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深度变换模型AI 解读

The increasing data complexity leads to the demand for more general and flexible modeling approaches. We consider a nonparametric transformation model with weak assumptions, which encompasses many popular models as special cases. A rank-based deep neural network (DNN) estimation approach is developed, with a loss function significantly different from the existing ones. It can accommodate outliers in response, which is a robustness property not broadly shared. For…

用于域泛化的域特定非参数回归AI 解读

We propose a domain-specific regression approach for domain generalization, taking into account possible heterogeneity among the datasets from different sources. In the proposed model, the domain-specific features are characterized through linear functionals of the marginal source distributions. The predictors are combined with the domain-specific linear functionals as inputs in the model. Using the source data sets, we estimate the domain-index function and the regression…

流式数据高维广义线性模型的自适应去偏 LassoAI 解读

Online statistical inference facilitates real-time analysis of sequentially collected data, making it different from traditional methods that rely on static datasets. This article introduces a novel approach to online inference in high-dimensional generalized linear models, where we update regression coefficient estimates and their standard errors upon each new data arrival. In contrast to existing methods that either require full dataset access or large-dimensional summary…

利用深度神经网络对删失数据进行非参数推断AI 解读

Abstract We propose a novel deep learning approach to nonparametric statistical inference for the conditional hazard function of survival time with right-censored data. We use a deep neural network (DNN) to approximate the logarithm of a conditional hazard function given covariates and obtain a DNN likelihood-based estimator of the conditional hazard function. Such an estimation approach enhances model flexibility and hence relaxes structural and functional assumptions on…

Wasserstein 生成式回归AI 解读

Abstract In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning framework, where a conditional generator is a function that can generate samples from a conditional distribution. The main idea is to estimate a conditional generator satisfying the constraint that it produces a good regression…

群体影像数据的检验与差异位置恢复AI 解读

In this article, we propose a multiscale adaptive test to detect differences between two samples of intrinsically smoothed image data in high-dimensional context. The test aggregates data from nearby locations using adaptive weights, significantly enhancing statistical power. We demonstrate that the test statistic converges to a Gumbel extreme value distribution under the null hypothesis. Moreover, we investigate its multiscale nature, showing that the chosen scales can grow…

基于 Bregman 散度的深度互密度比估计及其应用AI 解读

This article introduces a unified approach to estimating the mutual density ratio, defined as the ratio between the joint density function and the product of the individual marginal density functions of two random vectors. It serves as a fundamental measure for quantifying the relationship between two random vectors. Our method uses the Bregman divergence to construct the objective function and leverages deep neural networks to approximate the logarithm of the mutual density…

高维单指标模型假设检验的随机投影方法AI 解读

In this article, we consider the problem of hypothesis testing in high-dimensional single-index models. First, we study the feasibility of applying the classical F-test to a single-index model when the dimension of covariate vector and sample size are of the same order, and derive its asymptotic null distribution and asymptotic local power function. For the ultrahigh-dimensional single-index model, we construct F-statistics based on lower-dimensional random projections of…

利用去偏随机梯度下降进行在线推断AI 解读

Summary We propose a debiased stochastic gradient descent algorithm for online statistical inference with high-dimensional data. Our approach combines the debiasing technique developed in high-dimensional statistics with the stochastic gradient descent algorithm. It can be used to construct confidence intervals efficiently in an online fashion. Our proposed algorithm has several appealing aspects: as a one-pass algorithm, it reduces the time complexity; in addition, each…

条件抽样的深度生成方法AI 解读

We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed approach aims at learning a conditional generator, so that a random sample from the target conditional distribution can be obtained by transforming a sample drawn from a reference distribution. The conditional generator is estimated…

含成分协变量的高维线性对数对比模型稳健信号恢复AI 解读

In this article, we propose a robust signal recovery method for high-dimensional linear log-contrast models, when the error distribution could be heavy-tailed and asymmetric. The proposed method is built on the Huber loss with ℓ1 penalization. We establish the ℓ1 and ℓ2 consistency for the resulting estimator. Under conditions analogous to the irrepresentability condition and the minimum signal strength condition, we prove that the signed support of the slope parameter…

近似流形上的深度非参数回归：具有多项式前因子的非渐近误差界AI 解读

We study the properties of nonparametric least squares regression using deep neural networks. We derive nonasymptotic upper bounds for the excess risk of the empirical risk minimizer of feedforward deep neural regression. Our error bounds achieve minimax optimal rate and improve over the existing ones in the sense that they depend polynomially on the dimension of the predictor, instead of exponentially on dimension. We show that the neural regression estimator can circumvent…

高维响应多元回归的响应变量最优子集选择AI 解读

Summary This article investigates the statistical problem of response-variable selection with high-dimensional response variables and a diverging number of predictor variables with respect to the sample size in the framework of multivariate linear regression. A response best-subset selection model is proposed by introducing a 0-1 selection indicator for each response variable, and then a response best-subset selector is developed by introducing a separation parameter and a…

线性化最大秩相关估计AI 解读

Summary We propose a linearized maximum rank correlation estimator for the single-index model. Unlike the existing maximum rank correlation and other rank-based methods, the proposed estimator has a closed-form expression, making it appealing in theory and computation. The proposed estimator is robust to outliers in the response and its construction does not need knowledge of the unknown link function or the error distribution. Under mild conditions, it is shown to be…

厚尾、非对称或异方差误差下高维均值回归的稳健选择后推断AI 解读

We propose a robust post-selection inference method based on the Huber loss for the regression coefficients, when the error distribution is heavy-tailed and asymmetric in a high-dimensional linear model with an intercept term. The asymptotic properties of the resulting estimators are established under mild conditions. We also extend the proposed method to accommodate heteroscedasticity assuming the error terms are symmetric and other suitable conditions. Statistical tests…

再生核希尔伯特空间中稀疏加性分位数回归的预言不等式AI 解读

This paper considers the estimation of the sparse additive quantile regression (SAQR) in high-dimensional settings. Given the nonsmooth nature of the quantile loss function and the nonparametric complexities of the component function estimation, it is challenging to analyze the theoretical properties of ultrahigh-dimensional SAQR. We propose a regularized learning approach with a two-fold Lasso-type regularization in a reproducing kernel Hilbert space (RKHS) for SAQR. We…

基于凹惩罚成对融合的亚组分析AI 解读

An important step in developing individualized treatment strategies is correct identification of subgroups of a heterogeneous population to allow specific treatment for each subgroup. This article considers the problem using samples drawn from a population consisting of subgroups with different mean values, along with certain covariates. We propose a penalized approach for subgroup analysis based on a regression model, in which heterogeneity is driven by unobserved latent…

通过惩罚促进整合分析中的稀疏结构相似性AI 解读

For data with high-dimensional covariates but small sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of pooling information and outperforms single-dataset and several alternative multi-datasets methods. Under many scenarios, multiple datasets are expected to share common important covariates, that is, the corresponding models have similarity in their…

Cox模型中Lasso的预言机不等式AI 解读

We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequalities based on natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true regression coefficients. Similar results based on an extension of the restricted eigenvalue can be also proved…

高维回归的稀疏拉普拉斯收缩估计量AI 解读

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic associated with a graph as the penalty function. We call it the sparse Laplacian shrinkage (SLS) method. The SLS uses the minimax concave penalty for encouraging sparsity and Laplacian quadratic penalty for promoting smoothness among…

非参数可加模型中的变量选择AI 解读

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component…

用单调 B 样条半参数估计面板计数数据AI 解读

We study semiparametric likelihood-based methods for panel count data with proportional mean model E[ℕ(t)|Z]=Λ0(t)exp(β0TZ), where Z is a vector of covariates and Λ0(t) is the baseline mean function. We propose to estimate Λ0(t) and β0 jointly with Λ0(t) approximated by monotone B-splines and to compute the estimators using generalized Rosen algorithm proposed by Jamshidian (2004). We show that the proposed spline-based likelihood estimators of Λ0(t) are consistent with a…

用于变量选择的组桥方法AI 解读

Abstract In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The existing methods, including the lasso and group lasso, are designed for either variable selection or group selection, but not for both. We propose a group bridge approach that is capable of simultaneous selection at both the group and within-group individual variable…

高维部分线性模型中的 SCAD 惩罚回归AI 解读

We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be…