Benjamin B. Risk

Matthew Drexler, Benjamin Risk, James J Lah et al.

Conventional multimodal data integration methods provide a comprehensive assessment of the shared or unique structure within each individual data type but suffer from several limitations such as the inability to handle high-dimensional data and identify nonlinear structures. In this paper, we introduce DeepJIVE, a deep-learning approach to performing Joint and Individual Variance Explained (JIVE). We perform mathematical derivation and experimental validations using both synthetic and real-world 1D, 2D, and 3D datasets. Different strategies of achieving the identity and orthogonality constraints for DeepJIVE were explored, resulting in three viable loss functions. We found that DeepJIVE can successfully uncover joint and individual variations of multimodal datasets. Our application of DeepJIVE to the Alzheimer's Disease Neuroimaging Initiative (ADNI) also identified biologically plausible covariation patterns between the amyloid positron emission tomography (PET) and magnetic resonance (MR) images. In conclusion, the proposed DeepJIVE can be a useful tool for multimodal data analysis.

Ze Jin, Benjamin B. Risk, David S. Matteson

Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model to a linear latent factor model with any number of both non-Gaussian components (signals) and Gaussian components (noise), where observations are linear combinations of independent components. Although the individual Gaussian components are not identifiable, the Gaussian subspace is identifiable. We introduce an estimator along with its optimization approach in which non-Gaussian and Gaussian components are estimated simultaneously, maximizing the discrepancy of each non-Gaussian component from Gaussianity while minimizing the discrepancy of each Gaussian component from Gaussianity. When the number of non-Gaussian components is unknown, we develop a statistical test to determine it based on resampling and the discrepancy of estimated components. Through a variety of simulation studies, we demonstrate the improvements of our estimator over competing estimators, and we illustrate the effectiveness of the test to determine the number of non-Gaussian components. Further, we apply our method to real data examples and demonstrate its practical value.