Xin Gao

High-dimensional regression with multivariate responses poses significant challenges when data are collected across multiple platforms, each with potentially correlated outcomes. In this paper, we introduce a multi-platform multivariate high-dimensional linear regression (MM-HLR) model for simultaneously modeling within-platform correlation and cross-platform information fusion. Our approach incorporates a mixture of Lasso and group Lasso penalties to promote both individual predictor sparsity and cross-platform group sparsity, thereby enhancing interpretability and estimation stability. We develop an efficient computational algorithm based on iteratively reweighted least squares and block coordinate descent to solve the resulting regularized optimization problem. We establish theoretical guarantees for our estimator, including oracle bounds on prediction error, estimation accuracy, and support recovery under mild conditions. Our simulation studies confirm the method’s strong empirical performance, demonstrating low bias, small variance, and robustness across various dimensions. The analysis of real financial data further validates the performance gains achieved by incorporating multivariate responses and integrating data across multiple platforms.

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 the dynamic Ising model as a special case. We formulate a likelihood-based approach for parameter estimation and statistical inference. We achieve efficient parameter estimation in high-dimensional settings through the use of the pseudo-likelihood method. To perform model selection, a birth-and-death Markov chain Monte Carlo algorithm is proposed to explore the model space and select the most suitable model.

We consider data integration problems where correlated data are collected from multiple platforms. Within each platform, there are linear relationships between the responses and a collection of predictors. We extend the linear models to include random errors coming from a much wider family of sub‐Gaussian and subexponential distributions. The goal is to select important predictors across multiple platforms, where the number of predictors and the number of observations both increase to infinity. We combine the marginal densities of the responses obtained from different platforms to form a composite likelihood and propose a model selection criterion based on Bayesian composite posterior probabilities. Under some regularity conditions, we prove that the model selection criterion is consistent to recover the union support of the predictors with divergent true model size.

Graphical log-linear models are effective for representing complex structures that emerge from high-dimensional data. It is challenging to fit an appropriate model in the high-dimensional setting and many existing methods rely on a convenient class of models, called decomposable models, which lend well to a stepwise approach. However, these methods restrict the pool of candidate models from which they can search, and these methods are difficult to scale. It can be shown that a non-decomposable model can be approximated by the decomposable model which is its minimal triangulation, thus extending the convenient computational properties of decomposable models to any model. In this paper, we propose a local genetic algorithm with a crossover-hill-climbing operator, adapted for log-linear graphical models. We show that the graphical local genetic algorithm can be used successfully to fit non-decomposable models for both a low number of variables and a high number of variables. We use the posterior probability as a measure of fitness and parallel computing to decrease the computation time.

Linear mixed-effects models are widely used in applications to analyze clustered, hierarchical, and longitudinal data. Model selection in linear mixed models is more challenging than that of linear models as the parameter vector in a linear mixed model includes both fixed effects and variance component parameters. When selecting the variance components of the random effects, the variance of the random effects must be non-negative and the parameters may lie on the boundary of the parameter space. Therefore, classical model selection methods cannot be directly used to handle this situation. In this article, we propose a modified BIC for model selection with linear mixed-effects models that can solve the case when the variance components are on the boundary of the parameter space. Through the simulation results, we found that the modified BIC performed better than the regular BIC in most cases for linear mixed models. The modified BIC was also applied to a real dataset to choose the most-appropriate model.

We propose a non-parametric method to cluster mixed data containing both continuous and discrete random variables. The product space of the continuous and discrete sample space is transformed into a new product space based on adaptive quantization on the continuous part. Detection of cluster patterns on the product space is determined locally by using a weighted modified chi-squared test. Our algorithm does not require any user input since the number of clusters is determined automatically by data. Simulation studies and real data analysis results show that our proposed method outperforms the benchmark method, AutoClass, in various settings.

Background: Many methods under the umbrella of inter-rater agreement (IRA) have been proposed to evaluate how well two or more medical experts agree on a set of outcomes. The objective of this work was to assess key IRA statistics in the context of multiple raters with binary outcomes. Methods: We simulated the responses of several raters (2–5) with 20, 50, 300, and 500 observations. For each combination of raters and observations, we estimated the expected value and variance of four commonly used inter-rater agreement statistics (Fleiss’ Kappa, Light’s Kappa, Conger’s Kappa, and Gwet’s AC1). Results: In the case of equal outcome prevalence (symmetric), the estimated expected values of all four statistics were equal. In the asymmetric case, only the estimated expected values of the three Kappa statistics were equal. In the symmetric case, Fleiss’ Kappa yielded a higher estimated variance than the other three statistics. In the asymmetric case, Gwet’s AC1 yielded a lower estimated variance than the three Kappa statistics for each scenario. Conclusion: Since the population-level prevalence of a set of outcomes may not be known a priori, Gwet’s AC1 statistic should be favored over the three Kappa statistics. For meaningful direct comparisons between IRA measures, transformations between statistics should be conducted.