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双重稳健且计算高效的高维变量选择AI 解读

Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure (PCM) test. However, directly deploying PCM for variable selection brings computational challenges: testing a single variable involves a few machine learning fits, so testing $p$ variables requires $O(p)$ fits. Inspired by model-X ideas, we…

Mondrian 随机森林的统计推断AI 解读

Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees are constructed via a Mondrian process. We give precise bias and variance characterizations, along with a Berry-Esseen-type central limit theorem, for the Mondrian random forest regression estimator. By combining these results with a…

正态性并不容易：噪声对不依赖结构的估计的影响AI 解读

Structure-agnostic causal inference studies how well one can estimate a treatment effect given black-box machine learning estimates of nuisance functions (like the impact of confounders on treatment and outcomes). Here, we find that the answer depends in a surprising way on the distribution of the treatment noise. Focusing on the partially linear model of \citet{robinson1988root}, we first show that the widely adopted double machine learning (DML) estimator is minimax…

校正分位数回归的覆盖偏差AI 解读

We develop a collection of methods for adjusting the predictions of quantile regression to ensure coverage. Our methods are model agnostic and can be used to correct for high-dimensional overfitting bias with only minimal assumptions. Theoretical results show that the estimates we develop are consistent and facilitate accurate calibration in the proportional asymptotic regime where the ratio of the dimension of the data and the sample size converges to a constant. This is…

生成式贝叶斯滤波与参数学习AI 解读

Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to dynamic settings, enabling recursive posterior inference using simulation-based methods powered by deep neural networks. GBF does not require explicit density evaluations, making it particularly effective when observation or transition…

缺失随机下校准加权的一般方法AI 解读

We propose a unified class of calibration weighting methods based on weighted generalized entropy to handle missing at random (MAR) data with improved stability and efficiency. The proposed generalized entropy calibration (GEC) formulates weight construction as a convex optimization program that unifies entropy-based approaches and generalized regression weighting. Double robustness is achieved by augmenting standard covariate balancing with a debiasing constraint tied to…

重尾噪声下的正则化最小二乘学习达到极小极大最优AI 解读

This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial terms based on the well known integral operator framework. The dominant subgaussian component allows to achieve convergence rates that have previously only been derived under subexponential noise - a prevalent assumption in related work…

二元选择模型中的分组固定效应正则化AI 解读

We study the application of the grouped fixed effects approach to binary choice models for panel data in presence of severe complete separation. Through data loss, complete separation may lead to biased estimates of Average Partial Effects and imprecise inference. Moreover, forecasts are not available for units without variability in the response configuration. The grouped fixed effects approach discretizes unobserved heterogeneity via k-means clustering, thus reducing the…

高维噪声常微分方程中的向量场重构AI 解读

This work investigates the nonparametric estimation of the vector field of a noisy Ordinary Differential Equation (ODE) in high-dimensional ambient spaces, under the assumption that the initial conditions are sampled from a lower-dimensional structure. Specifically, let \( f:\mathbb{R}^{D}\to\mathbb{R}^{D} \) denote the vector field of the autonomous ODE \( y' = f(y) \). We observe noisy trajectories \( \tilde{y}_{X_i}(t_j) = y_{X_i}(t_j) + \varepsilon_{i,j} \), where \( y_{X_i}(t_j) \)…

半参数多元混合模型的最大平滑对数似然估计量的收敛速率AI 解读

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus is on the estimator that maximizes a smoothed log-likelihood function, which can be efficiently computed using a majorization-minimization algorithm. This smoothed likelihood applies a nonlinear regularization operator defined as the…

典型相关分析综述AI 解读

For over a century canonical correlations, variables, and related concepts have been studied across various fields, with contributions dating back to Jordan [1875] and Hotelling [1936]. This text surveys the evolution of canonical correlation analysis, a fundamental statistical tool, beginning with its foundational theorems and progressing to recent developments and open research problems. Along the way we introduce and review methods, notions, and fundamental concepts from…

高维回归中稳健且一致的模型评价准则AI 解读

Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the data and phenomenon, we need to determine an adequate value of the regularization parameter. Regarding the determination of the regularization parameter in the linear regression model, we often apply the information criteria like the AIC and…

面向高维结构化数据的自适应几何回归AI 解读

We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge in analyzing datasets with high ambient dimension but low intrinsic dimension, such as microbiome compositions, where traditional approaches fail to capture the underlying geometric structure. Starting from a k-nearest neighbor covering…

连接政策学习中的经验福利最大化与条件平均处理效应估计AI 解读

The goal of policy learning is to train a policy function that recommends a treatment given covariates to maximize population welfare. There are two major approaches in policy learning: the empirical welfare maximization (EWM) approach and the plug-in approach. The EWM approach is analogous to a classification problem, where one first builds an estimator of the population welfare, which is a functional of policy functions, and then trains a policy by maximizing the estimated…

高维函数线性模型中的变量选择与极小极大预测AI 解读

High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each predictor is a random element in an infinite-dimensional function space, and the number of functional predictors p can potentially be ultra-high. Assuming that each of the unknown coefficient functions belongs to some reproducing kernel…

整群随机试验中不完整结果与协变量的处理AI 解读

In cluster-randomized trials (CRTs), missing data can occur in various ways, including missing values in outcomes and baseline covariates at the individual or cluster level, or completely missing information for non-participants. Among the various types of missing data in CRTs, missing outcomes have attracted the most attention. However, no existing methods simultaneously address all aforementioned types of missing data in CRTs. To fill in this gap, we propose a…

合成工具变量：从稀疏关联到稀疏因果效应AI 解读

In many observational studies, researchers are often interested in studying the effects of multiple exposures on a single outcome. Standard approaches for high-dimensional data such as the lasso assume the associations between the exposures and the outcome are sparse. These methods, however, do not estimate the causal effects in the presence of unmeasured confounding. In this paper, we consider an alternative approach that assumes the causal effects in view are sparse. We…

稀疏且稳健的独立成分分析方法AI 解读

This work presents sparse invariant coordinate selection, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate selection, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent…

混合类型结果的高维回归：多元 spike-and-slab LASSOAI 解读

We consider a high-dimensional multi-outcome regression in which $q,$ possibly dependent, binary and continuous outcomes are regressed onto $p$ covariates. We model the observed outcome vector as a partially observed latent realization from a multivariate linear regression model. Our goal is to estimate simultaneously a sparse matrix ($B$) of latent regression coefficients (i.e., partial covariate effects) and a sparse latent residual precision matrix ($Ω$), which induces…

随机矩阵理论视角下的表示模型泛化：在循环网络中的应用AI 解读

We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompasses a range of architectures, from deep random-feature models to echo-state networks (ESNs) with recurrent dynamics. Working in the high-dimensional regime, we apply Random Matrix Theory to derive a closed-form expression for the asymptotic generalization error. We then apply this analysis to…

缺失非随机下基于模型聚类的变量选择统一框架AI 解读

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in…

存在溢出效应时惩罚合成控制估计的贝叶斯收缩先验AI 解读

Synthetic control (SC) methods are widely used to estimate the effects of policy interventions, especially those targeting specific geographic regions, referred to as units. These methods construct a weighted combination of untreated units, forming a "synthetic" control that approximates the counterfactual outcomes of the treated unit had the intervention not occurred. Although neighboring areas are often selected as controls due to their similarity in observed and…

因果正则化：样本内风险与样本外风险保证的权衡AI 解读

Invariant prediction uses the prediction stability of causal relationships across different environments to identify causal variables. Conversely, using causal variables gives prediction guarantees even in out-of-sample data settings. In this paper, we investigate the identification of causal-like models from in-sample data that ensure out-of-sample risk guarantees when predicting a target variable from an arbitrary set of covariates. Ordinary least squares minimizes…

具有时间依赖的高维时间序列自适应变点推断AI 解读

This paper investigates change point inference in high-dimensional time series. We begin by introducing a max-$L_2$-norm based test procedure, which demonstrates strong performance under dense alternatives. We then establish the asymptotic independence between our proposed statistic and the two max-$L_\infty$-based statistics introduced by Wang and Feng (2023). Building on this result, we develop an adaptive inference approach by applying the Cauchy combination method to…