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作者:Chen, Ziyuan; Yang, Ying; Yao, Fang
作者单位:Peking University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要:Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special cases. In this article, we propose a general framework for dynamic matrix recovery of low-rank matrices that evolve smoothly over time. We start from the setting that the observations are independent across time, then extend to the setting that both the design...
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作者:Ye, Shengbin; Senftle, Thomas P.; Li, Meng
作者单位:Rice University; Rice University
摘要:In the emerging field of materials informatics, a fundamental task is to identify physicochemically meaningful descriptors, or materials genes, which are engineered from primary features and a set of elementary algebraic operators through compositions. Standard practice directly analyzes the high-dimensional candidate predictor space in a linear model; statistical analyses are then substantially hampered by the daunting challenge posed by the astronomically large number of correlated predictor...
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作者:Cao, Yang; Sun, Xinwei; Yao, Yuan
作者单位:Hong Kong University of Science & Technology; Fudan University
摘要:Multiple comparisons in hypothesis testing often encounter structural constraints in various applications. For instance, in structural Magnetic Resonance Imaging for Alzheimer's Disease, the focus extends beyond examining atrophic brain regions to include comparisons of anatomically adjacent regions. These constraints can be modeled as linear transformations of parameters, where the sign patterns play a crucial role in estimating directional effects. This class of problems, encompassing total ...
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作者:Cattaneo, Matias D.; Feng, Yingjie; Underwood, William G.
作者单位:Princeton University; Tsinghua University
摘要:Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of uniformly estimating a dyadic Lebesgue density function, focusing on nonparametric kernel-based estimators taking the form of dyadic empirical processes. Our main contributions include the minimax-optimal uniform convergence rate of the dyadic kernel density est...
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作者:Liu, Mochuan; Wang, Yuanjia; Fu, Haoda; Zeng, Donglin
作者单位:University of North Carolina; University of North Carolina Chapel Hill; Columbia University; Eli Lilly; University of Michigan System; University of Michigan
摘要:Dynamic treatment regimen (DTR) is one of the most important tools to tailor treatment in personalized medicine. For many diseases such as cancer and type 2 diabetes mellitus (T2D), more aggressive treatments can lead to a higher efficacy but may also increase risk. However, few methods for estimating DTRs can take into account both cumulative benefit and risk. In this work, we propose a general statistical learning framework to learn optimal DTRs that maximize the reward outcome while control...
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作者:Li, Tianxi; Le, Can M.
作者单位:University of Minnesota System; University of Minnesota Twin Cities; University of California System; University of California Davis
摘要:Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While many methods have been proposed to address this problem in recent years, they usually assume that the true model belongs to a known class, which is not verifiable in most real-world applications. Consequently, network modeling based on these methods either suf...
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作者:Gallagher, Ian; Jones, Andrew; Bertiger, Anna; Priebe, Carey E.; Rubin-Delanchy, Patrick
作者单位:University of Bristol; Microsoft; Johns Hopkins University
摘要:When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of different embeddings-which can be on entirely different scales-by how easy it is to distinguish communities, in an information-theoretical sense. For common types of weighted graphs...
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作者:Xu, Maoran; Zhou, Hua; Hu, Yujie; Duan, Leo L.
作者单位:Duke University; University of California System; University of California Los Angeles; University of California System; University of California Los Angeles; State University System of Florida; University of Florida; State University System of Florida; University of Florida
摘要:In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of obtaining a point estimate via optimization, it is much more challenging to quantify their uncertainty. In the Bayesian framework, a major difficulty is that if assigning the prior associated with a p-dimensional measure, then there is zero posterior probability...
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作者:Yu, Xiufan; Li, Danning; Xue, Lingzhou
作者单位:University of Notre Dame; Northeast Normal University - China; Northeast Normal University - China; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要:Testing large covariance matrices is of fundamental importance in statistical analysis with high-dimensional data. In the past decade, three types of test statistics have been studied in the literature: quadratic form statistics, maximum form statistics, and their weighted combination. It is known that quadratic form statistics would suffer from low power against sparse alternatives and maximum form statistics would suffer from low power against dense alternatives. The weighted combination met...
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作者:Hu, Xiaoyu; Yao, Fang
作者单位:National University of Singapore; Peking University
摘要:Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of variables p is comparable to, or much larger than the sample size n. Despite an extensive literature on this topic, researchers have focused on modeling static principal eigenvectors, which are not suitable for stochastic processes that are dynamic in nature. To cha...