Covariate-Adjusted Tensor Classification in High Dimensions

In contemporary scientific research, it is often of great interest to predict a categorical response based on a high-dimensional tensor (i.e., multi-dimensional array) and additional covariates. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discri...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 114; no. 527; pp. 1305 - 1319
Main Authors: Pan, Yuqing, Mai, Qing, Zhang, Xin
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.07.2019
Taylor & Francis Group, LLC
Taylor & Francis Ltd
Subjects:
Algorithms
Classification
Computer simulation
Discriminant analysis
engineering
equations
Mathematical analysis
Multi-dimensional array
Multicategory classification
prediction
Regression analysis
Sparsity
Statistical methods
Statistics
Tensor classification and regression
Tensors
Theory and Methods
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary:In contemporary scientific research, it is often of great interest to predict a categorical response based on a high-dimensional tensor (i.e., multi-dimensional array) and additional covariates. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called the CATCH model (short for covariate-adjusted tensor classification in high-dimensions). The CATCH model efficiently integrates the covariates and the tensor to predict the categorical outcome. It also jointly explains the complicated relationships among the covariates, the tensor predictor, and the categorical response. The tensor structure is used to achieve easy interpretation and accurate prediction. To tackle the new computational and statistical challenges arising from the intimidating tensor dimensions, we propose a penalized approach to select a subset of the tensor predictor entries that affect classification after adjustment for the covariates. An efficient algorithm is developed to take advantage of the tensor structure in the penalized estimation. Theoretical results confirm that the proposed method achieves variable selection and prediction consistency, even when the tensor dimension is much larger than the sample size. The superior performance of our method over existing methods is demonstrated in extensive simulated and real data examples. Supplementary materials for this article are available online.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2018.1497500