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Unsupervised latent variable models-blind source separation (BSS) especially-enjoy a strong reputation for their interpretability. But they seldom combine the rich diversity of information available in multiple datasets, even though multidatasets yield insightful joint solutions otherwise unavailable in isolation. We present a direct, principled approach to multidataset combination that takes advantage of multidimensional subspace structures. In turn, we extend BSS models to capture the underlying modes of shared and unique variability across and within datasets. Our approach leverages joint information from heterogeneous datasets in a flexible and synergistic fashion. We call this method multidataset independent subspace analysis (MISA). Methodological innovations exploiting the Kotz distribution for subspace modeling, in conjunction with a novel combinatorial optimization for evasion of local minima, enable MISA to produce a robust generalization of independent component analysis (ICA), independent vector analysis (IVA), and independent subspace analysis (ISA) in a single unified model. We highlight the utility of MISA for multimodal information fusion, including sample-poor regimes ( N = 600 ) and low signal-to-noise ratio, promoting novel applications in both unimodal and multimodal brain imaging data.

Blind source separation algorithms such as independent component analysis (ICA) are widely used in the analysis of neuroimaging data. To leverage larger sample sizes, different data holders/sites may wish to collaboratively learn feature representations. However, such datasets are often privacy-sensitive, precluding centralized analyses that pool the data at one site. In this work, we propose a differentially private algorithm for performing ICA in a decentralized data setting. Due to the high dimension and small sample size, conventional approaches to decentralized differentially private algorithms suffer in terms of utility. When centralizing the data is not possible, we investigate the benefit of enabling limited collaboration in the form of generating jointly distributed random noise. We show that such (anti) correlated noise improves the privacy-utility trade-off, and can reach the same level of utility as the corresponding non-private algorithm for certain parameter choices. We validate this benefit using synthetic and real neuroimaging datasets. We conclude that it is possible to achieve meaningful utility while preserving privacy, even in complex signal processing systems.

Linear independent component analysis (ICA) is a standard signal processing technique that has been extensively used on neuroimaging data to detect brain networks with coherent brain activity (functional MRI) or covarying structural patterns (structural MRI). However, its formulation assumes that the measured brain signals are generated by a linear mixture of the underlying brain networks and this assumption limits its ability to detect the inherent nonlinear nature of brain interactions. In this paper, we introduce nonlinear independent component estimation (NICE) to structural MRI data to detect abnormal patterns of gray matter concentration in schizophrenia patients. For this biomedical application, we further addressed the issue of model regularization of nonlinear ICA by performing dimensionality reduction prior to NICE, together with an appropriate control of the complexity of the model and the usage of a proper approximation of the probability distribution functions of the estimated components. We show that our results are consistent with previous findings in the literature, but we also demonstrate that the incorporation of nonlinear associations in the data enables the detection of spatial patterns that are not identified by linear ICA. Specifically, we show networks including basal ganglia, cerebellum and thalamus that show significant differences in patients versus controls, some of which show distinct nonlinear patterns.