Statistica Sinica最新文献

The use of complex three-dimensional (3D) objects is growing in various applications as data collection techniques continue to evolve. Identifying and locating significant effects within these objects is essential for making informed decisions based on the data. This article presents an advanced nonparametric method for learning and inferring complex 3D objects, enabling accurate estimation of the underlying signals and efficient detection and localization of significant effects. The proposed method addresses the problem of analyzing irregular-shaped 3D objects by modeling them as functional data and utilizing trivariate spline smoothing based on triangulations to estimate the underlying signals. We develop a highly efficient procedure that accurately estimates the mean and covariance functions, as well as the eigenvalues and eigenfunctions. Furthermore, we rigorously establish the asymptotic properties of these estimators. Additionally, a novel approach for constructing simultaneous confidence corridors to quantify estimation uncertainty is presented, and the procedure is extended to accommodate comparisons between two independent samples. The finite-sample performance of the proposed methods is illustrated through numerical experiments and a real-data application using the Alzheimer's Disease Neuroimaging Initiative database.

Classical regression generally assumes that all subjects follow a common model with the same set of parameters. With ever advancing capabilities of modern technologies to collect more subjects and more covariates, it has become increasingly common that there exist subgroups of subjects, and each group follows a different regression model with a different set of parameters. In this article, we propose a new approach for subgroup analysis in regression modeling. Specifically, we model the relation between a response and a set of primary predictors, while we explicitly model the heterogenous association given another set of auxiliary predictors, through the interaction between the primary and auxiliary variables. We introduce penalties to induce the sparsity and group structures within the regression coefficients, and to achieve simultaneous feature selection for both primary predictors that are significantly associated with the response, as well as the auxiliary predictors that define the subgroups. We establish the asymptotic guarantees in terms of parameter estimation consistency and cluster estimation consistency. We illustrate our method with an analysis of the functional magnetic resonance imaging data from the Adolescent Brain Cognitive Development Study.

The Generative Adversarial Network (GAN) was recently introduced in the literature as a novel machine learning method for training generative models. It has many applications in statistics such as nonparametric clustering and nonparametric conditional independence tests. However, training the GAN is notoriously difficult due to the issue of mode collapse, which refers to the lack of diversity among generated data. In this paper, we identify the reasons why the GAN suffers from this issue, and to address it, we propose a new formulation for the GAN based on randomized decision rules. In the new formulation, the discriminator converges to a fixed point while the generator converges to a distribution at the Nash equilibrium. We propose to train the GAN by an empirical Bayes-like method by treating the discriminator as a hyper-parameter of the posterior distribution of the generator. Specifically, we simulate generators from its posterior distribution conditioned on the discriminator using a stochastic gradient Markov chain Monte Carlo (MCMC) algorithm, and update the discriminator using stochastic gradient descent along with simulations of the generators. We establish convergence of the proposed method to the Nash equilibrium. Apart from image generation, we apply the proposed method to nonparametric clustering and nonparametric conditional independence tests. A portion of the numerical results is presented in the supplementary material.

Multi-modal data are prevalent in many scientific fields. In this study, we consider the parameter estimation and variable selection for a multi-response regression using block-missing multi-modal data. Our method allows the dimensions of both the responses and the predictors to be large, and the responses to be incomplete and correlated, a common practical problem in high-dimensional settings. Our proposed method uses two steps to make a prediction from a multi-response linear regression model with block-missing multi-modal predictors. In the first step, without imputing missing data, we use all available data to estimate the covariance matrix of the predictors and the cross-covariance matrix between the predictors and the responses. In the second step, we use these matrices and a penalized method to simultaneously estimate the precision matrix of the response vector, given the predictors, and the sparse regression parameter matrix. Lastly, we demonstrate the effectiveness of the proposed method using theoretical studies, simulated examples, and an analysis of a multi-modal imaging data set from the Alzheimer's Disease Neuroimaging Initiative.