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存在隐蔽混杂的因果网络发现与推断AI 解读

This article proposes a novel causal discovery and inference method called GrIVET for a Gaussian directed acyclic graph with unmeasured confounders. GrIVET consists of an order-based causal discovery method and a likelihood-based inferential procedure. For causal discovery, we generalize the existing peeling algorithm to estimate the ancestral relations and candidate instruments in the presence of hidden confounders. Based on this, we propose a new procedure for instrumental…

存在混杂时的非线性因果发现AI 解读

This article introduces a causal discovery method to learn nonlinear relationships in a directed acyclic graph with correlated Gaussian errors due to confounding. First, we derive model identifiability under the sublinear growth assumption. Then, we propose a novel method, named the Deconfounded Functional Structure Estimation (DeFuSE), consisting of a deconfounding adjustment to remove the confounding effects and a sequential procedure to estimate the causal order of…

无效工具变量与 GWAS 汇总数据下的转录组关联研究因果推断AI 解读

Transcriptome-wide association studies (TWAS) have recently emerged as a popular tool to discover (putative) causal genes by integrating an outcome GWAS dataset with another gene expression/transcriptome GWAS (called eQTL) dataset. In our motivating and target application, we'd like to identify causal genes for low-density lipoprotein cholesterol (LDL), which is crucial for developing new treatments for hyperlipidemia and cardiovascular diseases. The statistical principle…

高维检验中渐近独立的U统计量AI 解读

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper constructs a family of U-statistics as unbiased estimators of the $\ell_{p}$-norms of those features. We show that under the null hypothesis, the U-statistics of different finite orders are asymptotically independent and normally distributed.…

大型有向无环图的似然比检验AI 解读

Inference of directional pairwise relations between interacting units in a directed acyclic graph (DAG), such as a regulatory gene network, is common in practice, imposing challenges because of lack of inferential tools. For example, inferring a specific gene pathway of a regulatory gene network is biologically important. Yet, frequentist inference of directionality of connections remains largely unexplored for regulatory models. In this article, we propose constrained…

高维约束最大似然推断AI 解读

Inference in a high-dimensional situation may involve regularization of a certain form to treat overparameterization, imposing challenges to inference. The common practice of inference uses either a regularized model, as in inference after model selection, or bias-reduction known as “debias.” While the first ignores statistical uncertainty inherent in regularization, the second reduces the bias inbred in regularization at the expense of increased variance. In this article,…

通过约束似然重建高斯有向无环图AI 解读

Directed acyclic graphs are widely used to describe directional pairwise relations. Such relations are estimated by reconstructing a directed acyclic graph's structure, which is challenging when the ordering of nodes of the graph is unknown. In such a situation, existing methods such as the neighbourhood and search-and-score methods have high estimation errors or computational complexities, especially when a local or sequential approach is used to enumerate edge directions…

高维均值的自适应双样本检验AI 解读

Several two-sample tests for high-dimensional data have been proposed recently, but they are powerful only against certain limited alternative hypotheses. In practice, since the true alternative hypothesis is unknown, it is unclear how to choose a powerful test. We propose an adaptive test that maintains high power across a wide range of situations, and study its asymptotic properties. Its finite sample performance is compared with existing tests. We apply it and other tests…

多个无向图的结构追寻AI 解读

Gaussian graphical models are useful to analyze and visualize conditional dependence relationships between interacting units. Motivated from network analysis under different experimental conditions, such as gene networks for disparate cancer subtypes, we model structural changes over multiple networks with possible heterogeneities. In particular, we estimate multiple precision matrices describing dependencies among interacting units through maximum penalized likelihood. Of…

无向图上的同步分组搜索与特征选择AI 解读

In high-dimensional regression, grouping pursuit and feature selection have their own merits while complementing each other in battling the curse of dimensionality. To seek a parsimonious model, we perform simultaneous grouping pursuit and feature selection over an arbitrary undirected graph with each node corresponding to one predictor. When the corresponding nodes are reachable from each other over the graph, regression coefficients can be grouped, whose absolute values…

基于似然的变量选择与精确参数估计AI 解读

In high-dimensional data analysis, feature selection becomes one means for dimension reduction, which proceeds with parameter estimation. Concerning accuracy of selection and estimation, we study nonconvex constrained and regularized likelihoods in the presence of nuisance parameters. Theoretically, we show that constrained L(0)-likelihood and its computational surrogate are optimal in that they achieve feature selection consistency and sharp parameter estimation, under one…