Search for: All records

This paper studies a tensor factor model that augments samples from multiple classes. The nuisance common patterns shared across classes are characterised by pervasive noises, and the patterns that distinguish different classes are represented by class‐specific components. Additionally, the pervasive component is modelled by the production of a low‐rank tensor latent factor and several factor loading matrices. This augmented tensor factor model can be expanded to a series of matrix variate tensor factor models and estimated using principal component analysis. The ranks of latent factors are estimated using a modified eigen‐ratio method. The proposed estimators have fast convergence rates and enjoy the blessing of dimensionality. The proposed factor model is applied to address the challenge of overlapping issues in image classification through a factor adjustment procedure. The procedure is shown to be powerful through synthetic experiments and an application to COVID‐19 pneumonia diagnosis from frontal chest X‐ray images.

 

In this article, we introduce an innovative hybrid quantum search algorithm, the Robust Non-oracle Quantum Search (RNQS), which is specifically designed to efficiently identify the minimum value within a large set of random numbers. Distinct from the Grover’s algorithm, the proposed RNQS algorithm circumvents the need for an oracle function that describes the true solution state, a feature often impractical for data science applications. Building on existing non-oracular quantum search algorithms, RNQS enhances robustness while substantially reducing running time. The superior properties of RNQS have been demonstrated through careful analysis and extensive empirical experiments. Our findings underscore the potential of the RNQS algorithm as an effective and efficient solution to combinatorial optimization problems in the realm of quantum computing.

 

This paper studies linear regression models for high dimensional multi-response data with a hybrid quantum computing algorithm. We propose an intuitively appealing estimation method based on identifying the linearly independent columns in the coefficient matrix. Our method relaxes the low rank constraint in the existing literature and allows the rank to diverge with dimensions. The linearly independent columns are selected by a novel non-oracular quantum search (NQS) algorithm which is significantly faster than classical search methods implemented on electronic computers. Besides, NQS achieves a near optimal computational complexity as existing quantum search algorithms but does not require any oracle information of the solution state. We prove the proposed estimation procedure enjoys desirable theoretical properties. Intensive numerical experiments are also conducted to demonstrate the finite sample performance of the proposed method, and a comparison is made with some popular competitors. The results show that our method outperforms all of the alternative methods under various circumstances.