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Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We propose an iterative variable selection scheme for high-dimensional data with binary outcomes. The scheme adopts a structured screen-and-select framework and uses non-local prior-based Bayesian model selection within the same. The…
Variable selection for recovering sparsity in nonadditive nonparametric models has been challenging. This problem becomes even more difficult due to complications in modeling unknown interaction terms among high dimensional variables. There…
Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric…
We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
This paper proposes a novel testing procedure for selecting a sparse set of covariates that explains a large dimensional panel. Our selection method provides correct false detection control while having higher power than existing…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero, covariates without relationships to the response often…
Feature screening approaches are effective in selecting active features from data with ultrahigh dimensionality and increasing complexity; however, the majority of existing feature screening approaches are either restricted to a univariate…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
We consider the problem of variable selection in varying-coefficient functional linear models, where multiple predictors are functions and a response is a scalar and depends on an exogenous variable. The varying-coefficient functional…
Variable selection in high dimensional space has challenged many contemporary statistical problems from many frontiers of scientific disciplines. Recent technology advance has made it possible to collect a huge amount of covariate…
Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model…