Integrating multi-source block-wise missing data in model selection

Xue, Fei; Qu, Annie

doi:10.48550/arxiv.1901.03797

Cited by 2 publications

(2 citation statements)

References 59 publications

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“…We later numerically compare our method with Li et al (2013) and other solutions. Xue and Qu (2019) studied regression of multi-source data with missing values involving neuroimaging features. However, the images were summarized as vectors, instead of tensors, and were placed on the predictor side, while the response was a scalar.…”

Section: Introductionmentioning

confidence: 99%

Partially Observed Dynamic Tensor Response Regression

Zhou

Sun

Zhang

et al. 2020

Preprint

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In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially observed, rendering many existing methods inapplicable. In this article, we develop a regression model with partially observed dynamic tensor as the response and external covariates as the predictor. We introduce the low-rank, sparsity and fusion structures on the regression coefficient tensor, and consider a loss function projected over the observed entries. We develop an efficient non-convex alternating updating algorithm, and derive the finite-sample error bound of the actual estimator from each step of our optimization algorithm. Unobserved entries in tensor response have imposed serious challenges. As a result, our proposal differs considerably in terms of estimation algorithm, regularity conditions, as well as theoretical properties, compared to the existing tensor completion or tensor response regression solutions. We illustrate the efficacy of our proposed method using simulations, and two real applications, a neuroimaging dementia study and a digital advertising study.

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Section: Introductionmentioning

confidence: 99%

Partially Observed Dynamic Tensor Response Regression

Zhou

Sun

Zhang

et al. 2020

Preprint

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“…recently proposed an integrative reduced-rank regression to model multivariate responses given multi-view data as predictors. Xue and Qu (2019) developed an estimating equations approach to accommodate block missing patterns in multimodal data. Their methods are supervised, but both focused on parameter estimation and variable selection instead of statistical inference.…”

Section: Introductionmentioning

confidence: 99%

Integrative Factor Regression and Its Inference for Multimodal Data Analysis

2019

Preprint

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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 employed in integrative analysis of multimodal data, and is particularly useful to overcome the curse of high dimensionality and high correlations of multimodal data. 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 thus bridges an important gap. We study the empirical performance of our methods through simulations, and further illustrate with a multimodal neuroimaging analysis.

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Integrating multi-source block-wise missing data in model selection

Cited by 2 publications

References 59 publications

Partially Observed Dynamic Tensor Response Regression

Partially Observed Dynamic Tensor Response Regression

Integrative Factor Regression and Its Inference for Multimodal Data Analysis

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