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ABSTRACT This paper studies the transfer learning problem for convolutional neural network models. A phase transition phenomenon has been empirically validated: The convolutional layer shifts from general to specific with respect to the target task as its depth increases. The paper suggests measuring the generality of convolutional layers through an easy‐to‐compute and tuning‐free statistic named projection correlation. The non‐asymptotic upper bounds for the estimation error of the proposed generality measure have been provided. Based on this generality measure, the paper proposes a forward‐adding‐layer‐selection algorithm to select general layers. The algorithm aims to find a cut‐off in the pre‐trained model according to where the phase transition from general to specific happens. Then, we propose to transfer only the general layers as specific layers can cause overfitting issues and hence hurt the prediction performance. The proposed algorithm is computationally efficient and can consistently estimate the true beginning of phase transition under mild conditions. Its superior empirical performance has been justified by various numerical experiments. 

The estimation of large precision matrices is crucial in modern multivariate analysis. Traditional sparsity assumptions, while useful, often fall short of accurately capturing the dependencies among features. This article addresses this limitation by focusing on precision matrix estimation for multivariate data characterized by a flexible yet unknown group structure. We introduce a novel approach that begins with the detection of this unknown group structure, clustering features within the low-dimensional space defined by the leading eigenvectors of the sample covariance matrix. Following this, we employ group-wise multivariate response linear regressions, guided by the identified group memberships, to estimate the precision matrix. We rigorously establish the theoretical foundations of our proposed method for both group detection and precision matrix estimation. The superior numerical performance of our approach is demonstrated through comprehensive simulation experiments and a comparative analysis with established methods in the field. Additionally, we apply our method to a real breast cancer dataset, showcasing its practical utility and effectiveness. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. 

This paper introduces a novel sampling technique based on the dynamics of a 2-state Quantum Walk (QW) in a one-dimensional space. By leveraging concepts from nonparametric statistics, specifically the kernel smoothing method, our approach addresses two key challenges in Quantum Walk sampling: discontinuities in sampling distributions and potential inaccuracies in limiting distributions. Our innovative method effectively mitigates these issues, leading to significant improvements in density estimation and sampling efficacy compared to traditional Quantum Walk distributions and sampling techniques. 

Abstract 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 study, we introduce BedDot, the first contact-free and bed-mounted continuous blood pressure monitoring sensor. Equipped with a seismic sensor, BedDot eliminates the need for external wearable devices and physical contact, while avoiding privacy or radiation concerns associated with other technologies such as cameras or radars. Using advanced preprocessing techniques and innovative AI algorithms, we extract time-series features from the collected bedseismogram signals and accurately estimate blood pressure with remarkable stability and robustness. Our user-friendly prototype has been tested with over 75 participants, demonstrating exceptional performance that meets all three major industry standards, which are the Association for the Advancement of Medical Instrumentation (AAMI) and Food and Drug Administration (FDA), and outperforms current state-of-the-art deep learning models for time series analysis. As a non-invasive solution for monitoring blood pressure during sleep and assessing cardiovascular health, BedDot holds immense potential for revolutionizing the field. 

Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there is certainly no shortage of FDR control strategies when selecting individual features, but the relevant works for structural change detection, such as profile analysis for piecewise constant coefficients and integration analysis with multiple data sources, are limited. In this paper, we propose a generalized knockoff procedure (GKnockoff) for FDR control under such problem settings. We prove that the GKnockoff possesses pairwise exchangeability, and is capable of controlling the exact FDR under finite sample sizes. We further explore GKnockoff under high dimensionality, by first introducing a new screening method to filter the high-dimensional potential structural changes. We adopt a data splitting technique to first reduce the dimensionality via screening and then conduct GKnockoff on the refined selection set. Furthermore, the powers of proposed methods are systematically studied. Numerical comparisons with other methods show the superior performance of GKnockoff, in terms of both FDR control and power. We also implement the proposed methods to analyze a macroeconomic dataset for detecting changes of driven effects of economic development on the secondary industry. 

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.