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Jiang Hu

Publications and source records attributed to Jiang Hu.

At least 73 records · Page 4Linked to original sources
arXiv2024

Revised BDS Test

In this paper, we focus on the BDS test, which is a nonparametric test of independence. Specifically, the null hypothesis $H_{0}$ of it is that $\{u_{t}\}$ is i.i.d. (independent and identically distributed), where $\{u_{t}\}$ is a random sequence. The BDS test is widely used in economics and finance, but it has a weakness that cannot be ignored: over-rejecting $H_{0}$ even if the length $T$ of $\{u_{t}\}$ is as large as $(100,2000)$. To improve the over-rejection problem of BDS test, considering that the correlation integral is the foundation of BDS test, we not only accurately describe the expectation of the correlation integral under $H_{0}$, but also calculate all terms of the asymptotic variance of the correlation integral whose order is $O(T^{-1})$ and $O(T^{-2})$, which is essential to improve the finite sample performance of BDS test. Based on this, we propose a revised BDS (RBDS) test and prove its asymptotic normality under $H_{0}$. The RBDS test not only inherits all the advantages of the BDS test, but also effectively corrects the over-rejection problem of the BDS test, which can be fully confirmed by the simulation results we presented. Moreover, based on the simulation results, we find that similar to BDS test, RBDS test would also be affected by the parameter estimations of the ARCH-type model, resulting in size distortion, but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the model. Besides, through some actual datasets that have been demonstrated to fit well with ARCH-type models, we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem, and the results reflect that, under the same condition, the performance of the RBDS test is more encouraging.

math.ST↗
arXiv2023

Decentralized Douglas-Rachford splitting methods for smooth optimization over compact submanifolds

We study decentralized smooth optimization problems over compact submanifolds. Recasting it as a composite optimization problem, we propose a decentralized Douglas-Rachford splitting algorithm, DDRS. When the proximal operator of the local loss function does not have a closed-form solution, an inexact version of DDRS, iDDRS, is also presented. Both algorithms rely on an ingenious integration of the nonconvex Douglas-Rachford splitting algorithm with gradient tracking and manifold optimization. We show that our DDRS and iDDRS achieve the best-known convergence rate of $\mathcal{O}(1/K)$. The main challenge in the proof is how to handle the nonconvexity of the manifold constraint. To address this issue, we utilize the concept of proximal smoothness for compact submanifolds. This ensures that the projection onto the submanifold exhibits convexity-like properties, which allows us to control the consensus error across agents. Numerical experiments on the principal component analysis are conducted to demonstrate the effectiveness of our decentralized DRS compared with the state-of-the-art ones.

math.OC↗
arXiv2023

Riemannian Smoothing Gradient Type Algorithms]{Riemannian Smoothing Gradient Type Algorithms for Nonsmooth Optimization Problem on Compact Riemannian Submanifold Embedded in Euclidean Space

In this paper, we introduce the notion of generalized $ε$-stationarity for a class of nonconvex and nonsmooth composite minimization problems on compact Riemannian submanifold embedded in Euclidean space. To find a generalized $ε$-stationarity point, we develop a family of Riemannian gradient-type methods based on the Moreau envelope technique with a decreasing sequence of smoothing parameters, namely Riemannian smoothing gradient and Riemannian smoothing stochastic gradient methods. We prove that the Riemannian smoothing gradient method has the iteration complexity of $\mathcal{O}(ε^{-3})$ for driving a generalized $ε$-stationary point. To our knowledge, this is the best-known iteration complexity result for the nonconvex and nonsmooth composite problem on manifolds. For the Riemannian smoothing stochastic gradient method, one can achieve the iteration complexity of $\mathcal{O}(ε^{-5})$ for driving a generalized $ε$-stationary point. Numerical experiments are conducted to validate the superiority of our algorithms.

math.OC↗
arXiv2023

Distributed estimation of spiked eigenvalues in spiked population models

The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the analysis of such massive data sets due to prohibitively long computing durations, memory constraints, communication overheads, and confidentiality considerations. In this paper, we propose distributed estimators of the spiked eigenvalues in spiked population models. The consistency and asymptotic normality of the distributed estimators are derived, and the statistical error analysis of the distributed estimators is provided as well. Compared to the estimation from the full sample, the proposed distributed estimation shares the same order of convergence. Simulation study and real data analysis indicate that the proposed distributed estimation and testing procedures have excellent properties in terms of estimation accuracy and stability as well as transmission efficiency.

math.ST↗
arXiv2023

Decentralized projected Riemannian gradient method for smooth optimization on compact submanifolds

We consider the problem of decentralized nonconvex optimization over a compact submanifold, where each local agent's objective function defined by the local dataset is smooth. Leveraging the powerful tool of proximal smoothness, we establish local linear convergence of the projected gradient descent method with a unit step size for solving the consensus problem over the nonconvex compact submanifold. This serves as the basis for designing and analyzing decentralized algorithms on manifolds. Subsequently, we propose two decentralized methods: the decentralized projected Riemannian gradient descent (DPRGD) and the decentralized projected Riemannian gradient tracking (DPRGT). We establish their convergence rates of $\mathcal{O}(1/\sqrt{K})$ and $\mathcal{O}(1/K)$, respectively, to reach a stationary point. To the best of our knowledge, DPRGT is the first decentralized algorithm to achieve exact convergence for solving decentralized optimization over a compact submanifold. Beyond the linear convergence results on the consensus, two key tools developed in the proof are the Lipschitz-type inequality of the projection operator and the Riemannian quadratic upper bound for smooth functions on the compact submanifold, which could be of independent interest. Finally, we demonstrate the effectiveness of our proposed methods compared to state-of-the-art ones through numerical experiments on eigenvalue problems and low-rank matrix completion.

math.OC↗
arXiv2023

MA-SAM: Modality-agnostic SAM Adaptation for 3D Medical Image Segmentation

The Segment Anything Model (SAM), a foundation model for general image segmentation, has demonstrated impressive zero-shot performance across numerous natural image segmentation tasks. However, SAM's performance significantly declines when applied to medical images, primarily due to the substantial disparity between natural and medical image domains. To effectively adapt SAM to medical images, it is important to incorporate critical third-dimensional information, i.e., volumetric or temporal knowledge, during fine-tuning. Simultaneously, we aim to harness SAM's pre-trained weights within its original 2D backbone to the fullest extent. In this paper, we introduce a modality-agnostic SAM adaptation framework, named as MA-SAM, that is applicable to various volumetric and video medical data. Our method roots in the parameter-efficient fine-tuning strategy to update only a small portion of weight increments while preserving the majority of SAM's pre-trained weights. By injecting a series of 3D adapters into the transformer blocks of the image encoder, our method enables the pre-trained 2D backbone to extract third-dimensional information from input data. The effectiveness of our method has been comprehensively evaluated on four medical image segmentation tasks, by using 10 public datasets across CT, MRI, and surgical video data. Remarkably, without using any prompt, our method consistently outperforms various state-of-the-art 3D approaches, surpassing nnU-Net by 0.9%, 2.6%, and 9.9% in Dice for CT multi-organ segmentation, MRI prostate segmentation, and surgical scene segmentation respectively. Our model also demonstrates strong generalization, and excels in challenging tumor segmentation when prompts are used. Our code is available at: https://github.com/cchen-cc/MA-SAM.

cs.CV↗
arXiv2023

Composite federated learning with heterogeneous data

We propose a novel algorithm for solving the composite Federated Learning (FL) problem. This algorithm manages non-smooth regularization by strategically decoupling the proximal operator and communication, and addresses client drift without any assumptions about data similarity. Moreover, each worker uses local updates to reduce the communication frequency with the server and transmits only a $d$-dimensional vector per communication round. We prove that our algorithm converges linearly to a neighborhood of the optimal solution and demonstrate the superiority of our algorithm over state-of-the-art methods in numerical experiments.

cs.LG↗
arXiv2023

Radiology-Llama2: Best-in-Class Large Language Model for Radiology

This paper introduces Radiology-Llama2, a large language model specialized for radiology through a process known as instruction tuning. Radiology-Llama2 is based on the Llama2 architecture and further trained on a large dataset of radiology reports to generate coherent and clinically useful impressions from radiological findings. Quantitative evaluations using ROUGE metrics on the MIMIC-CXR and OpenI datasets demonstrate that Radiology-Llama2 achieves state-of-the-art performance compared to other generative language models, with a Rouge-1 score of 0.4834 on MIMIC-CXR and 0.4185 on OpenI. Additional assessments by radiology experts highlight the model's strengths in understandability, coherence, relevance, conciseness, and clinical utility. The work illustrates the potential of localized language models designed and tuned for specialized domains like radiology. When properly evaluated and deployed, such models can transform fields like radiology by automating rote tasks and enhancing human expertise.

cs.CL↗
arXiv2023

Exact Separation of Eigenvalues of Large Dimensional Noncentral Sample Covariance Matrices

Let $ \bbB_n =\frac{1}{n}(\bbR_n + \bbT^{1/2}_n \bbX_n)(\bbR_n + \bbT^{1/2}_n \bbX_n)^* $ where $ \bbX_n $ is a $ p \times n $ matrix with independent standardized random variables, $ \bbR_n $ is a $ p \times n $ non-random matrix, representing the information, and $ \bbT_{n} $ is a $ p \times p $ non-random nonnegative definite Hermitian matrix. Under some conditions on $ \bbR_n \bbR_n^* $ and $ \bbT_n $, it has been proved that for any closed interval outside the support of the limit spectral distribution, with probability one there will be no eigenvalues falling in this interval for all $ p $ sufficiently large. The purpose of this paper is to carry on with the study of the support of the limit spectral distribution, and we show that there is an exact separation phenomenon: with probability one, the proper number of eigenvalues lie on either side of these intervals.

math.PR↗
arXiv2023

A CLT for the LSS of large dimensional sample covariance matrices with diverging spikes

In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSSs) of a large-dimensional sample covariance matrix when the population covariance matrices are involved with diverging spikes. This constitutes a nontrivial extension of the Bai-Silverstein theorem (BST) (Ann Probab 32(1):553--605, 2004), a theorem that has strongly influenced the development of high-dimensional statistics, especially in the applications of random matrix theory to statistics. Recently, there has been a growing realization that the assumption of uniform boundedness of the population covariance matrices in the BST is not satisfied in some fields, such as economics, where the variances of principal components may diverge as the dimension tends to infinity. Therefore, in this paper, we aim to eliminate this obstacle to applications of the BST. Our new CLT accommodates spiked eigenvalues, which may either be bounded or tend to infinity. A distinguishing feature of our result is that the variance in the new CLT is related to both spiked eigenvalues and bulk eigenvalues, with dominance being determined by the divergence rate of the largest spiked eigenvalues. The new CLT for LSS is then applied to test the hypothesis that the population covariance matrix is the identity matrix or a generalized spiked model. The asymptotic distributions of the corrected likelihood ratio test statistic and the corrected Nagao's trace test statistic are derived under the alternative hypothesis. Moreover, we present power comparisons between these two LSSs and Roy's largest root test. In particular, we demonstrate that except for the case in which the number of spikes is equal to one, the LSSs could exhibit higher asymptotic power than Roy's largest root test.

math.ST↗
arXiv2023

On the local convergence of the semismooth Newton method for composite optimization

In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establishing superlinear convergence rates of semismooth Newton-type methods for solving nonlinear equations usually postulate either nonsingularity of the B-Jacobian or smoothness of the equation. We investigate the feasibility of both conditions. For the nonsingularity condition, we present equivalent characterizations in broad generality, and illustrate that they are easy-to-check criteria for some examples. For the smoothness condition, we show that it holds locally for a large class of residual mappings derived from composite optimization problems. Furthermore, we investigate a relaxed version of the smoothness condition - smoothness restricted to certain active manifolds. We present a conceptual algorithm utilizing such structures and prove that it has a superlinear convergence rate.

math.OC↗
arXiv2023

Securing Cloud FPGAs Against Power Side-Channel Attacks: A Case Study on Iterative AES

The various benefits of multi-tenanting, such as higher device utilization and increased profit margin, intrigue the cloud field-programmable gate array (FPGA) servers to include multi-tenanting in their infrastructure. However, this property makes these servers vulnerable to power side-channel (PSC) attacks. Logic designs such as ring oscillator (RO) and time-to-digital converter (TDC) are used to measure the power consumed by security critical circuits, such as advanced encryption standard (AES). Firstly, the existing works require higher minimum traces for disclosure (MTD). Hence, in this work, we improve the sensitivity of the TDC-based sensors by manually placing the FPGA primitives inferring these sensors. This enhancement helps to determine the 128-bit AES key using 3.8K traces. Secondly, the existing defenses use ROs to defend against PSC attacks. However, cloud servers such as Amazon Web Services (AWS) block design with combinatorial loops. Hence, we propose a placement-based defense. We study the impact of (i) primitive-level placement on the AES design and (ii) additional logic that resides along with the AES on the correlation power analysis (CPA) attack results. Our results showcase that the AES along with filters and/or processors are sufficient to provide the same level or better security than the existing defenses.

cs.CR↗
arXiv2023

Analysis of the limiting spectral distribution of large dimensional General information-plus-noise type matrices

In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the "general information-plus-noise" type, as studied in [14]. Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in [14] to allow for all possible ratios of row to column of the underlying random matrix.

math.ST↗
arXiv2023

Achieving Consensus over Compact Submanifolds

We consider the consensus problem in a decentralized network, focusing on a compact submanifold that acts as a nonconvex constraint set. By leveraging the proximal smoothness of the compact submanifold, which encompasses the local singleton property and the local Lipschitz continuity of the projection operator on the manifold, and establishing the connection between the projection operator and general retraction, we show that the Riemannian gradient descent with a unit step size has locally linear convergence if the network has a satisfactory level of connectivity. Moreover, based on the geometry of the compact submanifold, we prove that a convexity-like regularity condition, referred to as the restricted secant inequality, always holds in an explicitly characterized neighborhood around the solution set of the nonconvex consensus problem. By leveraging this restricted secant inequality and imposing a weaker connectivity requirement on the decentralized network, we present a comprehensive analysis of the linear convergence of the Riemannian gradient descent, taking into consideration appropriate initialization and step size. Furthermore, if the network is well connected, we demonstrate that the local Lipschitz continuity endowed by proximal smoothness is a sufficient condition for the restricted secant inequality, thus contributing to the local error bound. We believe that our established results will find more application in the consensus problems over a more general proximally smooth set. Numerical experiments are conducted to validate our theoretical findings.

math.OC↗
arXiv2023

KOO approach for scalable variable selection problem in large-dimensional regression

An important issue in many multivariate regression problems is to eliminate candidate predictors with null predictor vectors. In large-dimensional (LD) setting where the numbers of responses and predictors are large, model selection encounters the scalability challenge. Knock-one-out (KOO) statistics hold promise to meet this challenge. In this paper, the almost sure limits and the central limit theorem of the KOO statistics are derived under the LD setting and mild distributional assumptions (finite fourth moments) of the errors. These theoretical results guarantee the strong consistency of a subset selection rule based on the KOO statistics with a general threshold. For enhancing the robustness of the selection rule, we also propose a bootstrap threshold for the KOO approach. Simulation results support our conclusions and demonstrate the selection probabilities by the KOO approach with the bootstrap threshold outperform the methods using Akaike information threshold, Bayesian information threshold and Mallow's C$_p$ threshold. We compare the proposed KOO approach with those based on information threshold to a chemometrics dataset and a yeast cell-cycle dataset, which suggests our proposed method identifies useful models.

math.ST↗
arXiv2023

Two-sample test of sparse stochastic block models

The paper discusses a statistical problem related to testing for differences between two sparse networks with community structures. The community-wise edge probability matrices have entries of order $O(n^{-1}/\log n)$, where $n$ represents the size of the network. The authors propose a test statistic that combines a method proposed by Wu et al. \cite{WuTwoSampleSBM2022} and a resampling process. They derive the asymptotic null distribution of the test statistic and provide a guarantee of asymptotic power against the alternative hypothesis. To evaluate the performance of the proposed test statistic, the authors conduct simulations and provide real data examples. The results indicate that the proposed test statistic performs well in practice.

stat.AP↗
arXiv2023

Decentralized Weakly Convex Optimization Over the Stiefel Manifold

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly convex in the ambient Euclidean space. Such optimization problems, albeit frequently encountered in applications, are quite challenging due to their non-smoothness and non-convexity. To tackle them, we propose an iterative method called the decentralized Riemannian subgradient method (DRSM). The global convergence and an iteration complexity of $\mathcal{O}(\varepsilon^{-2} \log^2(\varepsilon^{-1}))$ for forcing a natural stationarity measure below $\varepsilon$ are established via the powerful tool of proximal smoothness from variational analysis, which could be of independent interest. Besides, we show the local linear convergence of the DRSM using geometrically diminishing stepsizes when the problem at hand further possesses a sharpness property. Numerical experiments are conducted to corroborate our theoretical findings.

math.OC↗
arXiv2023

Machine Learning for Microprocessor Performance Bug Localization

The validation process for microprocessors is a very complex task that consumes substantial engineering time during the design process. Bugs that degrade overall system performance, without affecting its functional correctness, are particularly difficult to debug given the lack of a golden reference for bug-free performance. This work introduces two automated performance bug localization methodologies based on machine learning that aims to aid the debugging process. Our results show that, the evaluated microprocessor core performance bugs whose average IPC impact is greater than 1%, our best-performing technique is able to localize the exact microarchitectural unit of the bug $\sim$77\% of the time, while achieving a top-3 unit accuracy (out of 11 possible locations) of over 90% for bugs with the same average IPC impact. The proposed system in our simulation setup requires only a few seconds to perform a bug location inference, which leads to a reduced debugging time.

cs.AR↗