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用于神经网络贝叶斯学习与 MCMC 的迹类高斯先验AI 解读

Abstract This paper introduces a new neural network based prior for real valued functions. Each weight and bias of the neural network has an independent Gaussian prior, with the key novelty that the variances decrease in the width of the network in such a way that the resulting function is well defined in the limit of an infinite width network. We show that the induced posterior over functions is amenable to Monte Carlo sampling using Hilbert space Markov chain Monte Carlo…

贝叶斯融合：可扩展地统一分布式统计分析AI 解读

Abstract There has been considerable interest in addressing the problem of unifying distributed analyses into a single coherent inference, which arises in big-data settings, when working under privacy constraints, and in Bayesian model choice. Most existing approaches relied upon approximations of the distributed analyses, which have significant shortcomings—the quality of the inference can degrade rapidly with the number of analyses being unified, and can be substantially…

保形化生存分析AI 解读

Abstract In this paper, we develop an inferential method based on conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically…

多处理臂及可能包含析因结构的实验中的协变量调整AI 解读

Abstract Randomized experiments are the gold standard for causal inference and enable unbiased estimation of treatment effects. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This article provides a unified account of its utility for improving estimation efficiency in multiarmed experiments. We start with the commonly used additive and fully interacted models for regression adjustment in estimating average…

缺失数据的偏样本经验似然加权：逆概率加权的替代方法AI 解读

Abstract Inverse probability weighting (IPW) is widely used in many areas when data are subject to unrepresentativeness, missingness, or selection bias. An inevitable challenge with the use of IPW is that the IPW estimator can be remarkably unstable if some probabilities are very close to zero. To overcome this problem, at least three remedies have been developed in the literature: stabilizing, thresholding, and trimming. However, the final estimators are still IPW-type…

基于张量 CP 分解的矩阵时间序列建模AI 解读

Abstract We consider to model matrix time series based on a tensor canonical polyadic (CP)-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further…

复杂网络中的信息核心识别AI 解读

Abstract In a complex network, the core component with interesting structures is usually hidden within noninformative connections. The noises and bias introduced by the noninformative component can obscure the salient structure and limit many network modeling procedures’ effectiveness. This paper introduces a novel core–periphery model for the noninformative periphery structure of networks without imposing a specific form of the core. We propose spectral algorithms for core…

种子二元分割：快速且最优的变点检测通用方法AI 解读

Summary We propose seeded binary segmentation for large-scale changepoint detection problems. We construct a deterministic set of background intervals, called seeded intervals, in which single changepoint candidates are searched for. The final selection of changepoints based on these candidates can be done in various ways, adapted to the problem at hand. The method is thus easy to adapt to many changepoint problems, ranging from univariate to high dimensional. Compared to…

倾向得分在观察性因果研究设计中的作用AI 解读

Summary The design of any study, whether experimental or observational, that is intended to estimate the causal effects of a treatment condition relative to a control condition refers to those activities that precede any examination of outcome variables. As defined in our 1983 article (Rosenbaum & Rubin, 1983), the propensity score is the unit-level conditional probability of assignment to treatment versus control given the observed covariates; so the propensity score…

局部化保形预测：保形预测的广义推断框架AI 解读

Summary We propose a new inference framework called localized conformal prediction. It generalizes the framework of conformal prediction by offering a single-test-sample adaptive construction that emphasizes a local region around this test sample, and can be combined with different conformal scores. The proposed framework enjoys an assumption-free finite sample marginal coverage guarantee, and it also offers additional local coverage guarantees under suitable assumptions. We…

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…

通过偏内积进行协方差估计的可分离展开AI 解读

Summary The nonparametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are typically alleviated by assuming separability. However, separability is often questionable, sometimes even demonstrably inadequate. We propose a framework for the analysis of covariance operators of random surfaces that generalizes…

具有有限样本保证的简明通用去偏机器学习定理AI 解读

Summary Debiased machine learning is a meta-algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e., scalar summaries, of machine learning algorithms. For example, an analyst may seek the confidence interval for a treatment effect estimated with a neural network. We present a non-asymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies…

最小假设下稀疏图子的子抽样AI 解读

Summary We study the properties of two subsampling procedures for networks, vertex subsampling and $p$-subsampling, under the sparse graphon model. The consistency of network subsampling is demonstrated under the minimal assumptions of weak convergence of the corresponding network statistics and an expected subsample size growing to infinity more slowly than the number of vertices in the network. Furthermore, under appropriate sparsity conditions, we derive limiting…

高维高斯图模型的统一推断AI 解读

Summary Graphical models have become a popular tool for representing dependencies within large sets of variables and are crucial for representing causal structures. We provide results for uniform inference on high-dimensional graphical models, in which the number of target parameters $d$ is potentially much larger than the sample size, under approximate sparsity. Our results highlight how graphical models can be estimated and recovered using modern machine learning methods…

组成数据的稳健差异丰度检验AI 解读

Summary Differential abundance tests for compositional data are essential and fundamental in various biomedical applications, such as single-cell, bulk RNA-seq and microbiome data analysis. However, because of the compositional constraint and the prevalence of zero counts in the data, differential abundance analysis on compositional data remains a complicated and unsolved statistical problem. This article proposes a new differential abundance test, the robust differential…

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…

存在处理习惯化的时序实验中因果效应的极小极大设计AI 解读

Summary In many modern settings, such as an online marketplace, randomized experiments need to be executed over multiple time periods. In such temporal experiments, it has been observed that the effects of an intervention on an experimental unit may be large when the unit is first exposed to it, but then it attenuates after repeated exposures. This is typically due to units’ habituation to the intervention, or some other form of learning, such as when users gradually start…

数据整合：利用外部简化模型的参数估计比值AI 解读

Summary We consider the situation of estimating the parameters in a generalized linear prediction model, from an internal dataset, where the outcome variable $Y$ is binary and there are two sets of covariates, $X$ and $Z$. We have information from an external study that provides parameter estimates for a generalized linear model of $Y$ on $X$. We propose a method that makes limited assumptions about the similarity of the distributions in the two study populations. The method…

含高维干扰参数的广义线性模型检验AI 解读

Summary Generalized linear models often have high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional subvector of the model’s coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and are thus…

用于识别共同极端事件群组的球面聚类AI 解读

Summary There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results supporting this approach, but also demonstrate some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identifying concomitant extremes, and it results in a novel spherical $k$-principal-component…

基于 F 建模的方差经验贝叶斯估计AI 解读

Summary We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss functions. For one particular loss function, the resulting Bayes estimator relies on the marginal cumulative distribution function of the sample variances only. When replacing it with the empirical distribution function, we obtain an…

加权最小二乘估计的最优极小极大随机设计AI 解读

Summary This work studies an experimental design problem where the values of a predictor variable, denoted by $x$, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to $m(x)$, but it is not assumed that the model is correctly specified. It follows that the quantity of interest is the best linear approximation of $m(x)$, which is denoted by $\ell(x)$. It is shown that in this framework the ordinary least…

可交换关系数组的回归AI 解读

Summary Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression…