Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Markov neighborhood regression for statistical inference of high-dimensional generalized linear models.

ABSTRACT: High-dimensional inference is one of fundamental problems in modern biomedical studies. However, the existing methods do not perform satisfactorily. Based on the Markov property of graphical models and the likelihood ratio test, this article provides a simple justification for the Markov neighborhood regression method such that it can be applied to statistical inference for high-dimensional generalized linear models with mixed features. The Markov neighborhood regression method is highly attractive in that it breaks the high-dimensional inference problems into a series of low-dimensional inference problems. The proposed method is applied to the cancer cell line encyclopedia data for identification of the genes and mutations that are sensitive to the response of anti-cancer drugs. The numerical results favor the Markov neighborhood regression method to the existing ones.

SUBMITTER: Sun L

PROVIDER: S-EPMC9427730 | biostudies-literature | 2022 Sep

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Markov neighborhood regression for statistical inference of high-dimensional generalized linear models.

Sun Lizhe L Liang Faming F

Statistics in medicine 20220610 20

High-dimensional inference is one of fundamental problems in modern biomedical studies. However, the existing methods do not perform satisfactorily. Based on the Markov property of graphical models and the likelihood ratio test, this article provides a simple justification for the Markov neighborhood regression method such that it can be applied to statistical inference for high-dimensional generalized linear models with mixed features. The Markov neighborhood regression method is highly attract ...[more]

PMID: 35688606

Similar Datasets

Statistical Inference for High-Dimensional Generalized Linear Models with Binary Outcomes.

Project description:This paper develops a unified statistical inference framework for high-dimensional binary generalized linear models (GLMs) with general link functions. Both unknown and known design distribution settings are considered. A two-step weighted bias-correction method is proposed for constructing confidence intervals and simultaneous hypothesis tests for individual components of the regression vector. Minimax lower bound for the expected length is established and the proposed confidence intervals are shown to be rate-optimal up to a logarithmic factor. The numerical performance of the proposed procedure is demonstrated through simulation studies and an analysis of a single cell RNA-seq data set, which yields interesting biological insights that integrate well into the current literature on the cellular immune response mechanisms as characterized by single-cell transcriptomics. The theoretical analysis provides important insights on the adaptivity of optimal confidence intervals with respect to the sparsity of the regression vector. New lower bound techniques are introduced and they can be of independent interest to solve other inference problems in high-dimensional binary GLMs.

| S-EPMC10292730 | biostudies-literature

Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach.

Project description:The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into prevention strategies or treatment decisions for both patients and physicians. High dimensional inference, including confidence intervals and hypothesis testing, has sparked much interest. While much work has been done in the linear regression setting, there is lack of literature on inference for high dimensional generalized linear models. We propose a novel and computationally feasible method, which accommodates a variety of outcome types, including normal, binomial, and Poisson data. We use a "splitting and smoothing" approach, which splits samples into two parts, performs variable selection using one part and conducts partial regression with the other part. Averaging the estimates over multiple random splits, we obtain the smoothed estimates, which are numerically stable. We show that the estimates are consistent, asymptotically normal, and construct confidence intervals with proper coverage probabilities for all predictors. We examine the finite sample performance of our method by comparing it with the existing methods and applying it to analyze a lung cancer cohort study.

| S-EPMC8442657 | biostudies-literature

LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.

Project description:This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central χ2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

| S-EPMC6750760 | biostudies-literature

Transfer Learning under High-dimensional Generalized Linear Models

Project description: Not available

| S-EPMC10982637 | biostudies-literature

Testing generalized linear models with high-dimensional nuisance parameter.

Project description:Generalized linear models often have a 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 sub-vector 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 thus are computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that under certain regularity conditions, the type I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions.

| S-EPMC9933885 | biostudies-literature

Bayesian inference for generalized linear mixed models.

Project description:Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.

| S-EPMC2883299 | biostudies-literature

Optimal errors and phase transitions in high-dimensional generalized linear models.

Project description:Generalized linear models (GLMs) are used in high-dimensional machine learning, statistics, communications, and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, error-correcting codes, or benchmark models in neural networks. We evaluate the mutual information (or "free entropy") from which we deduce the Bayes-optimal estimation and generalization errors. Our analysis applies to the high-dimensional limit where both the number of samples and the dimension are large and their ratio is fixed. Nonrigorous predictions for the optimal errors existed for special cases of GLMs, e.g., for the perceptron, in the field of statistical physics based on the so-called replica method. Our present paper rigorously establishes those decades-old conjectures and brings forward their algorithmic interpretation in terms of performance of the generalized approximate message-passing algorithm. Furthermore, we tightly characterize, for many learning problems, regions of parameters for which this algorithm achieves the optimal performance and locate the associated sharp phase transitions separating learnable and nonlearnable regions. We believe that this random version of GLMs can serve as a challenging benchmark for multipurpose algorithms.

| S-EPMC6431156 | biostudies-literature

A Regularization-Based Adaptive Test for High-Dimensional Generalized Linear Models.

Project description:In spite of its urgent importance in the era of big data, testing high-dimensional parameters in generalized linear models (GLMs) in the presence of high-dimensional nuisance parameters has been largely under-studied, especially with regard to constructing powerful tests for general (and unknown) alternatives. Most existing tests are powerful only against certain alternatives and may yield incorrect Type I error rates under high-dimensional nuisance parameter situations. In this paper, we propose the adaptive interaction sum of powered score (aiSPU) test in the framework of penalized regression with a non-convex penalty, called truncated Lasso penalty (TLP), which can maintain correct Type I error rates while yielding high statistical power across a wide range of alternatives. To calculate its p-values analytically, we derive its asymptotic null distribution. Via simulations, its superior finite-sample performance is demonstrated over several representative existing methods. In addition, we apply it and other representative tests to an Alzheimer's Disease Neuroimaging Initiative (ADNI) data set, detecting possible gene-gender interactions for Alzheimer's disease. We also put R package "aispu" implementing the proposed test on GitHub.

| S-EPMC7425805 | biostudies-literature

Tests for regression coefficients in high dimensional partially linear models.

Project description:We propose a U-statistics test for regression coefficients in high dimensional partially linear models. In addition, the proposed method is extended to test part of the coefficients. Asymptotic distributions of the test statistics are established. Simulation studies demonstrate satisfactory finite-sample performance.

| S-EPMC7236654 | biostudies-literature

Testing a single regression coefficient in high dimensional linear models.

Project description:In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

| S-EPMC5484175 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data