论文检索

一般正则化下函数型线性回归的最优收敛速率AI 解读

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by employing general spectral regularization to approximate the slope function with certain smoothness assumptions. We establish optimal convergence rates for estimation and prediction errors associated with the proposed method under a Hölder type…

通过随机位移干预与交叉验证靶向学习自适应识别效应修饰因素AI 解读

In epidemiology, identifying subpopulations that are particularly vulnerable to exposures and those who may benefit differently from exposure-reducing interventions is essential. Factors such as age, gender-specific vulnerabilities, and physiological states such as pregnancy are critical for policymakers when setting regulatory guidelines. However, current semi-parametric methods for estimating heterogeneous treatment effects are often limited to binary exposures and can…

利用全局-局部先验改进数据整合下的小区域推断AI 解读

We present and apply methodology to improve inference for small area parameters by using data from several sources. This work extends Cahoy and Sedransk (2023) who showed how to integrate summary statistics from several sources. Our methodology uses hierarchical global-local prior distributions to make inferences for the proportion of individuals in Florida's counties who do not have health insurance. Results from an extensive simulation study show that this methodology will…

Lipschitz 损失正则化经验风险最小化中稀疏深度 ReLU 网络的近最优学习AI 解读

We propose a sparse deep ReLU network (SDRN) estimator of the regression function obtained from regularized empirical risk minimization with a Lipschitz loss function. Our framework can be applied to a variety of regression and classification problems. We establish novel non-asymptotic excess risk bounds for our SDRN estimator when the regression function belongs to a Sobolev space with mixed derivatives. We obtain a new nearly optimal risk rate in the sense that the SDRN…

一步平滑样条工具变量回归AI 解读

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique regularization parameter. We derive rates of the convergence for the estimator and its first derivative, which are uniform in the support of the endogenous variable. We also address the issue of imposing monotonicity in estimation and extend the…

比较高维时间序列的变量选择AI 解读

Given a pair of multivariate time-series data of the same length and dimensions, an approach is proposed to select variables and time intervals where the two series are significantly different. In applications where one time series is an output from a computationally expensive simulator, the approach may be used for validating the simulator against real data, for comparing the outputs of two simulators, and for validating a machine learning-based emulator against the…

高维双稀疏线性回归的极小极大最优方法AI 解读

In this paper, we focus our attention on the high-dimensional double sparse linear regression, that is, a combination of element-wise and group-wise sparsity. To address this problem, we propose an IHT-style (iterative hard thresholding) procedure that dynamically updates the threshold at each step. We establish the matching upper and lower bounds for parameter estimation, showing the optimality of our proposal in the minimax sense. More importantly, we introduce a fully…

含内生解释变量的商品组合选择模型：汽水税应用AI 解读

This paper proposes a Bayesian factor-augmented bundle choice model to estimate joint consumption as well as the substitutability and complementarity of multiple goods in the presence of endogenous regressors. The model extends the two primary treatments of endogeneity in existing bundle choice models: (1) endogenous market-level prices and (2) time-invariant unobserved individual heterogeneity. A Bayesian sparse factor approach is employed to capture high-dimensional error…

用算法替代人类决策者的统计检验AI 解读

This paper proposes a statistical framework of using artificial intelligence to improve human decision making. The performance of each human decision maker is benchmarked against that of machine predictions. We replace the diagnoses made by a subset of the decision makers with the recommendation from the machine learning algorithm. We apply both a heuristic frequentist approach and a Bayesian posterior loss function approach to abnormal birth detection using a nationwide…

高维相依数据中多解释变量与弱信号下的建模AI 解读

This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional response series is the sum of a linear regression with many observable explanatory variables and an error term driven by some latent common factors and an idiosyncratic noise. The common factors have dynamic dependence whereas the…

广义弹性网惩罚稀疏线性回归的迭代重加权算法框架AI 解读

The elastic net penalty is frequently employed in high-dimensional statistics for parameter regression and variable selection. It is particularly beneficial compared to lasso when the number of predictors greatly surpasses the number of observations. However, empirical evidence has shown that the $\ell_q$-norm penalty (where $0 < q < 1$) often provides better regression compared to the $\ell_1$-norm penalty, demonstrating enhanced robustness in various scenarios. In this…

桥型估计量的路径优化及其应用AI 解读

Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any possible value of the penalization parameter $λ$. In this paper we deal with the pathwise optimization for bridge-type problems; i.e. we are interested in the minimization of a loss function, such as negative log-likelihood or residual sum of…

用于验证与推断的边际因果流模型AI 解读

Investigating the marginal causal effect of an intervention on an outcome from complex data remains challenging due to the inflexibility of employed models and the lack of complexity in causal benchmark datasets, which often fail to reproduce intricate real-world data patterns. In this paper we introduce Frugal Flows, a novel likelihood-based machine learning model that uses normalising flows to flexibly learn the data-generating process, while also directly inferring the…

具有状态依赖广义双曲分布的隐马尔可夫图模型AI 解读

In this paper we develop a novel hidden Markov graphical model to investigate time-varying interconnectedness between different financial markets. To identify conditional correlation structures under varying market conditions and accommodate stylized facts embedded in financial time series, we rely upon the generalized hyperbolic family of distributions with time-dependent parameters evolving according to a latent Markov chain. We exploit its location-scale mixture…

纵向协变量与部分区间删失数据的联合建模：惩罚似然方法及其在Anti-PD1脑协作试验中的应用AI 解读

This article considers the joint modeling of longitudinal covariates and partly-interval censored time-to-event data. Longitudinal time-varying covariates play a crucial role in obtaining accurate clinically relevant predictions using a survival regression model. However, these covariates are often measured at limited time points and may be subject to measurement error. Further methodological challenges arise from the fact that, in many clinical studies, the event times of…

消除神经网络解释中的伪相关AI 解读

The existing algorithms for identification of neurons responsible for undesired and harmful behaviors do not consider the effects of confounders such as topic of the conversation. In this work, we show that confounders can create spurious correlations and propose a new causal mediation approach that controls the impact of the topic. In experiments with two large language models, we study the localization hypothesis and show that adjusting for the effect of conversation…

用马尔可夫转换因子模型刻画大维数据集AI 解读

We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent factors by means of Principal Component Analysis. We then cast the model in state-space form, and we estimate loadings and transition probabilities through an EM algorithm based on a modified version of the Baum-Lindgren-Hamilton-Kim filter…

SpaCE：空间混杂评测环境AI 解读

Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating causal inference methods designed to alleviate spatial confounding. Each dataset…

星系形成中的先天与后天因素：用因果机器学习研究环境对恒星形成的影响AI 解读

Understanding how galaxies form and evolve is at the heart of modern astronomy. With the advent of large-scale surveys and simulations, remarkable progress has been made in the last few decades. Despite this, the physical processes behind the phenomena, and particularly their importance, remain far from known, as correlations have primarily been established rather than the underlying causality. We address this challenge by applying the causal inference framework.…

大维矩阵因子模型的广义主成分分析AI 解读

Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo likelihood function, this paper introduces a Generalized Principal Component Analysis (GPCA) method for matrix factor model which takes the heteroscedasticity into account. Theoretically, we first derive the asymptotic distributions of the…

无排除限制的样本选择模型局部稳健半参数估计AI 解读

Existing identification and estimation methods for semiparametric sample selection models rely heavily on exclusion restrictions. However, it is difficult in practice to find a credible excluded variable that has a correlation with selection but no correlation with the outcome. In this paper, we establish a new identification result for a semiparametric sample selection model without the exclusion restriction. The key identifying assumptions are nonlinearity on the selection…

复合分位数因子模型AI 解读

This paper introduces the method of composite quantile factor model for factor analysis in high-dimensional panel data. We propose to estimate the factors and factor loadings across multiple quantiles of the data, allowing the estimates to better adapt to features of the data at different quantiles while still modeling the mean of the data. We develop the limiting distribution of the estimated factors and factor loadings, and an information criterion for consistent factor…

环境不变线性最小二乘AI 解读

This paper considers a multi-environment linear regression model in which data from multiple experimental settings are collected. The joint distribution of the response variable and covariates may vary across different environments, yet the conditional expectations of $y$ given the unknown set of important variables are invariant. Such a statistical model is related to the problem of endogeneity, causal inference, and transfer learning. The motivation behind it is…

Stein 传输用于贝叶斯推断AI 解读

We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen from a reproducing kernel Hilbert space and can be derived either through a suitable kernel ridge regression formulation or as an infinitesimal optimal transport map in the Stein geometry. The update equations of Stein transport resemble…