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条件密度估计的降维及其在高维因果推断中的应用AI 解读

We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form assumptions. To uncover the underlying sparsity structure of the data, we develop an innovative conditional dependence measure and a modified cross-validation procedure that enables data-driven variable selection, thereby circumventing the need…

随机实验异质性处理效应估计的去噪IPW-Lasso方法AI 解读

This paper proposes a new method for estimating conditional average treatment effects (CATE) in randomized experiments. We adopt inverse probability weighting (IPW) for identification; however, IPW-transformed outcomes are known to be noisy, even when true propensity scores are used. To address this issue, we introduce a noise reduction procedure and estimate a linear CATE model using Lasso, achieving both accuracy and interpretability. We theoretically show that denoising…

隐藏混杂下的预测后验AI 解读

Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the distribution shift across domains, or bias-inducing regularization schemes to enhance generalization. While recent developments in point prediction under hidden confounding attempt to mitigate these shortcomings, they generally do not provide…

多项式函数型回归中的多参数正则化与聚合AI 解读

Most of the recent results in polynomial functional regression have been focused on an in-depth exploration of single-parameter regularization schemes. In contrast, in this study we go beyond that framework by introducing an algorithm for multiple parameter regularization and presenting a theoretically grounded method for dealing with the associated parameters. This method facilitates the aggregation of models with varying regularization parameters. The efficacy of the…

在线与离线稳健多元线性回归AI 解读

We consider the robust estimation of the parameters of multivariate Gaussian linear regression models. To this aim we consider robust version of the usual (Mahalanobis) least-square criterion, with or without Ridge regularization. We introduce two methods each considered contrast: (i) online stochastic gradient descent algorithms and their averaged versions and (ii) offline fix-point algorithms. Under weak assumptions, we prove the asymptotic normality of the resulting…

统计与深度学习模型在概率电价预测中的不确定性量化分析AI 解读

Precise probabilistic forecasts are fundamental for energy risk management, and there is a wide range of both statistical and machine learning models for this purpose. Inherent to these probabilistic models is some form of uncertainty quantification. However, most models do not capture the full extent of uncertainty, which arises not only from the data itself but also from model and distributional choices. In this study, we examine uncertainty quantification in…

高维扩散过程漂移函数 Lasso 估计的抽样效应AI 解读

In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. We consider both a general linear form for the drift function and the particular case of the Ornstein-Uhlenbeck (OU) process. Assuming sparsity of the parameter vector, we examine the statistical behavior of the Lasso estimator for the unknown parameter. Our primary…

基于去偏组图Lasso的多稀疏精度矩阵统计推断AI 解读

Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates and model selection consistency under irrepresentability conditions. Based on these results, we construct debiased estimators that are asymptotically Gaussian, allowing hypothesis testing for linear combinations of precision matrix entries…

向量 Copula 变分推断与相关分块后验近似AI 解读

The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a common choice is to assume independence between multivariate blocks in a partition of the parameter space. While this simplifies the problem it can reduce accuracy. This paper proposes using vector copulas to capture dependence between the blocks parsimoniously. Tailored multivariate marginals are constructed using learnable transport maps. We call the…

依赖结构下变量选择的最优性与计算壁垒AI 解读

We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem do not exist. Specifically, we analyze the variable selection problem and provide the optimal sample complexity with exact dependence on the problem parameters for both known and unknown sparsity settings. Moreover, we establish a sample…

二次渐近机制下核随机矩阵与核回归的普适性AI 解读

Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus thus far has been on studying the proportional asymptotic regime, $n \asymp d$, where $n$ is the number of training samples and $d$ is the dimension of the dataset. In the proportional regime, under certain conditions on the data distribution, the kernel random matrix involved in KRR exhibits behavior akin to that of…

变换ℓ1正则化的稳健主成分分析：面向精细理解AI 解读

Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations, such as nuclear norm and $\ell_1$ norm, to approximate the rank of a matrix and the $\ell_0$ functional (the number of non-zero elements) of another. In this work, we advocate a nonconvex regularization method, referred to as transformed $\ell_1$…

惩罚混合模型：高维回归中批次效应与未观测混杂的调整AI 解读

Confounding can lead to spurious associations. Typically, one must observe confounders in order to adjust for them, but in high-dimensional settings, recent research has shown that it becomes possible to adjust even for unobserved confounders. The methods for carrying out these adjustments, however, have not been thoroughly investigated. In this study, we derive a confounding framework in which the signal, bias, and variability can be cleanly partitioned and quantified,…

不确定性下的最优正则化：分布鲁棒性与凸性约束AI 解读

Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent work has characterized optimal regularizers for well-specified data distributions, practical deployments are often complicated by distributional uncertainty and the need to enforce structural constraints such as convexity. In this paper,…

引用网络的双向共因子分析AI 解读

One compelling use of citation networks is to characterize papers by their relationships to the surrounding literature. We propose a method to characterize papers by embedding them into two distinct "co-factor" spaces: one describing how papers send citations, and the other describing how papers receive citations. This approach presents several challenges. First, older documents cannot cite newer documents, and thus it is not clear that co-factors are even identifiable. We…

模型里有什么？变量选择准则与模型搜索方法的比较AI 解读

For many scientific questions, understanding the underlying mechanism is the goal. To help investigators better understand the underlying mechanism, variable selection is a crucial step that permits the identification of the most associated regression variables of interest. A variable selection method consists of model evaluation using an information criterion and a search of the model space. Here, we provide a comprehensive comparison of variable selection methods using…

基于贝叶斯镜像统计量的错误发现率控制AI 解读

Simultaneously performing variable selection and inference in high-dimensional models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of specific statistical procedures to accurately select the most important predictors in a high-dimensional space, while being able to control some form of selection error. In this work we adapt the Mirror Statistic approach to False Discovery Rate (FDR)…

高维回归中树引导特征聚合的直接方法AI 解读

In high-dimensional linear models, sparsity is often exploited to reduce variability and achieve parsimony. Equi-sparsity, where one assumes that predictors can be aggregated into groups sharing the same effects, is an alternative parsimonious structure that can be more suitable in certain applications. Previous work has clearly demonstrated the benefits of exploiting equi-sparsity in the presence of ``rare features'' (Yan and Bien 2021). In this work, we propose a new…

超越疾病研究：用倾斜 knockoffs 控制次级表型变量选择AI 解读

Researchers in biomedical studies often work with samples that are not selected uniformly at random from the population of interest, a major example being a case-control study. While these designs are motivated by specific scientific questions, it is often of interest to use the data collected to pursue secondary lines of investigations. In these cases, ignoring the fact that observations are not sampled uniformly at random can lead to spurious results. For example, in a…

校准反事实共形公平性：分布偏移下的覆盖率平等AI 解读

We present Calibrated Counterfactual Conformal Fairness ($C^3F$), a post-hoc procedure that targets group-conditional coverage parity under covariate shift. $C^3F$ combines importance-weighted conformal calibration with a counterfactual regularizer based on path-specific effects in a structural causal model. The method estimates group-specific nonconformity quantiles using likelihood-ratio weights so that coverage degrades gracefully with the second moment of the weights. We…

梯度提升回归的统计推断AI 解读

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure that allows for a central limit theorem (CLT) for boosting. With these…

Bagging 正则化 M 估计量的精确渐近理论AI 解读

We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a heterogeneous collection of $M \ge 1$ regularized M-estimators, each trained with (possibly different) subsample sizes, convex differentiable losses, and convex regularizers. We operate under the proportional asymptotics regime, where the sample…

多变量时间序列的稳定空间AI 解读

This paper jointly addresses the challenges of non-stationarity and high dimensionality in analysing multivariate time series. Building on the classical concept of cointegration, we introduce a more flexible notion, called stability space, aimed at capturing stationary components in settings where traditional assumptions may not hold. Based on the dimensionality reduction techniques of Partial Least Squares and Principal Component Analysis, we proposed two non-parametric…

回声状态网络的随机矩阵视角：从精确偏差—方差刻画到最优正则化AI 解读

We present a rigorous asymptotic analysis of Echo State Networks (ESNs) in a teacher student setting with a linear teacher with oracle weights. Leveraging random matrix theory, we derive closed form expressions for the asymptotic bias, variance, and mean-squared error (MSE) as functions of the input statistics, the oracle vector, and the ridge regularization parameter. The analysis reveals two key departures from classical ridge regression: (i) ESNs do not exhibit double…