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高维图模型中使用单链接的稳定网络推断AI 解读

Stability, akin to reproducibility, is crucial in statistical analysis. This paper examines the stability of sparse network inference in high-dimensional graphical models, where selected edges should remain consistent across different samples. Our study focuses on the Graphical Lasso and its decomposition into two steps, with the first step involving hierarchical clustering using single linkage.We provide theoretical proof that single linkage is stable, evidenced by…

使用大量预测变量的时间序列预测AI 解读

We propose a novel approach for time series forecasting with many predictors, referred to as the GO-sdPCA, in this paper. The approach employs a variable selection method known as the group orthogonal greedy algorithm and the high-dimensional Akaike information criterion to mitigate the impact of irrelevant predictors. Moreover, a novel technique, called peeling, is used to boost the variable selection procedure so that many factor-relevant predictors can be included in…

强相关结构下岭插值估计量的精确分析：随机对偶理论视角AI 解读

We consider fully row/column-correlated linear regression models and study several classical estimators (including minimum norm interpolators (GLS), ordinary least squares (LS), and ridge regressors). We show that \emph{Random Duality Theory} (RDT) can be utilized to obtain precise closed form characterizations of all estimators related optimizing quantities of interest, including the \emph{prediction risk} (testing or generalization error). On a qualitative level out…

相关因子回归模型中岭插值器的精确风险分析AI 解读

We consider correlated \emph{factor} regression models (FRM) and analyze the performance of classical ridge interpolators. Utilizing powerful \emph{Random Duality Theory} (RDT) mathematical engine, we obtain \emph{precise} closed form characterizations of the underlying optimization problems and all associated optimizing quantities. In particular, we provide \emph{excess prediction risk} characterizations that clearly show the dependence on all key model parameters,…

存在测量误差时的协变量平衡AI 解读

In recent years, there is a growing body of causal inference literature focusing on covariate balancing methods. These methods eliminate observed confounding by equalizing covariate moments between the treated and control groups. The validity of covariate balancing relies on an implicit assumption that all covariates are accurately measured, which is frequently violated in observational studies. Nevertheless, the impact of measurement error on covariate balancing is unclear,…

法官工具变量设计中的多维聚类AI 解读

Estimates in judge designs run the risk of being biased due to the many judge identities that are implicitly or explicitly used as instrumental variables. The usual method to analyse judge designs, via a leave-out mean instrument, eliminates this many instrument bias only in case the data are clustered in at most one dimension. What is left out in the mean defines this clustering dimension. How most judge designs cluster their standard errors, however, implies that there are…

改进的经验贝叶斯多元多重检验与效应量估计方法AI 解读

Estimating the sharing of genetic effects across different conditions is important to many statistical analyses of genomic data. The patterns of sharing arising from these data are often highly heterogeneous. To flexibly model these heterogeneous sharing patterns, Urbut et al. (2019) proposed the multivariate adaptive shrinkage (MASH) method to jointly analyze genetic effects across multiple conditions. However, multivariate analyses using MASH (as well as other multivariate…

一般回归误差假设下无岭最小二乘估计量的预测与估计风险AI 解读

In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression error structure, assuming independent and identically distributed errors with zero mean and common variance. In this paper, we explore prediction risk as well as estimation risk under more general regression error assumptions, highlighting…

通过稳健估计处理暴露缺失的因果推断AI 解读

How to deal with missing data in observational studies is a common concern for causal inference. When the covariates are missing at random (MAR), multiple approaches have been provided to help solve the issue. However, if the exposure is MAR, few approaches are available and careful adjustments on both missingness and confounding issues are required to ensure a consistent estimate of the true causal effect on the response. In this article, a new inverse probability weighting…

双向聚类的渐近理论AI 解读

This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an open issue. The existing theory for two-way clustering inference requires identical distributions across clusters (implied by the so-called separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing…

多重线性回归的灵活经验贝叶斯方法及其与惩罚回归的联系AI 解读

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of normal distributions by a finite mixture of normal distributions; and (ii) the use of variational approximations to efficiently estimate prior hyperparameters and compute approximate posteriors. Combining these two ideas results in fast…

从因果视角评估多模态时间序列预测模型的稳健性AI 解读

AI systems are notorious for their fragility; minor input changes can potentially cause major output swings. When such systems are deployed in critical areas like finance, the consequences of their uncertain behavior could be severe. In this paper, we focus on multi-modal time-series forecasting, where imprecision due to noisy or incorrect data can lead to erroneous predictions, impacting stakeholders such as analysts, investors, and traders. Recently, it has been shown that…

基于经验贝叶斯平滑的最优得分估计AI 解读

We study the problem of estimating the score function of an unknown probability distribution $ρ^*$ from $n$ independent and identically distributed observations in $d$ dimensions. Assuming that $ρ^*$ is subgaussian and has a Lipschitz-continuous score function $s^*$, we establish the optimal rate of $\tilde Θ(n^{-\frac{2}{d+4}})$ for this estimation problem under the loss function $\|\hat s - s^*\|^2_{L^2(ρ^*)}$ that is commonly used in the score matching literature,…

混杂条件下决策策略的预测表现比较AI 解读

Predictive models are often introduced to decision-making tasks under the rationale that they improve performance over an existing decision-making policy. However, it is challenging to compare predictive performance against an existing decision-making policy that is generally under-specified and dependent on unobservable factors. These sources of uncertainty are often addressed in practice by making strong assumptions about the data-generating mechanism. In this work, we…

Harold Zuercher 的偏好具有时间可分性吗？AI 解读

This paper proposes an empirical model of dynamic discrete choice to allow for non-separable time preferences, generalizing the well-known Rust (1987) model. Under weak conditions, we show the existence of value functions and hence well-defined optimal choices. We construct a contraction mapping of the value function and propose an estimation method similar to Rust's nested fixed point algorithm. Finally, we apply the framework to the bus engine replacement data. We improve…

通过逆概率加权估计赔款准备金：微观链梯法AI 解读

Claim reserving primarily relies on macro-level models, with the Chain-Ladder method being the most widely adopted. These methods were heuristically developed without minimal statistical foundations, relying on oversimplified data assumptions and neglecting policyholder heterogeneity, often resulting in conservative reserve predictions. Micro-level reserving, utilizing stochastic modeling with granular information, can improve predictions but tends to involve less attractive…

数字时代电子金融市场的概率模型与统计方法AI 解读

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional…

处理分配不平衡下双重稳健估计量的校准AI 解读

Machine learning methods, particularly the double machine learning (DML) estimator (Chernozhukov et al., 2018), are increasingly popular for the estimation of the average treatment effect (ATE). However, datasets often exhibit unbalanced treatment assignments where only a few observations are treated, leading to unstable propensity score estimations. We propose a simple extension of the DML estimator which undersamples data for propensity score modeling and calibrates scores…

Cluster GARCH：具有聚类依赖结构的多元波动模型AI 解读

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH…

数据驱动的切换实验：理论权衡与经验贝叶斯设计AI 解读

We study the design and analysis of switchback experiments conducted on a single aggregate unit. The design problem is to partition the continuous time space into intervals and switch treatments between intervals, in order to minimize the estimation error of the treatment effect. We show that the estimation error depends on four factors: carryover effects, periodicity, serially correlated outcomes, and impacts from simultaneous experiments. We derive a rigorous bias-variance…

二元 de Bruijn 过程AI 解读

Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome successes of past events. Presented here is a novel approach for modelling binary time series data called a binary de Bruijn process which takes into account temporal correlation. The structure is derived from de Bruijn Graphs - a directed…

逐节点 L0 惩罚回归：高维稀疏精度矩阵估计AI 解读

We propose Nodewise Loreg, a nodewise $L_0$-penalized regression method for estimating high-dimensional sparse precision matrices. We establish its asymptotic properties, including convergence rates, support recovery, and asymptotic normality under high-dimensional sub-Gaussian settings. Notably, the Nodewise Loreg estimator is asymptotically unbiased and normally distributed, eliminating the need for debiasing required by Nodewise Lasso. We also develop a desparsified…

带阈值识别的生物标志物引导自适应富集生存试验设计AI 解读

Biomarker-guided designs are increasingly used to evaluate personalized treatments based on patients' biomarker status in Phase II and III clinical trials. With adaptive enrichment, these designs can improve the efficiency of evaluating the treatment effect in biomarker-positive patients by increasing their proportion in the randomized trial. While time-to-event outcomes are often used as the primary endpoint to measure treatment effects for a new therapy in severe diseases…

基于最优传输的多元随机占优及模型基准比较AI 解读

Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little has been done in the multivariate scenario, wherein an agent has to decide between different multivariate outcomes. By exploiting a characterization of multivariate first stochastic dominance in terms of couplings, we introduce a…