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通过贝叶斯线性规划控制信号发现与定位AI 解读

Scientists often must simultaneously localize and discover signals. For instance, in genetic fine-mapping, high correlations between nearby genetic variants make it hard to identify the exact locations of causal variants. So the statistical task is to output as many disjoint regions containing a signal as possible, each as small as possible, while controlling false positives. Similar problems arise in any application where signals cannot be perfectly localized, such as…

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基于平滑欧拉示性数变换的随机形状建模与统计推断AI 解读

In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two chi-squared statistic-based algorithms for testing hypotheses on random shapes. Simulation studies are presented to validate our mathematical derivations and to compare our algorithms with state-of-the-art methods to demonstrate the utility of…

图对齐随机分区模型（GARP）AI 解读

Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the biological relations of the clusters. The increasing availability of large genomic data requires new statistical tools to perform model-based clustering and infer the relationship between homogeneous subgroups of units. Motivated by…

基于Tyler M估计量的大维形状矩阵检验AI 解读

Tyler's M estimator, as a robust alternative to the sample covariance matrix, has been widely applied in robust statistics. However, classical theory on Tyler's M estimator is mainly developed in the low-dimensional regime for elliptical populations. It remains largely unknown when the parameter of dimension p grows proportionally to the sample size n for general populations. By utilizing the eigenvalues of Tyler's M estimator, this article develops tests for the identity…

高维矩阵值序列的建模与学习AI 解读

We propose a new matrix factor model, named RaDFaM, which is strictly derived based on the general rank decomposition and assumes a structure of a high-dimensional vector factor model for each basis vector. RaDFaM contributes a novel class of low-rank latent structure that makes tradeoff between signal intensity and dimension reduction from the perspective of tensor subspace. Based on the intrinsic separable covariance structure of RaDFaM, for a collection of matrix-valued…

高维因子模型中基于自助样本协方差矩阵的共同因子个数检验AI 解读

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked…

共形预测集的选择与聚合AI 解读

Conformal prediction is a generic methodology for finite-sample valid distribution-free prediction. This technique has garnered a lot of attention in the literature partly because it can be applied with any machine learning algorithm that provides point predictions to yield valid prediction regions. Of course, the efficiency (width/volume) of the resulting prediction region depends on the performance of the machine learning algorithm. In the context of point prediction,…

Sharp-SSL：用于半监督学习的选择性高维轴对齐随机投影AI 解读

We propose a new method for high-dimensional semi-supervised learning problems based on the careful aggregation of the results of a low-dimensional procedure applied to many axis-aligned random projections of the data. Our primary goal is to identify important variables for distinguishing between the classes; existing low-dimensional methods can then be applied for final class assignment. To this end, we score projections according to their class-distinguishing ability; for…

聚类干扰下随机政策效应的高效非参数估计AI 解读

Interference occurs when a unit's treatment (or exposure) affects another unit's outcome. In some settings, units may be grouped into clusters such that it is reasonable to assume that interference, if present, only occurs between individuals in the same cluster, i.e., there is clustered interference. Various causal estimands have been proposed to quantify treatment effects under clustered interference from observational data, but these estimands either entail treatment…

相关阈值筛选后高斯变量集合的独立性推断AI 解读

We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. This set is selected via a very simple approach: these are the variables for which the correlation with all other variables falls below some threshold. Unlike other settings in selective inference, failure to account for the selection step leads to excessively conservative (as opposed to anti-conservative) results. We propose a new test that conditions…

半监督模型中的极值统计AI 解读

We consider extreme value analysis in a semi-supervised setting, where we observe, next to the n data on the target variable, n+m data on one or more covariates.This is called the semi-supervised model with n labeled and m unlabeled data.By exploiting the tail dependence between the target variable and the covariates, we derive estimators for the extreme value index and extreme quantiles of the target variable in this setting and establish their asymptotic behavior.Our…

广义贝叶斯加性回归树：突破条件共轭限制AI 解读

Bayesian additive regression trees have seen increased interest in recent years due to their ability to combine machine learning techniques with principled uncertainty quantification. The Bayesian backfitting algorithm used to fit BART models, however, limits their application to a small class of models for which conditional conjugacy exists. In this article, we greatly expand the domain of applicability of BART to arbitrary generalized BART models by introducing a very…

不完美计算机模型的 Sobolev 校准AI 解读

Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer models, Sobolev calibration, which can rule out calibration parameters that generate overfitting calibrated functions. We prove that the Sobolev calibration enjoys desired theoretical properties including fast convergence rate, asymptotic…

CARE：组成数据的大型精度矩阵估计AI 解读

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this…

未观测混杂下因果推断的双重有效与双重锐性敏感性分析AI 解读

We consider the problem of constructing bounds on the average treatment effect (ATE) when unmeasured confounders exist but have bounded influence. Specifically, we assume that omitted confounders could not change the odds of treatment for any unit by more than a fixed factor. We derive the sharp partial identification bounds implied by this assumption by leveraging distributionally robust optimization, and we propose estimators of these bounds with several novel robustness…

利用辅助信息的含噪矩阵补全统计推断AI 解读

This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent factors; the other part models the effects of the observed covariates through a coefficient matrix which is composed of high-dimensional column vectors. We model the observational pattern of the responses through a logistic regression of the…

通过非可逆模拟回火实现自动再生模拟AI 解读

Simulated Tempering (ST) is an MCMC algorithm for complex target distributions that operates on a path between the target and a more amenable reference distribution. Crucially, if the reference enables i.i.d. sampling, ST is regenerative and can be parallelized across independent tours. However, the difficulty of tuning ST has hindered its widespread adoption. In this work, we develop a simple nonreversible ST (NRST) algorithm, a general theoretical analysis of ST, and an…

带稀疏惩罚的稳健个性化联邦学习AI 解读

Federated learning (FL) is an emerging topic due to its advantage in collaborative learning with distributed data. Due to the heterogeneity in the local data-generating mechanism, it is important to consider personalization when developing federated learning methods. In this work, we propose a personalized federated learning (PFL) method to address the robust regression problem. Specifically, we aim to learn the regression weight by solving a Huber loss with the sparse fused…

大型有向网络上的重复故障建模AI 解读

Many lifeline infrastructure systems consist of thousands of components configured in a complex directed network. Disruption of the infrastructure constitutes a recurrent failure process over a directed network. Statistical inference for such network recurrence data is challenging because of the large number of nodes with irregular connections among them. Motivated by 16 years of Scottish Water operation records, we propose a network Gamma-Poisson Autoregressive NHPP (GPAN)…

标签分布迁移下的双重灵活估计AI 解读

In studies ranging from clinical medicine to policy research, complete data are usually available from a population P, but the quantity of interest is often sought for a related but different population Q which only has partial data. We consider the setting when both outcome Y and covariate X are available from P but only X is available from Q, under the label shift assumption; that is, the conditional distribution of X given Y is the same in the two populations. To estimate…

未观测事件参数的置信区间AI 解读

Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics and related fields, which was extensively studied in the context of point estimation. In this work we introduce a novel interval estimation scheme for unobserved events. Our proposed framework applies selective inference, as we construct…

基于多项比较首选结果的排序推断AI 解读

This paper considers ranking inference of $n$ items based on the observed data on the top choice among $M$ randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for $M$-way ranking with only the top choice observed and is an extension of the celebrated Bradley-Terry-Luce model that corresponds to $M=2$. Under a uniform sampling scheme in which any $M$ distinguished items are selected for comparisons with probability $p$ and the…

高维时间序列中可解释且高效的无限阶向量自回归模型AI 解读

As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long been hindered by its non-identifiability, computational intractability, and difficulty of interpretation, especially for high-dimensional time series. This paper proposes a novel sparse infinite-order VAR model for high-dimensional time…

高维数据的无模型统计推断AI 解读

This article aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we propose a new test statistic and show that its asymptotic distribution is χ2 distribution whose degree of freedom does not depend on the unknown population distribution. We further conduct power analysis under local alternative hypotheses. In…