Leveraging mixed and incomplete outcomes via reduced-rank modeling

Chongliang Luo, Jian Liang, Gen Li, Fei Wang, Changshui Zhang, Dipak K. Dey, Kun Chen

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Multivariate outcomes with multivariate features of possibly high dimension are routinely produced in various fields. In many real-world problems, the collected outcomes are of mixed types, including continuous measurements, binary indicators and counts, and a substantial proportion of values may also be missing. Regardless of their types, these mixed outcomes are often interrelated, representing diverse reflections or views of the same underlying data generation mechanism. As such, an integrative multivariate model can be beneficial. We develop a mixed-outcome reduced-rank regression, which effectively enables information sharing among different prediction tasks. Our approach integrates mixed and partially observed outcomes belonging to the exponential dispersion family, by assuming that all the outcomes are associated through a shared low-dimensional subspace spanned by the features. A general singular value regularized criterion is proposed, and we establish a non-asymptotic performance bound for the proposed estimators in the context of supervised learning with mixed outcomes from an exponential family and under a general sampling scheme of missing data. An iterative singular value thresholding algorithm is developed for optimization with convergence guarantee. The effectiveness of our approach is demonstrated by simulation studies and an application on predicting health-related outcomes in longitudinal studies of aging.

Original languageEnglish
Pages (from-to)378-394
Number of pages17
JournalJournal of Multivariate Analysis
StatePublished - Sep 2018


  • Generalized linear model
  • Integrative learning
  • Missing data
  • Multivariate regression


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