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超越 Matérn：一类可解释的合流超几何协方差函数AI 解读

The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses exponentially decaying tails, and thus, may not be suitable for modeling polynomially decaying dependence. This problem can be remedied using polynomial…

可能含异常批次的流式聚类数据实时回归分析AI 解读

This paper develops an incremental learning algorithm based on quadratic inference function (QIF) to analyze streaming datasets with correlated outcomes such as longitudinal data and clustered data. We propose a renewable QIF (RenewQIF) method within a paradigm of renewable estimation and incremental inference, in which parameter estimates are recursively renewed with current data and summary statistics of historical data, but with no use of any historical subject-level raw…

强化学习框架下A/B测试的动态因果效应评估AI 解读

A/B testing, or online experiment is a standard business strategy to compare a new product with an old one in pharmaceutical, technological, and traditional industries. Major challenges arise in online experiments of two-sided marketplace platforms (e.g., Uber) where there is only one unit that receives a sequence of treatments over time. In those experiments, the treatment at a given time impacts current outcome as well as future outcomes. The aim of this article is to…

基于小波的函数型数据独立性检验及脑磁图连接应用AI 解读

Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification, while a model-free method only provides a correlation measure which is inadequate to test independence. In this paper, we adopt the Hilbert–Schmidt Independence Criterion (HSIC) to measure the dependency between two random functions. We…

贝叶斯 Bootstrap 尖峰厚尾 LASSOAI 解读

The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find local posterior modes. Trading off uncertainty quantification for computational speed, these strategies have enabled spike-and-slab deployments at scales that would be previously unfeasible. We build on one recent development in this strand…

具有形状约束成对相关函数的聚集点过程半参数拟合优度检验AI 解读

Specification of a parametric model for the intensity function is a fundamental task in statistics for spatial point processes. It is, therefore, crucial to be able to assess the appropriateness of a suggested model for a given point pattern dataset. For this purpose, we develop a new class of semiparametric goodness-of-fit tests for the specified parametric first-order intensity, without assuming a full data generating mechanism that is needed for the existing popular Monte…

通过纵向生物标志物曲线配准分析未知起点的事件时间AI 解读

In observational studies, the time origin of interest for time-to-event analysis is often unknown, such as the time of disease onset. Existing approaches to estimating the time origins are commonly built on extrapolating a parametric longitudinal model, which rely on rigid assumptions that can lead to biased inferences. In this paper, we introduce a flexible semiparametric curve registration model. It assumes the longitudinal trajectories follow a flexible common shape…

存在局部最优解时的统计推断AI 解读

We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic normality and the bootstrap approach. In particular, we analyze the coverage deficiency due to finite number of random initializations. We also investigate the…

存在未测量混杂时多重处理效应的识别AI 解读

Identification of treatment effects in the presence of unmeasured confounding is a persistent problem in the social, biological, and medical sciences. The problem of unmeasured confounding in settings with multiple treatments is most common in statistical genetics and bioinformatics settings, where researchers have developed many successful statistical strategies without engaging deeply with the causal aspects of the problem. Recently there have been a number of attempts to…

用于多模态数据分析的正交化核去偏机器学习AI 解读

Multimodal imaging has transformed neuroscience research. While it presents unprecedented opportunities, it also imposes serious challenges. Particularly, it is difficult to combine the merits of the interpretability attributed to a simple association model with the flexibility achieved by a highly adaptive nonlinear model. In this article, we propose an orthogonalized kernel debiased machine learning approach, which is built upon the Neyman orthogonality and a form of…

非零均值函数下非平稳数据的谱密度估计AI 解读

We introduce a new approach for nonparametric spectral density estimation based on the subsampling technique, which we apply to the important class of nonstationary time series. These are almost periodically correlated sequences. In contrary to existing methods, our technique does not require demeaning of the data. On the simulated data examples, we compare our estimator of spectral density function with the classical one. Additionally, we propose a modified estimator, which…

稀疏主题模型：计算效率、近最优算法与统计推断AI 解读

Sparse topic modeling under the probabilistic latent semantic indexing (pLSI) model is studied. Novel and computationally fast algorithms for estimation and inference of both the word-topic matrix and the topic-document matrix are proposed and their theoretical properties are investigated. Both minimax upper and lower bounds are established and the results show that the proposed algorithms are rate-optimal, up to a logarithmic factor. Moreover, a refitting algorithm is…

高维线性混合模型中随机效应的推断与估计AI 解读

We consider three problems in high-dimensional linear mixed models. Without any assumptions on the design for the fixed effects, we construct asymptotic statistics for testing whether a collection of random effects is zero, derive an asymptotic confidence interval for a single random effect at the parametric rate n, and propose an empirical Bayes estimator for a part of the mean vector in ANOVA type models that performs asymptotically as well as the oracle Bayes estimator.…

梯度外积降维方法及其在高维分类中的应用AI 解读

Sufficient dimension reduction (SDR) has progressed steadily. However, its ability to improve general function estimation or classification has not been well received, especially for high-dimensional data. In this article, we first devise a local linear smoother for high dimensional nonparametric regression and then utilise it in the outer-product-of-gradient (OPG) approach of SDR. We call the method high-dimensional OPG (HOPG). To apply SDR to classification in…

通过图嵌入检测一般超图中的社区结构AI 解读

Conventional network data have largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a novel method for detecting community structure in general hypergraph networks, uniform or non-uniform. The proposed method introduces a null vertex to augment a nonuniform hypergraph into a uniform multi-hypergraph, and then embeds the…

控制错误率的特征筛选阈值选择AI 解读

Hard thresholding rule is commonly adopted in feature screening procedures to screen out unimportant predictors for ultrahigh-dimensional data. However, different thresholds are required to adapt to different contexts of screening problems and an appropriate thresholding magnitude usually varies from the model and error distribution. With an ad-hoc choice, it is unclear whether all of the important predictors are selected or not, and it is very likely that the procedures…

函数型数据的在线估计AI 解读

Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically update the estimates of mean and covariance functions for functional data. The kernel-type estimates can be decomposed into two sufficient statistics depending on the data-driven bandwidths. We propose to approximate the future optimal…

与算法无关的变量重要性推断的一般框架AI 解读

In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response - in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may…

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…

高维可交换数组的统计推断AI 解读

We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over the rectangles and subsequently develop novel multiplier bootstraps with theoretical guarantees. These theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate…

具有分组未观测异质性的大规模纵向广义线性模型AI 解读

This article provides methods for flexibly capturing unobservable heterogeneity from longitudinal data in the context of an exponential family of distributions. The group memberships of individual units are left unspecified, and their heterogeneity is influenced by group-specific unobservable factor structures. The model includes, as special cases, probit, logit, and Poisson regressions with interactive fixed effects along with unknown group membership. We discuss a…

杠杆效应估计：核函数与效率AI 解读

This article proposes more efficient estimators for the leverage effect than the existing ones. The idea is to allow for nonuniform kernel functions in the spot volatility estimates or the aggregated returns. This finding highlights a critical difference between the leverage effect and integrated volatility functionals, where the uniform kernel is optimal. Another distinction between these two cases is that the overlapping estimators of the leverage effect are more efficient…

含成分协变量的高维线性对数对比模型稳健信号恢复AI 解读

In this article, we propose a robust signal recovery method for high-dimensional linear log-contrast models, when the error distribution could be heavy-tailed and asymmetric. The proposed method is built on the Huber loss with ℓ1 penalization. We establish the ℓ1 and ℓ2 consistency for the resulting estimator. Under conditions analogous to the irrepresentability condition and the minimum signal strength condition, we prove that the signed support of the slope parameter…

一类优化问题的推断：置信域与覆盖误差的有限样本界AI 解读

This article describes three methods for carrying out nonasymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation under shape restrictions, estimation of models of discrete games, and estimation based on grouped data. The partially identified parameters are characterized by restrictions that involve the unknown population means of observed random…