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International Journal of Information Technology

Predicting vehicle prices via quantum-assisted feature selection

David Von Dollen, Florian Neukart, Daniel Weimer, Thomas Bäck

Published Jul 21, 2023• 10 citations
Publisher

Abstract

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 $$(1471.02 \pm {135.6})$$ ( 1471.02 ± 135.6 ) vs. similar methodologies such as greedy selection $$(1707.2 \pm {168})$$ ( 1707.2 ± 168 ) , recursive feature elimination $$(1678.3 \pm {143.7})$$ ( 1678.3 ± 143.7 ) , and all features $$(1546.2 \pm {154}$$ ( 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.

DOI
10.1007/s41870-023-01370-z

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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.
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 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 (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.
Support vector machines are powerful and frequently used machine learning methods for classification and regression tasks, which rely on the construction of kernel matrices. While crucial for the performance of this machine learning approach, choosing the most suitable kernel is highly problem-dependent. The emergence of quantum computers and quantum machine learning techniques provides new possibilities for generating powerful quantum kernels. Within this work, we solve a real-world price forecasting problem using fidelity and projected quantum kernels, which are promising candidates for the utility of near-term quantum computing. In our analysis, we examine and validate the most auspicious quantum kernels from literature and compare their performance with an optimized classical kernel. Unlike previous work on quantum support vector machines, our dataset includes categorical features that need to be encoded as numerical features, which we realize by using the one-hot-encoding scheme. One-hot-encoding, however, increases the dimensionality of the dataset significantly, which collides with the current limitations of noisy intermediate scale quantum computers. To overcome these limitations, we use autoencoders to learn a low-dimensional representation of the feature space that still maintains the most important information of the original data. To examine the impact of autoencoding, we compare the results of the encoded date with the results of the original, unencoded dataset. We could demonstrate that quantum kernels are comparable to or even better than the classical support vector machine kernels regarding the mean absolute percentage error scores for both encoded and unencoded datasets.
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.
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.