[Paper Review] Efficient Quantum One-Class Support Vector Machines for Anomaly Detection Using Randomized Measurements and Variable Subsampling

Michael Kölle, Afrae Ahouzi+5 more|arXiv (Cornell University)|Jul 30, 2024

Spectroscopy Techniques in Biomedical and Chemical ResearchBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This paper proposes a hybrid quantum-classical approach combining variable subsampling, randomized measurements, and rotated feature bagging to enable efficient quantum one-class SVMs for anomaly detection. By integrating these techniques, the method achieves linear time complexity in both data size and feature count while significantly improving average precision and training/testing speed, despite high variance due to randomized measurements.

ABSTRACT

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large datasets. In recent work, quantum randomized measurements kernels and variable subsampling were proposed, as two independent methods to address this problem. The former achieves higher average precision, but suffers from variance, while the latter achieves linear complexity to data size and has lower variance. The current work focuses instead on combining these two methods, along with rotated feature bagging, to achieve linear time complexity both to data size and to number of features. Despite their instability, the resulting models exhibit considerably higher performance and faster training and testing times.

Motivation & Objective

• To address the scalability limitations of quantum one-class SVMs due to quadratic time complexity with data size and exponential dependence on qubits.
• To improve performance and efficiency by combining variable subsampling with quantum randomized measurements kernels.
• To reduce exponential time complexity in qubits by introducing rotated feature bagging in variable subsampling ensembles.
• To achieve faster training and inference times while maintaining high average precision in anomaly detection.
• To explore the trade-offs between performance, stability, and computational efficiency in quantum kernel-based anomaly detection.

Proposed method

• The method employs variable subsampling to train multiple quantum OC-SVMs on reduced feature subsets, reducing time complexity to linear in data size.
• Randomized measurements are used to compute quantum kernel matrices efficiently, enabling high average precision but introducing high variance.
• Rotated feature bagging transforms input features via random rotations before subsampling, reducing the effective dimensionality and mitigating exponential qubit dependence.
• Ensemble predictions are aggregated using a maximum combination function across subsampled models to improve robustness and performance.
• The approach combines quantum Inversion Test kernels and randomized measurements within a variable subsampling framework to balance speed and accuracy.
• The method uses a modified feature map that applies random rotations to input features, allowing efficient application of randomized measurements in high-dimensional settings.

Experimental results

Research questions

• RQ1 Can Variable Subsampling Quantum OC-SVM ensembles benefit from the utilization of Randomized Kernel Measurements, and is there a performance trade-off?
• RQ2 Can the use of Rotated Feature Bagging on these Variable Subsampling ensembles assist in reducing the exponential time complexity with respect to the number of qubits/features?
• RQ3 Does combining variable subsampling with randomized measurements and rotated feature bagging lead to improved time complexity and performance over individual methods?
• RQ4 How does the variance of the resulting models compare to classical or quantum baselines, and can it be mitigated?
• RQ5 What is the impact of ensemble size and maximum subsample size on model stability and performance?

Key findings

• The proposed method, variable subsampling with rotated feature bagging and randomized measurements (VS-RFB-RM), achieves linear time complexity in both data size and number of features/qubits.
• Despite high variance, the VS-RFB-RM method achieves the highest average precision among all tested quantum methods on the Credit Card dataset.
• Training and testing times are drastically reduced compared to unmitigated randomized measurements, which exhibit exponential time complexity in qubits.
• The method with rotated feature bagging successfully mitigates the exponential time dependence of randomized measurements, enabling use on high-dimensional data.
• The performance improvement from combining randomized measurements with variable subsampling is surprising, as it increases average precision while also accelerating training and inference.
• The high variance is attributed to the randomized measurements kernel, the maximum score combination function, and potentially insufficient ensemble size and subsample limits.