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凸与非凸矩阵感知的高维统计理论AI 解读

The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to this problem, establishing minimax error rates when the number of measurements is sufficiently large relative to the rank and dimension of the low-rank matrix, though a precise comparison of these procedures still remains unexplored. In…

单变量引导的稀疏回归AI 解读

In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive for stability and interpretation of the model. Through comprehensive simulations and applications to real-world datasets, we demonstrate that UniLasso outperforms Lasso in various settings, particularly in terms of sparsity and model…

易错计数数据的推断：二项卷积框架下的估计AI 解读

Measurement error in count data is common but underexplored in the literature, particularly in contexts where observed scores are bounded and arise from discrete scoring processes. Motivated by applications in oral reading fluency assessment, we propose a binomial convolution framework that extends binary misclassification models to settings where only the aggregate number of correct responses is observed, and errors may involve both overcounting and undercounting the number…

多元时间序列异常检测的无监督策略基准比较AI 解读

Anomaly detection in multivariate time series is an important problem across various fields such as healthcare, financial services, manufacturing or physics detector monitoring. Accurately identifying when unexpected errors or faults occur is essential, yet challenging, due to the unknown nature of anomalies and the complex interdependencies between time series dimensions. In this paper, we investigate transformer-based approaches for time series anomaly detection, focusing…

未知方差高斯模型中的L2范数后验收缩AI 解读

The testing-based approach is a fundamental tool for establishing posterior contraction rates. Although the Hellinger metric is attractive owing to the existence of a desirable test function, it is not directly applicable in Gaussian models, because translating the Hellinger metric into more intuitive metrics typically requires strong boundedness conditions. When the variance is known, this issue can be addressed by directly constructing a test function relative to the $L_2$-…

重尾相依矩阵与算子之和的无维界AI 解读

We prove deviation inequalities for sums of high-dimensional random matrices and operators with dependence and {\rc heavy tails}. Estimation of high-dimensional matrices is a concern for numerous modern applications. However, most results are stated for independent observations. Therefore, it is critical to derive results for dependent and heavy-tailed matrices. In this paper, we derive a dimension-free upper bound on the deviation of the sums. Thus, the bound does not…

多变量长期剖面监测及其在KW51铁路桥中的应用AI 解读

Structural Health Monitoring (SHM) plays a pivotal role in modern civil engineering, providing critical insights into the health and integrity of infrastructure systems. This work presents a novel multivariate long-term profile monitoring approach to eliminate fluctuations in the measured response quantities, e.g., caused by environmental influences or measurement error. Our methodology addresses critical challenges in SHM and combines supervised methods with unsupervised,…

确定性离散线性时不变微分代数系统中的因果发现AI 解读

Discovering pure causes or driver variables in deterministic LTI systems is of vital importance in the data-driven reconstruction of causal networks. A recent work by Kathari and Tangirala, proposed in 2022, formulated the causal discovery method as a constraint identification problem. The constraints are identified using a dynamic iterative PCA (DIPCA)-based approach for dynamical systems corrupted with Gaussian measurement errors. The DIPCA-based method works efficiently…

密集纵向数据的动态因果中介分析AI 解读

Intensive longitudinal data, characterized by frequent measurements across numerous time points, are increasingly common due to advances in wearable devices and mobile health technologies. We consider evaluating causal mediation pathways between time-varying exposures, time-varying mediators, and a final, distal outcome using such data. Addressing mediation questions in these settings is challenging due to numerous potential exposures, complex mediation pathways, and…

消费者行为的形态：时间序列的符号与拓扑分析AI 解读

Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time-series data present challenges for effective clustering. This study evaluates three unsupervised clustering approaches, Symbolic Aggregate approXimation (SAX), enhanced SAX (eSAX), and Topological Data Analysis (TDA), applied to 20 Google Trends keywords…

网络干扰下异质处理效应的随机化推断AI 解读

We develop randomization-based tests for heterogeneous treatment effects in the presence of network interference. Leveraging the exposure mapping framework, we study a broad class of null hypotheses that represent various forms of constant treatment effects in networked populations. These null hypotheses, unlike the classical Fisher sharp null, are not sharp due to unknown parameters and multiple potential outcomes. Existing conditional randomization procedures either fail…

底层有向混合图上的簇图：聚合层面因果效应识别AI 解读

The do-calculus is a sound and complete tool for identifying causal effects in acyclic directed mixed graphs (ADMGs) induced by structural causal models (SCMs). However, in many real-world applications, especially in high-dimensional setting, constructing a fully specified ADMG is often infeasible. This limitation has led to growing interest in partially specified causal representations, particularly through cluster-directed mixed graphs (C-DMGs), which group variables into…

结合可观测特征的单指标分位数因子模型AI 解读

We propose a characteristics-augmented quantile factor (QCF) model, where unknown factor loading functions are linked to a large set of observed individual-level (e.g., bond- or stock-specific) covariates via a single-index projection. The single-index specification offers a parsimonious, interpretable, and statistically efficient way to nonparametrically characterize the time-varying loadings, while avoiding the curse of dimensionality in flexible nonparametric models.…

利用专家混合模型估计依从者平均因果效应AI 解读

Treatment non-compliance, where individuals deviate from their assigned experimental conditions, frequently complicates the estimation of causal effects. To address this, we introduce a novel learning framework based on a mixture of experts architecture to estimate the Complier Average Causal Effect (CACE). Our framework provides a flexible alternative to classical instrumental variable methods by relaxing their strict monotonicity and exclusion restriction assumptions. We…

为后续工具变量回归学习处理变量表征AI 解读

Traditional instrumental variable (IV) estimators face a fundamental constraint: they can only accommodate as many endogenous treatment variables as available instruments. This limitation becomes particularly challenging in settings where the treatment is presented in a high-dimensional and unstructured manner (e.g. descriptions of patient treatment pathways in a hospital). In such settings, researchers typically resort to applying unsupervised dimension reduction techniques…

充分降维中的精度矩阵正则化以改进二次判别分类AI 解读

Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original feature-space dimension, precision matrix estimation becomes unstable and, as a result, increases the variability of the linear dimension reduction (LDR) matrix. Ultimately, this fact causes suboptimal supervised classification. To address…

异质性、不确定性与学习：半参数识别和估计AI 解读

We provide identification results for a broad class of learning models in which continuous outcomes depend on three types of unobservables: known heterogeneity, initially unknown heterogeneity that may be revealed over time, and transitory uncertainty. We consider a common environment where the researcher only has access to a short panel on choices and realized outcomes. We establish identification of the outcome equation parameters and the distribution of the unobservables,…

干扰程度：存在干扰时因果推断的一般框架AI 解读

One core assumption typically adopted for valid causal inference is that of no interference between experimental units, i.e., the outcome of an experimental unit is unaffected by the treatments assigned to other experimental units. This assumption can be violated in real-life experiments, which significantly complicates the task of causal inference. As the number of potential outcomes increases, it becomes challenging to disentangle direct treatment effects from…

条件矩限制的双重机器学习：工具变量回归、近端因果学习及拓展AI 解读

Solving conditional moment restrictions (CMRs) is a key problem considered in statistics, causal inference, and econometrics, where the aim is to solve for a function of interest that satisfies some conditional moment equalities. Specifically, many techniques for causal inference, such as instrumental variable (IV) regression and proximal causal learning (PCL), are CMR problems. Most CMR estimators use a two-stage approach, where the first-stage estimation is directly…

泊松有向图模型的似然比检验AI 解读

Directed acyclic graphs are widely used to describe the causal effects among random variables, and the inference of those causal effects has become an popular topic in statistics and machine learning, and has wide applications in neuroinformatics, bioinformatics and so on. However, most studies focus on the estimation or inference of the directional relations among continuous random variables, those among discrete random variables have not gained much attentions. In this…

时间序列分位数与预期短缺回归中的自归一化推断AI 解读

This paper proposes valid inference tools, based on self-normalization, in time series expected shortfall regressions and, as a corollary, also in quantile regressions. Extant methods for such time series regressions, based on a bootstrap or direct estimation of the long-run variance, are computationally more involved, require the choice of tuning parameters and have serious size distortions when the regression errors are strongly serially dependent. In contrast, our…

不定概率理论AI 解读

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes the following contributions: (1) An observer-centered framework in which experimental outcomes are represented as distributions combining ground truth with observation error; (2) The introduction of three independence candidate axioms…

利用特异性进行观察研究中的因果推断AI 解读

Hill's specificity criterion has been highly influential in biomedical and epidemiological research. However, it remains controversial and its application often relies on subjective and qualitative analysis without a comprehensive and rigorous causal theory. Focusing on unmeasured confounding adjustment with multiple treatments and multiple outcomes, this paper develops a formal and quantitative framework for leveraging specificity for causal inference in observational…

利用外部对照提高随机试验累积发生率估计的精度AI 解读

Augmenting the control arm in clinical trials with external data can improve statistical power for demonstrating treatment effects. In many time-to-event outcome trials, participants are subject to truncation by death. Direct application of methods for competing risks analysis on the joint data may introduce bias, for example, due to covariate shifts between the populations. In this work, we consider transportability of the conditional cause-specific hazard of the event of…