in this selection process is that the search over the space of features to find the subset of k optimal features is a known NP-Hard problem. In this work, we study metrics for encoding the combinatorial search as a binary quadratic model, such as Generalized Mean Information Coefficient and Pearson Correlation Coefficient in application to the underlying regression problem of price prediction. We compare predictive model performance in regards to leveraging quantum-assisted vs. classical subroutines for the search, using minimum redundancy maximal relevancy as the heuristic for our approach. We cross validate predictive models on a real world problem of price prediction, and show a performance improvement of mean absolute error scores for our quantum-assisted method (1471.02±135.6)(1471.02 \pm {135.6})(1471.02±135.6) ( 1471.02 ± 135.6 ) vs. similar methodologies such as greedy selection (1707.2±168)(1707.2 \pm {168})(1707.2±168) ( 1707.2 ± 168 ) , recursive feature elimination (1678.3±143.7)(1678.3 \pm {143.7})(1678.3±143.7) ( 1678.3 ± 143.7 ) , and all features (1546.2±154(1546.2 \pm {154}(1546.2±154 ( 1546.2 ± 154 ). Our findings show that by leveraging quantum assisted routines we find solutions which increase the quality of predictive model output while reducing the input dimensionality to the learning algorithm on synthetic and real-world data.
Abstract Unsupervised feature selection is essential for high-dimensional machine learning tasks, as it improves model quality and efficiency while providing interpretable insights into datasets. However, existing methods often struggle to simultaneously achieve robustness, reliability, interpretability, and computational efficiency. Furthermore, feature selection in quantum machine learning remains largely unexplored despite the potential of quantum approaches to capture complex feature interactions. In this work, we propose the Quantum Hybrid Feature Selector, a novel unsupervised feature selection framework that combines quantum-enhanced feature extraction with interpretable scoring algorithms. Our main contributions are threefold: we introduce a quantum hybrid autoencoder pipeline that couples feature extraction with feature ranking in the original input space, we define three scoring mechanisms: SHAP-based scoring, correlation-matrix scoring, and weight-based analysis, that relate latent features to original features without requiring external predictive models, and we provide comprehensive empirical evaluation on synthetic and real-world benchmarks with statistical validation. On Madelon-style synthetic datasets, our quantum SCM achieves up to 23.5% improvement in Mean Informative Rank and 9.7% improvement in Informative Ratio compared to classical alternatives, with all improvements statistically significant at p<0.001p < 0.001p<0.001 p < 0.001 . On the Communities and Crime dataset with injected noise features, both quantum and classical SCM variants achieve near-perfect noise elimination, demonstrating effective denoising capability on real-world data. We also show that expert input is essential for evaluating feature selectors, as different methods emphasize distinct aspects of the data despite similar aggregate metrics. Finally, we evaluate QHFS under realistic hardware noise conditions using device-informed simulations based on IBM superconducting quantum processors, demonstrating graceful performance degradation and systematic improvement with increased shot budgets, which supports the practical viability of our approach on near-term quantum devices.