Quantum Feature Selection with Variance Estimation

The promise of quantum computation to achieve a speedup over classical computation led to a surge of interest in exploring new quantum algorithms for data analysis problems. Feature Selection, a technique that selects the most relevant features from a dataset, is a critical step in data analysis. With several Quantum Feature Selection techniques proposed in the literature, this study exhibits the potential of quantum algorithms to enhance Feature Selection and other tasks that leverage the variance. This study proposes a novel quantum algorithm for estimating the variance over a set of real data. Importantly, after state preparation, the algorithm's complexity exhibits logarithmic characteristics in both its width and depth. The quantum algorithm applies to the Feature Selection problem by designing a Hybrid Quantum Feature Selection (HQFS) algorithm. This work showcases an implementation of HQFS and assesses it on two synthetic datasets and a real dataset.