论文检索

高维组成数据均值的两样本检验AI 解读

Compositional data are ubiquitous in many scientific endeavours. Motivated by microbiome and metagenomic research, we consider a two-sample testing problem for high-dimensional compositional data and formulate a testable hypothesis of compositional equivalence for the means of two latent log basis vectors. We propose a test through the centred log-ratio transformation of the compositions. The asymptotic null distribution of the test statistic is derived and its power against…

分位数回归中的边际线性效应检验AI 解读

Summary The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the…

多元时间序列的半参数动态 max-copula 模型AI 解读

Summary The paper presents a novel non-linear framework for the construction of flexible multivariate dependence structure (i.e. copulas) from existing copulas based on a straightforward ‘pairwise max-’rule. The newly constructed max-copula has a closed form and has strong interpretability. Compared with the classical ‘linear symmetric’ mixture copula, the max-copula can be viewed as a ‘non-linear asymmetric’ framework. It is capable of modelling asymmetric dependence and…

高维混合模型成分协方差矩阵的结构检验AI 解读

Summary By studying the family of p-dimensional scale mixtures, the paper shows for the first time a non-trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated Marčenko–Pastur law. A different and new limit is found and characterized. The reasons for failure of the Marčenko–Pastur limit in this situation are found to be a strong dependence between the p-co-ordinates of the mixture. Next, we address…

矩阵变量回归与包络模型AI 解读

Summary Modern technology often generates data with complex structures in which both response and explanatory variables are matrix valued. Existing methods in the literature can tackle matrix-valued predictors but are rather limited for matrix-valued responses. We study matrix variate regressions for such data, where the response Y on each experimental unit is a random matrix and the predictor X can be either a scalar, a vector or a matrix, treated as non-stochastic in terms…

基于去稀疏化保守 Lasso 的高维参数渐近诚实置信区域AI 解读

In this paper we consider the conservative Lasso which we argue penalizes more correctly than the Lasso and show how it may be desparsified in the sense of van de Geer et al. (2014) in order to construct asymptotically honest (uniform) confidence bands. In particular, we develop an oracle inequality for the conservative Lasso only assuming the existence of a certain number of moments. This is done by means of the Marcinkiewicz–Zygmund inequality. We allow for heteroskedastic…

采用连续尖峰与厚尾混合先验的稀疏信号贝叶斯估计AI 解读

We introduce a new framework for estimation of sparse normal means, bridging the gap between popular frequentist strategies (LASSO) and popular Bayesian strategies (spike-and-slab). The main thrust of this paper is to introduce the family of Spike-and-Slab LASSO (SS-LASSO) priors, which form a continuum between the Laplace prior and the point-mass spike-and-slab prior. We establish several appealing frequentist properties of SS-LASSO priors, contrasting them with these two…

高维删失分位数回归AI 解读

Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. We propose a two-step penalization procedure, which accommodates stochastic integral…

预测的高维渐近理论：岭回归与正则化判别分析AI 解读

We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p,n\to\infty$ and $p/n\to\gamma>0$, and allow for arbitrary covariance among the features. For both methods, we provide an explicit and efficiently computable expression for the limiting predictive risk, which depends only on the spectrum of the feature-covariance matrix, the…

稀疏学习的路径式坐标优化：算法与理论AI 解读

The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: warm start initialization, active set updating and strong rule for coordinate preselection. Such a complex algorithmic structure grants superior empirical performance, but also poses significant challenge to theoretical…

LASSO与近似消息传递的调参一致性AI 解读

This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as $n$, the…

奇异子空间的速率最优扰动界及高维统计应用AI 解读

Perturbation bounds for singular spaces, in particular Wedin’s $\mathop{\mathrm{sin}}\nolimits \Theta$ theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning and applied mathematics. In this paper, we establish separate perturbation bounds, measured in both spectral and Frobenius $\mathop{\mathrm{sin}}\nolimits \Theta$ distances, for the left and right singular subspaces. Lower bounds, which show that the individual…

仿射估计量聚合的最优界AI 解读

We study the problem of aggregation of estimators when the estimators are not independent of the data used for aggregation and no sample splitting is allowed. If the estimators are deterministic vectors, it is well known that the minimax rate of aggregation is of order $\log(M)$, where $M$ is the number of estimators to aggregate. It is proved that for affine estimators, the minimax rate of aggregation is unchanged: it is possible to handle the linear dependence between the…

We revisit the classic semi‐parametric problem of inference on a low‐dimensional parameter θ0 in the presence of high‐dimensional nuisance parameters η0. We depart from the classical setting by allowing for η0 to be so high‐dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η0, we consider the use of statistical or machine learning (ML) methods, which are particularly…

高维内生回归变量与工具变量下的稀疏线性模型及 ℓ₁ 正则化两阶段最小二乘AI 解读

We explore the validity of the 2-stage least squares estimator with l1-regularization in both stages, for linear triangular models where the numbers of endogenous regressors in the main equation and instruments in the first-stage equations can exceed the sample size, and the regression coefficients are sufficiently sparse. For this l1-regularized 2-stage least squares estimator, we first establish finite-sample performance bounds and then provide a simple practical method…

偏态模型聚类的变量选择：识别新的睡眠表型AI 解读

In sleep research, applying finite mixture models to sleep characteristics captured 8 through multiple data types, including self-reported sleep diary, a wrist monitor capturing movement (actigraphy), and brain waves (polysomnography), may suggest new phenotypes that reflect underlying disease mechanisms. However, a direct mixture model application is challenging because there are many sleep variables from which to choose, and sleep variables are often highly skewed even in…

结构层级约束下的组正则化估计AI 解读

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. Weak or strong structural hierarchy requires that the existence of an interaction term implies at least one or both associated main effects to be present in the model. Lately, this problem has attracted a lot of attention, but existing computational algorithms converge slow even with a moderate number of predictors. Moreover, in contrast to…

尖峰与厚尾LASSOAI 解读

Despite the wide adoption of spike-and-slab methodology for Bayesian variable selection, its potential for penalized likelihood estimation has largely been overlooked. In this article, we bridge this gap by cross-fertilizing these two paradigms with the Spike-and-Slab LASSO procedure for variable selection and parameter estimation in linear regression. We introduce a new class of self-adaptive penalty functions that arise from a fully Bayes spike-and-slab formulation,…

充分利用因子模型中的维度优势AI 解读

Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the blessing of dimensionality has not yet been fully embraced in the literature: much of the available data is often ignored in constructing covariance matrix estimates. If our goal is to accurately estimate a covariance matrix of a set of…

超高维加性模型中的误差方差估计AI 解读

Error variance estimation plays an important role in statistical inference for high-dimensional regression models. This article concerns with error variance estimation in high-dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations that are even higher in nonparametric models than linear…

基于特征簇进行估计与推断的一般框架AI 解读

Applied statistical problems often come with prespecified groupings to predictors. It is natural to test for the presence of simultaneous group-wide signal for groups in isolation, or for multiple groups together. Current tests for the presence of such signals include the classical F-test or a t-test on unsupervised group prototypes (either group centroids or first principal components). In this article, we propose test statistics that aim for power improvements over these…

ECA：非高斯分布下的高维椭圆成分分析AI 解读

We present a robust alternative to principal component analysis (PCA)—called elliptical component analysis (ECA)—for analyzing high-dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical data. To cope with heavy-tailed elliptical distributions, a multivariate rank statistic is exploited. At the model-level, we consider two settings: either that the leading eigenvectors of the covariance matrix are nonsparse or that…

多无效矩条件下的自适应弹性网GMM估计：模型与矩条件联合选择AI 解读

This article develops the adaptive elastic net generalized method of moments (GMM) estimator in large-dimensional models with potentially (locally) invalid moment conditions, where both the number of structural parameters and the number of moment conditions may increase with the sample size. The basic idea is to conduct the standard GMM estimation combined with two penalty terms: the adaptively weighted lasso shrinkage and the quadratic regularization. It is a one-step…

基于稀疏投影的高维变点估计AI 解读

Summary Change points are a very common feature of ‘big data’ that arrive in the form of a data stream. We study high dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the co-ordinates. The challenge is to borrow strength across the co-ordinates to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called inspect for estimation of the change points: first,…