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International Conference on Agents and Artificial Intelligence (ICAART)

Evaluating Quantum Support Vector Regression Methods for Price Forecasting Applications

Horst Stühler, Daniel Pranjić, Christian Tutschku

Published Jan 1, 2024• 5 citations
Publisher

Abstract

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.

DOI
10.5220/0012351400003636

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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.
High-Frequency Financial Forecasting is important in algorithmic trading as it helps make decisions based on high-frequency data in milliseconds. This challenge has been found to be unsolvable using conventional machine learning approaches, such as classical Support Vector Machines (SVMs), Random Forest (RF), and deep learning models, which were not able to capture the nonlinear and high-dimensional patterns embedded in the high-frequency datasets, leading to poor prediction performance. This paper proposes a Supervised Quantum Support Vector Machine (QSVM) model, which is tailored for the high-frequency financial forecasting task. The QSVM can effectively encode the market information and enhance the predictability while maintaining the computational efficiency through quantum feature mapping and high-dimensional Hilbert space. This process includes encoding of tick-level market microstructure data, stock and futures prices, and technical indicators into quantum states and subsequent training using a quantum-classical hybrid optimization loop. Classical SVM, Random Forest, LSTM, and hybrid QML are used as the benchmarks for the proposed QSVM using forecasting accuracy, RMSE, MAPE, computational latency, and Sharpe ratio. The results obtained from the experiment show that the QSVM has better accuracy (91.2%), RMSE (0.018), and latency (22 ms) as well. Hence, the QSVM shows better performance when compared to other methods and is capable of modeling the markets that have a fast change in dynamics. High-dimensional quantum kernel plays a part in enhancing the ability to separate non-linearities. Therefore, the QSVM could be a potential solution to apply in algorithmic trading. The limitations are hardware constraints of NISQ and restrictions on the size of the dataset. Future directions of research will include the scalability of the model and the use of ensemble approaches.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
This article analyzes the issue of accurately predicting the price and sales volume of retail products based on classical and quantum approaches. The classical Support Vector Regression (SVR) model was evaluated in comparison with the Quantum Support Vector Regression (QSVR) model based on quantum computing. Latent representations of the data were obtained through dimensionality reduction using an autoencoder and utilized for forecasting. The experimental results demonstrated that the QSVR model outperforms the classical SVR model in terms of MAE, MSE, and R2 indicators. The study effectively employed quantum kernel functions, data re-uploading feature maps, and the COBYLA optimization algorithm. The findings confirm the practical potential of quantum machine learning methods.
Abstract Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights. Benchmarking these methods is crucial to gain robust insights and to understand their practical utility. In this work, we present a comprehensive large-scale study examining QKMs based on fidelity quantum kernels (FQKs) and projected quantum kernels (PQKs) across a manifold of design choices. Our investigation encompasses both classification and regression tasks for five dataset families and 64 datasets, systematically comparing the use of FQKs and PQKs quantum support vector machines and kernel ridge regression. This resulted in over 20,000 models that were trained and optimized using a state-of-the-art hyperparameter search to ensure robust and comprehensive insights. We delve into the importance of hyperparameters on model performance scores and support our findings through rigorous correlation analyses. Additionally, we provide an in-depth analysis addressing the design freedom of PQKs and explore the underlying principles responsible for learning. Our goal is not to identify the best-performing model for a specific task but to uncover the mechanisms that lead to effective QKMs and reveal universal patterns.
This paper introduces a generalized quantum-classical dual kernel learning method for Support Vector Machines (SVMs), extending its application to both classification and regression tasks. Our method combines quantum and classical kernels via an adaptively weighted linear combination, forming a dual kernel learning technique that outperforms models relying solely on either kernel type. In this paper, we demonstrate the effectiveness of our approach on several real-world datasets in terms of classification accuracy and for regression, highR2R^{2}R2-score and low Root Mean Square Error (RMSE). Furthermore, we evaluate the dual kernel model on both ideal and noisy quantum backends using the IBM Qiskit toolkit. Under ideal conditions, the dual kernel method consistently maintains superior performance compared to purely classical or quantum kernels. While the presence of noise may affect performance, the dual kernel still achieves results that are competitive with the best individual kernels, underscoring its robustness and practical viability in real-world applications.
Abstract Quantum machine learning is a rapidly growing field at the intersection of quantum computing and machine learning. In this work, we examine our quantum machine learning models, which are based on quantum support vector classification (QSVC) and quantum support vector regression (QSVR). We investigate these models using a quantum-circuit simulator, both with and without noise, as well as the IonQ Harmony quantum processor. For the QSVC tasks, we use a dataset containing fraudulent credit card transactions and image datasets (the MNIST and the Fashion-MNIST datasets); for the QSVR tasks, we use a financial dataset and a materials dataset. For the classification tasks, the performance of our QSVC models using 4 qubits of the trapped-ion quantum computer was comparable to that obtained from noiseless quantum-circuit simulations. The result is consistent with the analysis of our device-noise simulations with varying qubit-gate error rates. For the regression tasks, applying a low-rank approximation to the noisy quantum kernel, in combination with hyperparameter tuning in ε-SVR, improved the performance of the QSVR models on the near-term quantum device. Our results suggest that the quantum kernel, as described by our shallow quantum circuit, can be effectively used for both QSVC and QSVR tasks, indicating its resistance to noise and its adaptability to various datasets.