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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…

通过互补压缩检验两样本高维线性回归系数AI 解读

We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and response vectors along directions that are complementary in sign in a subset of the coordinates, a process which we call “complementary sketching.” The resulting projected covariates and responses are aggregated to form two test…

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…

可逆多维扩散的非参数贝叶斯推断AI 解读

We study nonparametric Bayesian models for reversible multidimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to Gaussian priors and p-exponential priors, which are shown to converge to the truth at the optimal…

Sobolev 椭球中在线非参数回归的筛随机梯度下降估计AI 解读

The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. in nonparametric regression, one assumes that the regression function belongs to a pre-specified infinite-dimensional function space (the hypothesis space). in the online setting, when the observations come in a stream, it is computationally-preferable to iteratively update an estimate rather than refitting an entire model repeatedly.…

受约束分类中的生物标志物线性组合AI 解读

Multiple biomarkers are often combined to improve disease diagnosis. The uniformly optimal combination, i.e., with respect to all reasonable performance metrics, unfortunately requires excessive distributional modeling, to which the estimation can be sensitive. An alternative strategy is rather to pursue local optimality with respect to a specific performance metric. Nevertheless, existing methods may not target clinical utility of the intended medical test, which usually…

删失寿命的非参数二元密度估计AI 解读

It is well known that estimation of a bivariate cumulative distribution function of a pair of right censored lifetimes presents challenges unparalleled to the univariate case where a product-limit Kaplan–Meyer’s methodology typically yields optimal estimation, and the literature on optimal estimation of the joint probability density is next to none. The paper, for the first time in the survival analysis literature, develops the theory and methodology of sharp minimax and…

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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…

同步压缩变换的渐近分析：面向非线性时频分析的统计推断AI 解读

We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and nonnull cases. The intricate nonlinear interaction of different quantities in SST is quantified by carefully analyzing relevant multivariate complex Gaussian random variables. Specifically, we provide the quotient distribution of dependent and improper complex Gaussian random variables. Then a central limit theorem result for SST…

非同质多层网络的全局与逐层社区检测AI 解读

In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on the same set of subjects, where each network is obtained in a related but different experiment condition or application scenario. Such datasets can be modeled by multilayer networks where each layer is a separate network itself while different layers are associated and share some common information. The present paper studies community detection in a…

无穷远有多远？有限混合模型的贝叶斯非参数视角AI 解读

Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. Following a Bayesian nonparametric perspective, we introduce a new class of priors: the Normalized Independent Point Process. We investigate the probabilistic properties of this new class and present many special cases. In particular, we provide an explicit formula for the distribution of the implied partition, as well as the posterior characterization of…

Lp 损失下多元位置的仿射等变推断AI 解读

We consider the fundamental problem of estimating the location of a d-variate probability measure under an Lp loss function. The naive estimator, that minimizes the usual empirical Lp risk, has a known asymptotic behavior but suffers from several deficiencies for p≠2, the most important one being the lack of equivariance under general affine transformations. In this work, we introduce a collection of Lp location estimators μˆnp,ℓ that minimize the size of suitable…

存在未观测混杂时条件与平均处理效应的界AI 解读

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning…

高维中心极限定理与自助法近似的改进AI 解读

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its distribution plays a key role in many high-dimensional estimation and testing problems. Using a novel iterative randomized Lindeberg method, the paper derives new bounds for the distributional approximation errors. These new bounds…

具有有限样本保证的新型 Edgeworth 展开AI 解读

We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean balls and the set of all half-spaces. These results allow to account for an impact of higher-order moments or cumulants of the considered distributions; the obtained error terms depend on a sample size and a dimension explicitly. The new…

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…

具有测量误差的李群非参数回归AI 解读

This paper develops a foundation of methodology and theory for nonparametric regression with Lie group-valued predictors contaminated by measurement errors. Our methodology and theory are based on harmonic analysis on Lie groups, which is largely unknown in statistics. We establish a novel deconvolution regression estimator, and study its rate of convergence and asymptotic distribution. We also provide asymptotic confidence intervals based on the asymptotic distribution of…

使用近似共充分抽样检验拟合优度与条件独立性AI 解读

Goodness-of-fit (GoF) testing is ubiquitous in statistics, with direct ties to model selection, confidence interval construction, conditional independence testing, and multiple testing, just to name a few applications. While testing the GoF of a simple (point) null hypothesis provides an analyst great flexibility in the choice of test statistic while still ensuring validity, most GoF tests for composite null hypotheses are far more constrained, as the test statistic must…

隐式平滑下的高维中心极限定理与自助近似AI 解读

Nonasymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry–Esseen bounds for such approximations with respect to the multivariate Kolmogorov distance, in the context of a sum of n random vectors that are p-dimensional and i.i.d. Up to now, a growing line of work has established bounds with mild logarithmic dependence on p. However, the problem of developing corresponding…

量化回归风险与公平性权衡的极小极大框架AI 解读

We propose a theoretical framework for the problem of learning a real-valued function which meets fairness requirements. This framework is built upon the notion of α-relative (fairness) improvement of the regression function which we introduce using the theory of optimal transport. Setting α=0 corresponds to the regression problem under the Demographic Parity constraint, while α=1 corresponds to the classical regression problem without any constraints. For α∈(0,1) the…

高维模型中平滑泛函的估计：自助链与高斯近似AI 解读

Let X(n) be an observation sampled from a distribution Pθ(n) with an unknown parameter θ, θ being a vector in a Banach space E (most often, a high-dimensional space of dimension d). We study the problem of estimation of f(θ) for a functional f:E↦R of some smoothness s>0 based on an observation X(n)∼Pθ(n). Assuming that there exists an estimator θˆn=θˆn(X(n)) of parameter θ such that n(θˆ n−θ) is sufficiently close in distribution to a mean zero Gaussian random vector in E,…

最小范数插值估计与正则化经验风险最小化的稳健性AI 解读

This article develops a general theory for minimum norm interpolating estimators and regularized empirical risk minimizers (RERM) in linear models in the presence of additive, potentially adversarial, errors. In particular, no conditions on the errors are imposed. A quantitative bound for the prediction error is given, relating it to the Rademacher complexity of the covariates, the norm of the minimum norm interpolator of the errors and the size of the subdifferential around…

二元响应下高维个体化阈值的非正则与极小极大估计AI 解读

Given a large number of covariates Z, we consider the estimation of a high-dimensional parameter θ in an individualized linear threshold θTZ for a continuous variable X, which minimizes the disagreement between sign(X−θTZ) and a binary response Y. While the problem can be formulated into the M-estimation framework, minimizing the corresponding empirical risk function is computationally intractable due to discontinuity of the sign function. Moreover, estimating θ even in the…