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Optimal Sparse Linear Prediction for Block-missing Multi-modality Data Without Imputation

In modern scientific research, data are often collected from multiple modalities. Since different modalities could provide complementary information, statistical prediction methods using multimodality data could deliver better prediction performance than using single modality data. However, one special challenge for using multimodality data is related to block-missing data. In practice, due to dropouts or the high cost of measures, the observations of a certain modality can be missing completely for some subjects. In this paper, we propose a new direct sparse regression procedure using covariance from multimodality data (DISCOM). Our proposed DISCOM method includes two steps to find the optimal linear prediction of a continuous response variable using block-missing multimodality predictors. In the first step, rather than deleting or imputing missing data, we make use of all available information to estimate the covariance matrix of the predictors and the cross-covariance vector between the predictors and the response variable. The proposed new estimate of the covariance matrix is a linear combination of the identity matrix, the estimates of the intra-modality covariance matrix and the cross-modality covariance matrix. Flexible estimates for both the sub-Gaussian and heavy-tailed cases are considered. In the second step, based on the estimated covariance matrix and the estimated cross-covariance vector, an extended Lasso-type estimator is used to deliver a sparse estimate of the coefficients in the optimal linear prediction. The number of samples that are effectively used by DISCOM is the minimum number of samples with available observations from two modalities, which can be much larger than the number of samples with complete observations from all modalities. The effectiveness of the proposed method is demonstrated by theoretical studies, simulated examples, and a real application from the Alzheimer’s Disease Neuroimaging Initiative. The comparison between DISCOM and some existing methods also indicates the advantages of our proposed method.

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Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION [JASA]; Vol.115 No.531 September 2020

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1406 - 1419

Bahasa

English

ISBN/ISSN

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Klasifikasi

-

Tipe Isi

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Tipe Media

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Tipe Pembawa

-

Edisi

-

Subjek

PREDICTION
SPARSE REGRESSION
LASSO
MULTI-MODALITY
BLOCK-MISSING
HUBER’S M-ESTIMATE

Info Detail Spesifik

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Pernyataan Tanggungjawab

Guan Yu, Quefeng Li, Dinggang Shen, Yufeng Liu

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