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Multi-group data, which include the same set of variables on separate groups of samples, are commonly seen in practice. Such data structure consists of data from multiple groups and can be challenging to analyze due to data heterogeneity. We propose a novel Joint and Individual Component Regression (JICO) model to analyze multi-group data. Our proposed model decomposes the response into shared and group-specific components, which are driven by low-rank approximations of joint and individual structures from the predictors respectively. The joint structure has the same regression coefficients across multiple groups, whereas individual structures have group-specific regression coefficients. We formulate this framework under the representation of latent components and propose an iterative algorithm to solve for the joint and individual scores. We us the Continuum Regression (CR) to estimate the latent scores, which provides a unified framework that covers the Ordinary Least Squares (OLS), the Partial Least Squares (PLS), and the Principal Component Regression (PCR) as its special cases. We show that JICO attains a good balance between global and group-specific models and remains flexible due to the usage of CR. We conduct simulation studies and analysis of an Alzheimer's disease dataset to further demonstrate the effectiveness of JICO. R package of JICO is available online at . for this article are available online. [ABSTRACT FROM AUTHOR]

Data are generated at an unprecedented rate and scale these days across many disciplines. The field of streaming data analysis has emerged as a result of new data collection and storage technologies in various areas, such as air pollution monitoring, detection of traffic congestion, disease surveillance, and recommendation systems. In this paper, we consider the problem of model estimation for data streams in reproducing kernel Hilbert spaces. We propose an adaptive supervised learning method with a data sparsity constraint that uses limited storage spaces and can handle nonstationary models. We demonstrate the competitive performance of the proposed method using simulations and analysis of the bike sharing dataset. [ABSTRACT FROM AUTHOR]

Many biomedical studies collect data of mixed types of variables from multiple groups of subjects. Some of these studies aim to find the group‐specific and the common variation among all these variables. Even though similar problems have been studied by some previous works, their methods mainly rely on the Pearson correlation, which cannot handle mixed data. To address this issue, we propose a latent mixed Gaussian copula (LMGC) model that can quantify the correlations among binary, ordinal, continuous, and truncated variables in a unified framework. We also provide a tool to decompose the variation into the group‐specific and the common variation over multiple groups via solving a regularized M‐estimation problem. We conduct extensive simulation studies to show the advantage of our proposed method over the Pearson correlation‐based methods. We also demonstrate that by jointly solving the M‐estimation problem over multiple groups, our method is better than decomposing the variation group by group. We also apply our method to a Chlamydia trachomatis genital tract infection study to demonstrate how it can be used to discover informative biomarkers that differentiate patients. [ABSTRACT FROM AUTHOR]

Generalized linear models often have high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional subvector of the model's coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and are thus computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that, under certain regularity conditions, the Type-I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions. [ABSTRACT FROM AUTHOR]

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is particularly useful to overcome the curse of high dimensionality and high correlations. However, there is little work on statistical inference for factor analysis-based supervised modeling of multimodal data. In this article, we consider an integrative linear regression model that is built upon the latent factors extracted from multimodal data. We address three important questions: how to infer the significance of one data modality given the other modalities in the model; how to infer the significance of a combination of variables from one modality or across different modalities; and how to quantify the contribution, measured by the goodness of fit, of one data modality given the others. When answering each question, we explicitly characterize both the benefit and the extra cost of factor analysis. Those questions, to our knowledge, have not yet been addressed despite wide use of factor analysis in integrative multimodal analysis, and our proposal bridges an important gap. We study the empirical performance of our methods through simulations, and further illustrate with a multimodal neuroimaging analysis. [ABSTRACT FROM AUTHOR]