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This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression approach. The primary motivation is to estimate an…
Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…
In multi-state models based on high-dimensional data, effective modeling strategies are required to determine an optimal, ideally parsimonious model. In particular, linking covariate effects across transitions is needed to conduct joint…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
The goal of reinforcement learning (RL) is to let an agent learn an optimal control policy in an unknown environment so that future expected rewards are maximized. The model-free RL approach directly learns the policy based on data samples.…
In the fight against hard-to-treat diseases such as cancer, it is often difficult to discover new treatments that benefit all subjects. For regulatory agency approval, it is more practical to identify subgroups of subjects for whom the…
In this manuscript, we study the problem of scalar-on-distribution regression; that is, instances where subject-specific distributions or densities, or in practice, repeated measures from those distributions, are the covariates related to a…
We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…
For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training…
In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…
Logistic regression is widely used in many areas of knowledge. Several works compare the performance of lasso and maximum likelihood estimation in logistic regression. However, part of these works do not perform simulation studies and the…
In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive…
Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the…
We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection…
We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…
Interpretable rationales for model predictions play a critical role in practical applications. In this study, we develop models possessing interpretable inference process for structured prediction. Specifically, we present a method of…
We address a classical problem in statistics: adding two-way interaction terms to a regression model. As the covariate dimension increases quadratically, we develop an estimator that adapts well to this increase, while providing accurate…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…