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高维谱匹配：基于普适性的协方差推断AI 解读

We propose a new spectrum matching framework based on universality for high-dimensional covariance inference. The method constructs reference distributions for a broad class of spectral statistics by generating an auxiliary Gaussian matrix whose covariance spectrum matches that of the target covariance, with validity justified by universality. This framework accommodates both known and unknown covariance settings and adapts to different inferential targets, including…

通过剖面化迁移学习消除混杂AI 解读

Unmeasured confounders are a major source of bias in regression-based effect estimation and causal inference. In this paper, we propose a new profiled transfer learning framework, ProTrans, to address confounding effects in the target dataset, when additional source datasets with similar confounding structures are available. We introduce the concept of profiled residuals to characterize the shared confounding patterns between source and target datasets. By incorporating…

空间干扰效应的高维检测AI 解读

Modeling interference effects in high-dimensional settings presents significant challenges due to the complexity of underlying dependence structures. Existing approaches often rely on explicit and homogeneous assumptions, limiting their applicability in real-world scenarios. In this paper, we introduce a novel low-rank and sparse treatment effect model that leverages high-dimensional techniques to identify interference structures without restrictive parametric assumptions.…

离散观测函数型数据的协方差检验：何时有效、如何实施AI 解读

For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a pool-smoothing strategy to construct an FPC-based test statistic, allowing the number of estimated eigenfunctions to grow with the sample size. This yields a consistently nonparametric test, while the challenge arises from the concurrence of diverging…

微分方程建模中的非参数先验学习AI 解读

This article addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a prediction function of the prior distribution from historical training datasets. We introduce hyper-prior and hyper-posterior distributions and derive a generalization error estimate, which accommodates data-dependent priors by extending the…

离散观测函数集合的常微分方程模型AI 解读

Abstract The exploration of dynamic systems governed by ordinary differential equations (ODEs) holds great interest in the field of statistics. Existing research mainly focuses on a single function. This study generalizes the scope to analyse a collection of functions observed at discretized times, with sampling frequencies varying from sparse to dense designs. The range of ODE models studied caters to diverse dynamic systems, and includes the complex nonlinear and…

重复测量数据的深度回归AI 解读

Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected deep neural network (DNN) estimators with flexible shapes. A novel theoretical framework allowing arbitrary sampling frequency is established by adopting empirical process techniques to tackle clustered dependence. We then consider the DNN…

离散观测数据的函数主成分分析理论AI 解读

Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on eigen-decomposition plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely, the perturbation analysis of covariance operator for diverging number of eigencomponents…

快速信号区域检测及其全基因组关联研究应用AI 解读

Research on the localization of the genetic basis associated with diseases or traits has been widely conducted in the last few decades. Scan methods have been developed for region-based analysis in whole-genome association studies, helping us better understand how genetics influences human diseases or traits, especially when the aggregated effects of multiple causal variants are present. In this paper, we propose a fast and effective algorithm coupling with high-dimensional…

Green 匹配：复杂动力系统参数估计的高效方法AI 解读

Abstract Parameters of differential equations are essential to characterize intrinsic behaviours of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green’s matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate…

动态矩阵恢复AI 解读

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…

Abstract The aim of this article is to establish a causal link between the policies implemented by technology companies and the outcomes they yield within intricate temporal and/or spatial dependent experiments. We propose a novel temporal/spatio-temporal Varying Coefficient Decision Process model, capable of effectively capturing the evolving treatment effects in situations characterized by temporal and/or spatial dependence. Our methodology encompasses the decomposition of…

广义可加模型的在线平滑回拟合AI 解读

We propose an online smoothing backfitting method for generalized additive models coupled with local linear estimation. The idea can be extended to general nonlinear optimization problems. The strategy is to use an appropriate-order expansion to approximate the nonlinear equations and store the coefficients as sufficient statistics which can be updated in an online manner by the dynamic candidate bandwidth method. We investigate the statistical and algorithmic convergences…

高维函数型数据的最优线性判别分析AI 解读

Most of existing methods of functional data classification deal with one or a few processes. In this work we tackle classification of high-dimensional functional data, in which each observation is potentially associated with a large number of functional processes, p, which is comparable to or even much larger than the sample size n. The challenge arises from the complex inter-correlation structures among multiple functional processes, instead of a diagonal correlation for a…

高维动态主成分分析AI 解读

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…

空间平稳函数场的弱可分性检验AI 解读

For spatially dependent functional data, a generalized Karhunen-Loève expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient model to investigate the space-time interactions, but may not hold for complex spatio-temporal processes. In this work, we introduce the concept of weak separability, and propose a formal test to examine its validity for non-replicated…

离散观测数据的函数型线性回归：从理想到现实AI 解读

Summary Despite extensive studies on functional linear regression, there exists a fundamental gap in theory between the ideal estimation from fully observed covariate functions and the reality that one can only observe functional covariates discretely with noise. The challenge arises when deriving a sharp perturbation bound for the estimated eigenfunctions in the latter case, which renders existing techniques for functional linear regression not applicable. We use a pooling…

通过错误率控制数据驱动地选择变点数量AI 解读

In multiple change-point analysis, one of the main difficulties is to determine the number of change-points. Various consistent selection methods, including the use of Schwarz information criterion and cross-validation, have been proposed to balance the model fitting and complexity. However, there is lack of systematic approaches to provide theoretical guarantee of significance in determining the number of changes. In this paper, we introduce a data-adaptive selection…

稀疏纵向观测的内蕴黎曼函数型数据分析AI 解读

A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from…

含污染观测的流形上函数型回归AI 解读

Summary We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold, but is observable only in an infinite-dimensional space. Contamination of the predictor due to discrete or noisy measurements is also accounted for. By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the contamination level.…

不依赖特定分布与相关结构的高维均值双样本检验AI 解读

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This two-sample test based on a nontrivial extension of the one-sample central limit theorem (Ann. Probab. 45 (2017) 2309–2352) provides a practically useful procedure with rigorous theoretical guarantees on its size and power assessment. In…

内在黎曼函数型数据分析AI 解读

In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen–Loève expansion for Riemannian random processes. This framework also features an approach to compare objects from different tensor Hilbert spaces, which paves the way for asymptotic analysis in Riemannian functional data analysis. Built upon…

从多组高斯序列到函数型数据：一种 Stein 估计方法AI 解读

Summary We expand the notion of Gaussian sequence models to n experiments and propose a Stein estimation strategy which relies on pooling information across experiments. An oracle inequality is established to assess conditional risks given the underlying effects, based on which we can quantify the size of relative error and obtain a tuning-free recovery strategy that is easy to compute, produces model parsimony and extends to unknown variance. We show that the simultaneous…

混合内积空间及其在函数型数据分析中的应用AI 解读

We introduce the concept of mixture inner product spaces associated with a given separable Hilbert space, which feature an infinite-dimensional mixture of finite-dimensional vector spaces and are dense in the underlying Hilbert space. Any Hilbert valued random element can be arbitrarily closely approximated by mixture inner product space valued random elements. While this concept can be applied to data in any infinite-dimensional Hilbert space, the case of functional data…