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Neurocomputing

Quantum annealing-based feature selection

Daniel Pranjić, Bharadwaj Chowdary Mummaneni, Christian Tutschku

Published Oct 15, 2025• 0 citations
Publisher

Abstract

Feature selection is crucial for enhancing the accuracy and efficiency of machine learning models. This work investigates the possibility of the usefulness of a quantum annealer to tackle the challenge of selecting features based on maximizing mutual information (MI) and conditional mutual information (CMI). Calculating the optimal feature set for maximum MI and CMI remains computationally intractable for large datasets on classical computers, even with approximation methods. This study employs a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) formulation, enabling its solution on a quantum annealer. Importantly, the study demonstrates the relevancy of this approach in identifying the best feature combinations that maximizes the MI and CMI. To showcase its real-world applicability, we apply MIQUBO to forecasting the price of used excavators. Our results demonstrate that using the MIQUBO approach there is an improvement in the prediction of machine learning models for datasets, with a smaller MI concentration on a subset of all features. • Problem Addressed: We tackle the computationally difficult problem of feature selection for machine learning models, specifically by maximizing mutual information (MI) and conditional mutual information (CMI) between features and the target variable. • Proposed Solution: We employ the adiabatic quantum computation paradigm to tackle this problem. The study utilizes a hybrid annealing approach, specifically the D-Wave Kerberos framework, which combines classical and quantum algorithms to solve the complex optimization problem. The feature selection task is reformulated as a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) problem, which can be solved on a quantum annealer. • Real-World Application: The MIQUBO method is applied to a practical, real-world scenario: forecasting the prices of used excavators. • Key Findings: The research demonstrates that using the MIQUBO approach leads to an improvement in the prediction performance of machine learning models. This is particularly true for datasets where the mutual information is less concentrated on a small subset of features.

DOI
10.1016/j.neucom.2025.131673

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Feature selection is crucial for enhancing the accuracy and efficiency of machine learning models. This work investigates the possibility of the usefulness of a quantum annealer to tackle the challenge of selecting features based on maximizing mutual information (MI) and conditional mutual information (CMI). Calculating the optimal feature set for maximum MI and CMI remains computationally intractable for large datasets on classical computers, even with approximation methods. This study employs a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) formulation, enabling its solution on a quantum annealer. Importantly, the study demonstrates the relevancy of this approach in identifying the best feature combinations that maximizes the MI and CMI. To showcase its real-world applicability, we apply MIQUBO to forecasting the price of used excavators. Our results demonstrate that using the MIQUBO approach there is an improvement in the prediction of machine learning models for datasets, with a smaller MI concentration on a subset of all features. • Problem Addressed: We tackle the computationally difficult problem of feature selection for machine learning models, specifically by maximizing mutual information (MI) and conditional mutual information (CMI) between features and the target variable. • Proposed Solution: We employ the adiabatic quantum computation paradigm to tackle this problem. The study utilizes a hybrid annealing approach, specifically the D-Wave Kerberos framework, which combines classical and quantum algorithms to solve the complex optimization problem. The feature selection task is reformulated as a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) problem, which can be solved on a quantum annealer. • Real-World Application: The MIQUBO method is applied to a practical, real-world scenario: forecasting the prices of used excavators. • Key Findings: The research demonstrates that using the MIQUBO approach leads to an improvement in the prediction performance of machine learning models. This is particularly true for datasets where the mutual information is less concentrated on a small subset of features.
Feature selection is crucial for enhancing the accuracy and efficiency of machine learning models.Calculating the optimal feature set for maximum mutual information (MI) and conditional mutual information (CMI) remains computationally intractable for large datasets on classical computers, even with approximation methods.This study employs a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) formulation, enabling its solution on a quantum annealer.To showcase its real-world applicability, we apply MIQUBO to forecasting the price of used excavators.Our results indicate that using the MIQUBO approach there might be an improvement in the prediction of machine learning models for datasets, with a smaller MI concentration.
Feature selection is crucial for enhancing the accuracy and efficiency of machine learning (ML) models. This work investigates the utility of quantum annealing for the feature selection process in an ML-pipeline, used for maximizing the mutual information (MI) or conditional mutual information (CMI) of the underlying feature space. Calculating the optimal set of features that maximize the MI or CMI is computationally intractable for large datasets on classical computers, even with approximative methods. This study employs a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) formulation, enabling its solution on a quantum annealer. We demonstrate the capability of this approach to identify the best feature combinations that maximize the MI or CMI. To showcase its real-world applicability, we solve the MIQUBO problem to forecast the prices of used excavators. Our results demonstrate that for datasets with a small MI concentration the MIQUBO approach can provide a significant improvement over MI-only based approaches, dependent on the dimension of the selected feature space.
Feature selection plays an important role in improving the efficiency of machine learning models for credit card fraud and default detection. We formulate the feature selection problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which we solve using quantum annealers. We propose three new formulations based on this framework that improve the efficiency and flexibility of machine learning models. We benchmark the proposed methods, existing approaches from the literature, and also compare with classical feature-selection methods such as Random Forest feature importance and a combination of mutual information and Spearman correlation. Extensive experiments show that feature selection using quantum computers consistently performs better than the classical methods. Our experiments show the promise of using quantum computers in machine learning tasks in financial risk assessment applications.
Feature selection, the task of identifying the most informative subset of attributes from a large feature pool, is an NP-hard problem central to Information Retrieval (IR) and Recommender Systems (RS). This paper presents Team SYZYGY’s submission to Task 1 of the QuantumCLEF 2026 Lab, formulating feature selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem solved on a D-Wave quantum annealer. For Task 1A (IR), we introduce five information-theoretic QUBO formulations that organically balance feature relevance and redundancy without hard cardinality constraints, combining mutual information, conditional mutual information, interaction information, and two normalized weighted mutual information variants. On the MQ2007 benchmark, our best configurations reduce the feature count from 46 to just 21 to 24 while surpassing both the full feature and recursive feature elimination baselines. For Task 1B (RS), a simplified collaborative driven QUBO aligns content based similarity with real user behavior, with the simulated annealer successfully improving over the full feature baseline while the physical quantum annealer is hampered by embedding complications. Across both tasks, quantum hardware completes sampling an order of magnitude faster than simulated annealing, though run to run inconsistencies on the physical QPU remain a key open challenge.
Hyperspectral images (HSIs) showing objects belonging to several distinct target classes are characterized by dozens of spectral bands being available. However, some of these spectral bands are redundant and/or noisy, and hence, selecting highly informative and trustworthy bands for each class is a vital step for classification and for saving internal storage space; then the selected bands are termed a highly informative spectral band subset. We use a mutual information (MI)-based method to select the spectral band subset of a given class and two additional binary quantum classifiers, namely a quantum boost (Qboost) and a quantum boost plus (Qboost-Plus) classifier, to classify a two-label dataset characterized by the selected band subset. We pose both our MI-based band subset selection problem and the binary quantum classifiers as a quadratic unconstrained binary optimization (QUBO) problem. Such a quadratic problem is solvable with the help of conventional optimization techniques. However, the QUBO problem is an NP-hard global optimization problem, and hence, it is worthwhile for applying a quantum annealer. Thus, we adapted our MI-based optimization problem for selecting highly informative bands for each class of a given HSI to be run on a D-Wave quantum annealer. After the selection of these highly informative bands for each class, we employ our binary quantum classifiers to a two-label dataset on the D-Wave quantum annealer. In addition, we provide a novel multilabel classifier exploiting an error-encoding output code when using our binary quantum classifiers. As a real-world dataset in Earth observation, we used the well-known AVIRIS HSI of Indian Pine, north-western Indiana, USA. We can demonstrate that the MI-based band subset selection problem can be run on a D-Wave quantum annealer that selects the highly informative spectral band subset for each target class in the Indian Pine HSI. We can also prove that our binary quantum classifiers and our novel multilabel classifier generate a correct two- and multilabel dataset characterized by their selected bands and with high accuracy such as having been produced by conventional classifiers-and even better in some instances.
Using Quantum Computers to solve problems in Recommender Systems that classical computers cannot address is a worthwhile research topic. In this paper, we use Quantum Annealers to address the feature selection problem in recommendation algorithms. This feature selection problem is a Quadratic Unconstrained Binary Optimization(QUBO) problem. By incorporating Counterfactual Analysis, we significantly improve the performance of the item-based KNN recommendation algorithm compared to using pure Mutual Information. Extensive experiments have demonstrated that the use of Counterfactual Analysis holds great promise for addressing such problems.