An official website of the United States government
In this article, we investigate the problem of simultaneous change point inference and structure recovery in the context of high dimensional Gaussian graphical models with possible abrupt changes. In particular, motivated by neighborhood selection, we incorporate a threshold variable and an unknown threshold parameter into a joint sparse regression model which combines p l1-regularized node-wise regression problems together. The change point estimator and the corresponding estimated coefficients of precision matrices are obtained together. Based on that, a classifier is introduced to distinguish whether a change point exists. To recover the graphical structure correctly, a data-driven thresholding procedure is proposed. In theory, under some sparsity conditions and regularity assumptions, our method can correctly choose a homogeneous or heterogeneous model with high accuracy. Furthermore, in the latter case with a change point, we establish estimation consistency of the change point estimator, by allowing the number of nodes being much larger than the sample size. Moreover, it is shown that, in terms of structure recovery of Gaussian graphical models, the proposed thresholding procedure achieves model selection consistency and controls the number of false positives. The validity of our proposed method is justified via extensive numerical studies. Finally, we apply our proposed method to the S&P 500 dataset to show its empirical usefulness.
more »
« less
Drawing inferences for High‐dimensional Linear Models: A Selection‐assisted Partial Regression and Smoothing Approach
Inference for high-dimensional models is challenging as regular asymptotic the- ories are not applicable. This paper proposes a new framework of simultaneous estimation and inference for high-dimensional linear models. By smoothing over par- tial regression estimates based on a given variable selection scheme, we reduce the problem to a low-dimensional least squares estimation. The procedure, termed as Selection-assisted Partial Regression and Smoothing (SPARES), utilizes data split- ting along with variable selection and partial regression. We show that the SPARES estimator is asymptotically unbiased and normal, and derive its variance via a non- parametric delta method. The utility of the procedure is evaluated under various simulation scenarios and via comparisons with the de-biased LASSO estimators, a major competitor. We apply the method to analyze two genomic datasets and obtain biologically meaningful results.
more »
« less
- Award ID(s):
- 1712962
- PAR ID:
- 10106524
- Date Published:
- Journal Name:
- Biometrics
- ISSN:
- 1541-0420
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We combine weighting and Bayesian prediction in a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the probability of inclusion. We incorporate all the variables that are used in the weighting adjustment under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We improve small area estimation by dealing with different complex issues caused by real-life applications to obtain robust inference at finer levels for subdomains of interest. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and is implemented in the open-source R package rstanarm and available for public use. We evaluate the design-based properties of the Bayesian procedure. Simulation studies illustrate how the model-based prediction and weighting inference can outperform classical weighting. We apply the method to the New York Longitudinal Study of Wellbeing. The new approach generates smoothed weights and increases efficiency for robust finite population inference, especially for subsets of the population.more » « less
-
Categorical data analysis becomes challenging when high-dimensional sparse covariates are involved, which is often the case for omics data. We introduce a statistical procedure based on multinomial logistic regression analysis for such scenarios, including variable screening, model selection, order selection for response categories, and variable selection. We perform our procedure on high-dimensional gene expression data with 801 patients, 2426 genes, and five types of cancerous tumors. As a result, we recommend three finalized models: one with 74 genes achieves extremely low cross-entropy loss and zero predictive error rate based on a five-fold cross-validation; and two other models with 31 and 4 genes, respectively, are recommended for prognostic multi-gene signatures.more » « less
-
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional estimation techniques can be seen as variable selection that leads to a smaller set of variables (a “submodel”) where classical linear regression applies. We analyze linear regression estimators resulting from model selection by proving estimation error and linear representation bounds uniformly over sets of submodels. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in meaningfully interpreting the linear regression estimator obtained after exploring and reducing the variables and also in justifying post-model-selection inference. All results are derived under no model assumptions and are nonasymptotic in nature.more » « less
-
null (Ed.)Predictive models play a central role in decision making. Penalized regression approaches, such as least absolute shrinkage and selection operator (LASSO), have been widely used to construct predictive models and explain the impacts of the selected predictors, but the estimates are typically biased. Moreover, when data are ultrahigh-dimensional, penalized regression is usable only after applying variable screening methods to downsize variables. We propose a stepwise procedure for fitting generalized linear models with ultrahigh dimensional predictors. Our procedure can provide a final model; control both false negatives and false positives; and yield consistent estimates, which are useful to gauge the actual effect size of risk factors. Simulations and applications to two clinical studies verify the utility of the method.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
