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主题模型中稀疏主题分布的似然估计及 Wasserstein 文档距离应用AI 解读

This paper studies the estimation of high-dimensional, discrete, possibly sparse, mixture models in the context of topic models. The data consists of observed multinomial counts of p words across n independent documents. In topic models, the p×n expected word frequency matrix is assumed to be factorized as a p×K word-topic matrix A and a K×n topic-document matrix T. Since columns of both matrices represent conditional probabilities belonging to probability simplices, columns…

随机森林的平均准确率下降：不一致性与 Sobol-MDA 解决方案AI 解读

Summary Variable importance measures are the main tools used to analyse the black-box mechanisms of random forests. Although the mean decrease accuracy is widely accepted as the most efficient variable importance measure for random forests, little is known about its statistical properties. In fact, the definition of mean decrease accuracy varies across the main random forest software. In this article, our objective is to rigorously analyse the behaviour of the main mean…

基于似然的稀疏协方差估计：近端距离算法AI 解读

Summary This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties, and enables optimization of the resulting nonconvex objective by solving a…

通过隐式正则化进行高维线性回归AI 解读

Summary Many statistical estimators for high-dimensional linear regression are $M$-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined through a discretized gradient dynamic system under overparameterization. We show that, under suitable restricted isometry conditions, overparameterization leads to implicit regularization: if we directly apply gradient descent to the…

调整Benjamini–Hochberg方法以控制knockoff变量选择的错误发现率AI 解读

Summary We consider the knockoff-based multiple testing set-up of Barber & Candès (2015). for variable selection in multiple regression. The method of Benjamini & Hochberg (1995) and an adaptive version of it are adjusted to this set-up, transforming them to valid $p$-value-based, false discovery rate-controlling methods that do not rely on specifying the correlation structure of the explanatory variables. Simulations and real data applications show that the proposed methods…

高维典型相关分析的显著性检验AI 解读

Summary We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a postselection inference approach to canonical correlation analysis. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the Euclidean norm of the canonical correlations maximized over subsets of variables of…

Hilbert 空间中的条件独立检验及函数型数据应用AI 解读

Abstract We study the problem of testing the null hypothesis that X and Y are conditionally independent given Z, where each of X, Y and Z may be functional random variables. This generalises testing the significance of X in a regression model of scalar response Y on functional regressors X and Z. We show, however, that even in the idealised setting where additionally (X, Y, Z) has a Gaussian distribution, the power of any test cannot exceed its size. Further modelling…

高维贝叶斯变量选择中不依赖维度的混合时间AI 解读

Abstract Yang et al. proved that the symmetric random walk Metropolis–Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel Markov chain Monte Carlo (MCMC) sampler using an informed proposal scheme, which we prove achieves a much faster mixing time that is independent of the number of covariates, under the assumptions of Yang et al. To the best of our knowledge, this is the first high-dimensional…

贝叶斯稀疏线性回归的神经元化先验AI 解读

Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficulties in both computations and flexibilities of prior choices. To ease these challenges, we propose the neuronized priors to unify and extend some popular shrinkage priors, such as Laplace, Cauchy, horseshoe, and spike-and-slab priors. A neuronized prior can be written as the…

保护个体数据的高维异质研究整合回归AI 解读

Evidence-based decision making often relies on meta-analyzing multiple studies, which enables more precise estimation and investigation of generalizability. Integrative analysis of multiple heterogeneous studies is, however, highly challenging in the ultra high-dimensional setting. The challenge is even more pronounced when the individual-level data cannot be shared across studies, known as DataSHIELD contraint. Under sparse regression models that are assumed to be similar…

核常微分方程AI 解读

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for…

一致稀疏深度学习：理论与计算AI 解读

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most O(n/ log (n)) connections and nice…

含分类变量的变量选择：模型选择视角AI 解读

In the context of a Gaussian multiple regression model, we address the problem of variable selection when in the list of potential predictors there are factors, that is, categorical variables. We adopt a model selection perspective, that is, we approach the problem by constructing a class of models, each corresponding to a particular selection of active variables. The methodology is Bayesian and proceeds by computing the posterior probability of each of these models. We…

利用参数化决策分析实现快速、最优与目标导向预测AI 解读

Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parameterized actions for Bayesian decision…

Wald 检验中的 Hauck–Donner 效应：检测、临界点与参数空间刻画AI 解读

The Wald test remains ubiquitous in statistical practice despite shortcomings such as its inaccuracy in small samples and lack of invariance under reparameterization. This article develops on another but lesser-known shortcoming called the Hauck–Donner effect (HDE) whereby a Wald test statistic is no longer monotone increasing as a function of increasing distance between the parameter estimate and the null value. Resulting in an upward biased p-value and loss of power, the…

结合网络嵌入的有向社区检测AI 解读

Community detection in network data aims at grouping similar nodes sharing certain characteristics together. Most existing methods focus on detecting communities in undirected networks, where similarity between nodes is measured by their node features and whether they are connected. In this article, we propose a novel method to conduct network embedding and community detection simultaneously in a directed network. The network embedding model introduces two sets of vectors to…

工具变量下局部平均处理效应的高维模型辅助推断AI 解读

Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be estimated through regression models, such as instrument propensity score and treatment and outcome regression models. We develop a computationally tractable method in high-dimensional settings where the numbers of regression terms…

可能存在多次周期结构变化的非平稳时间序列稳健推断AI 解读

Motivated by two examples concerning global warming and monthly total import and export by China, we study time series that contain a nonparametric periodic component with an unknown period, a nonparametric trending behavior and also additive covariate effects. Further, as the amplitude function may change at some known or unknown change-point(s), we extend our model to take this dynamical periodicity into account and introduce two change-point estimators. To the best of…

高维混频工具变量回归AI 解读

This article introduces a high-dimensional linear IV regression for the data sampled at mixed frequencies. We show that the high-dimensional slope parameter of a high-frequency covariate can be identified and accurately estimated leveraging on a low-frequency instrumental variable. The distinguishing feature of the model is that it allows handing high-dimensional datasets without imposing the approximate sparsity restrictions. We propose a Tikhonov-regularized estimator and…

局部关联图模型与混合凸指数族AI 解读

The notion of multivariate total positivity has proved to be useful in finance and psychology but may be too restrictive in other applications. In this paper, we propose a concept of local association, where highly connected components in a graphical model are positively associated and study its properties. Our main motivation comes from gene expression data, where graphical models have become a popular exploratory tool. The models are instances of what we term mixed convex…

删失分位数回归过程的可扩展估计与推断AI 解读

Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge for large-scale data with many covariates. In this paper, we focus on a smoothed martingale-based sequential estimating equations approach, to which scalable gradient-based algorithms can be applied. Theoretically, we provide a unified…

近似核主成分分析：计算与统计之间的权衡AI 解读

Kernel methods are powerful learning methodologies that allow to perform nonlinear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistical consistency of most of these approximate kernel methods is not well understood except for kernel ridge regression wherein it has been shown that the random…

干预特定平均结局的连续时间目标最小损失估计AI 解读

This paper generalizes the targeted minimum loss-based estimation (TMLE) framework to allow for estimating the effects of time-varying interventions in settings where both interventions, covariates, and outcome can happen at subject-specific time-points on an arbitrarily fine time-scale. TMLE is a general template for constructing asymptotically linear substitution estimators for smooth low-dimensional parameters in infinite-dimensional models. Existing longitudinal TMLE…

利用正则化 Riesz 表示元对全局与局部参数进行去偏机器学习AI 解读

Summary We provide adaptive inference methods, based on $\ell _1$ regularization, for regular (semiparametric) and nonregular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of nonregular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a…