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随机非线性定义域上函数型数据的可解释判别分析：阿尔茨海默病应用AI 解读

Abstract We introduce a novel framework for the classification of functional data supported on nonlinear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer’s disease from their cortical surface geometry and associated cortical thickness map. The proposed model is based upon a reformulation of the classification problem as a regularized multivariate functional linear regression model. This allows us to adopt a…

众多弱工具变量与无效工具变量下的工具变量估计AI 解读

Abstract We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the ‘sparsest rule’, which is equivalent to the plurality rule but becomes operational in computation algorithms, we investigate and prove the advantages of non-convex penalized approaches over other IV estimators based on two-step selections, in terms of selection consistency and accommodation for individually weak IVs.…

GENIUS-MAWII：应对大量弱且无效工具变量的稳健孟德尔随机化AI 解读

Abstract Mendelian randomization (MR) addresses causal questions using genetic variants as instrumental variables. We propose a new MR method, G-Estimation under No Interaction with Unmeasured Selection (GENIUS)-MAny Weak Invalid IV, which simultaneously addresses the 2 salient challenges in MR: many weak instruments and widespread horizontal pleiotropy. Similar to MR-GENIUS, we use heteroscedasticity of the exposure to identify the treatment effect. We derive influence…

用不完全 U 统计量检验可能不规则模型中的大量约束AI 解读

Abstract We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order or even larger than the number of observed samples. Moreover, standard distributional approximations may be invalid due to irregularities in the null hypothesis. We propose a general testing methodology that aims to circumvent…

协变量漂移下预测集的双重稳健校准AI 解读

Abstract Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semi-parametric efficiency theory for more efficient uncertainty quantification. We consider the problem of obtaining well-calibrated prediction regions that can data adaptively account for a shift in the distribution of covariates between training and test data. Under a…

高维多项分布检验及其文本分析应用AI 解读

Abstract Motivated by applications in text mining and discrete distribution inference, we test for equality of probability mass functions of K groups of high-dimensional multinomial distributions. Special cases of this problem include global testing for topic models, two-sample testing in authorship attribution, and closeness testing for discrete distributions. A test statistic, which is shown to have an asymptotic standard normal distribution under the null hypothesis, is…

非参数多元有限混合模型的完整模型估计AI 解读

Abstract This paper addresses the problem of full-model estimation for non-parametric finite mixture models. It presents an approach for selecting the number of components and the subset of discriminative variables (i.e. the subset of variables having different distributions among the mixture components) by considering an upper bound on the number of components (this number being allowed to increase with the sample size). The proposed approach considers a discretization of…

网络潜在生长过程的根节点与社区推断AI 解读

Abstract Many statistical models for networks overlook the fact that most real-world networks are formed through a growth process. To address this, we introduce the Preferential Attachment Plus Erdős–Rényi model, where we let a random network G be the union of a preferential attachment (PA) tree T and additional Erdős–Rényi (ER) random edges. The PA tree captures the underlying growth process of a network where vertices/edges are added sequentially, while the ER component…

通过平均场变分近似进行贝叶斯模型选择AI 解读

Abstract This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference that allows latent variables and model misspecification. Concretely, we show a Bernstein–von Mises (BvM) theorem for the variational distribution from MF under possible model misspecification, which implies the distributional convergence of MF variational approximation to a normal distribution…

Rajendra Bhansali 对《因果模型的参数化与模拟》的讨论意见AI 解读

Contribution: My own introduction to the subject area of this paper is through the notion of Granger causality, a topic which has attracted much attention in time series analysis and related disciplines, including signal processing. The authors have proposed a new approach to causal models. However, this involves working with full density functions. It seems to me that, from a data analysis point of view, the authors’ approach might be a bit too general, and it might be…

Heather Battey对《因果模型的参数化与模拟》的讨论评论AI 解读

My brief comment relates to the inferential discussion of Section 5. The sample-space factorization of the joint probability from the marginal structural model induces a parameter-space factorization of the likelihood function, with the implication that θZX is orthogonal to (⁠θY|X*,ϕYZ|X*⁠) in the sense of, e.g. Cox and Reid (1987), and leading to the simplified asymptotic covariance matrix of Theorem 5.1. The parameter cut discussed at the beginning of Section 5 also…

Richard Guo 对《因果模型的参数化与模拟》的讨论：两种分解与密度比AI 解读

I congratulate Evans and Didelez warmly on this innovative and inspiring paper. Here, I offer my interpretation of the approach in terms of two factorizations and a density ratio. Any distribution over Z,X,Y can be factorized in two ways: Factorization C−1 is the usual one; it is factorization A−1 that is the focus of the two authors. More concretely, suppose ϕZY∣X(z,y∣x) is a conditional copula density, i.e. for every value of x, (z,y)↦ϕZY∣X(z,y∣x) is a density function…

马丁努森对《因果模型的参数化与模拟》的讨论AI 解读

I congratulate the authors on an interesting and useful contribution to the literature on causal inference. The authors propose a nice way of generating data so that a given causal structure of interest is preserved. This is a handy tool to have when for instance one needs to generate data to investigate small sample performance of a new inference procedure. I find it less attractive to use the suggested procedure for estimation purposes as is also alluded to in the paper…

A. Philip Dawid对《因果模型的参数化与模拟》的讨论意见AI 解读

When discussing causal inference in sequential problems, the authors only consider interventions that set their target variables to pre-specified fixed values. A more practically relevant aim, as considered by Dawid and Didelez (2010), is to assess the effect of a pre-specified dynamic treatment strategy, which details how each decision is to depend (possibly even stochastically) on previously observed variables. Can the methods of this paper be applied to this case?

从极端数据估计指向根节点的有向树AI 解读

Abstract We propose a new method to estimate a root-directed spanning tree from extreme data. Prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of a max-linear Bayesian network, which has been designed for modelling causality in extremes. The algorithm estimates bivariate scores and returns a root-directed spanning tree. It performs extremely well on benchmark data and on new…

通过迭代投影奇异值分解进行半参数张量因子分析AI 解读

Abstract This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively…

多元函数型数据的梯度同步性及脑连接应用AI 解读

Abstract Quantifying the association between components of multivariate random curves is of general interest and is a ubiquitous and basic problem that can be addressed with functional data analysis. An important application is the problem of assessing functional connectivity based on functional magnetic resonance imaging (fMRI), where one aims to determine the similarity of fMRI time courses that are recorded on anatomically separated brain regions. In the functional brain…

Abstract This paper presents a conformal inference method for out-of-distribution testing that leverages side information from labelled outliers, which are commonly underutilized or even discarded by conventional conformal p-values. This solution is practical and blends inductive and transductive inference strategies to adaptively weight conformal p-values, while also automatically leveraging the most powerful model from a collection of one-class and binary classifiers.…

预算约束下组合治疗的最优个体化治疗规则AI 解读

Abstract The individualized treatment rule (ITR), which recommends an optimal treatment based on individual characteristics, has drawn considerable interest from many areas such as precision medicine, personalized education, and personalized marketing. Existing ITR estimation methods mainly adopt 1 of 2 or more treatments. However, a combination of multiple treatments could be more powerful in various areas. In this paper, we propose a novel double encoder model (DEM) to…

Abstract The aim of this article is to establish a causal link between the policies implemented by technology companies and the outcomes they yield within intricate temporal and/or spatial dependent experiments. We propose a novel temporal/spatio-temporal Varying Coefficient Decision Process model, capable of effectively capturing the evolving treatment effects in situations characterized by temporal and/or spatial dependence. Our methodology encompasses the decomposition of…

同时方向推断AI 解读

Abstract We consider the problem of inference on the signs of n>1 parameters. We aim to provide 1−α post hoc confidence bounds on the number of positive and negative (or non-positive) parameters, with a simultaneous guarantee, for all subsets of parameters. We suggest to start by using the data to select the direction of the hypothesis test for each parameter; then, adjust the p-values of the one-sided hypotheses for the selection, and use the adjusted p-values for…

HulC：利用凸包构造置信区域AI 解读

Abstract We develop and analyse the HulC, an intuitive and general method for constructing confidence sets using the convex hull of estimates constructed from subsets of the data. Unlike classical methods which are based on estimating the (limiting) distribution of an estimator, the HulC is often simpler to use and effectively bypasses this step. In comparison to the bootstrap, the HulC requires fewer regularity conditions and succeeds in many examples where the bootstrap…

因果模型的参数化与模拟AI 解读

Abstract Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, the object of interest is often a marginal quantity of this other probability distribution. This creates many practical complications for statistical inference, even where the problem is non-parametrically identified. In particular, it is difficult to perform likelihood-based inference, or even to…

关于“通过深度学习自动检测时间序列变点”讨论的作者回复AI 解读

Detecting change points in data is challenging because of the range of possible types of change and types of behaviour of data when there is no change. Statistically efficient methods for detecting a change will depend on both of these features, and it can be difficult for a practitioner to develop an appropriate detection method for their application of interest. We show how to automatically generate new offline detection methods based on training a neural network. Our…