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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.
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Improved Shrinkage Prediction under a Spiked Covariance Structure
We develop a novel shrinkage rule for prediction in a high-dimensional non-exchangeable hierarchical Gaussian model with an unknown spiked covariance structure. We propose a family of priors for the mean parameter, governed by a power hyper-parameter, which encompasses independent to highly dependent scenarios. Corresponding to popular loss functions such as quadratic, generalized absolute, and Linex losses, these prior models induce a wide class of shrinkage predictors that involve quadratic forms of smooth functions of the unknown covariance. By using uniformly consistent estimators of these quadratic forms, we propose an efficient procedure for evaluating these predictors which outperforms factor model based direct plug-in approaches. We further improve our predictors by considering possible reduction in their variability through a novel coordinate-wise shrinkage policy that only uses covariance level information and can be adaptively tuned using the sample eigen structure. Finally, we extend our disaggregate model based methodology to prediction in aggregate models. We propose an easy-to-implement functional substitution method for predicting linearly aggregated targets and establish asymptotic optimality of our proposed procedure. We present simulation experiments as well as real data examples illustrating the efficacy of the proposed method.
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- Award ID(s):
- 1934568
- PAR ID:
- 10348850
- Date Published:
- Journal Name:
- Journal of machine learning research
- Volume:
- 22
- Issue:
- 180
- ISSN:
- 1532-4435
- Page Range / eLocation ID:
- 1 - 40
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
