Independent vector analysis with sparse inverse covariance estimation

A fundamental task in the analysis of multiple sets of data is the source recovery problem when little is known about the observed data. Real-world applications for this problem include the analysis of medical imaging such as fMRIs, multi-modal disinformation detection, video surveillance, and molecular data fusion, among others. Independent Vector Analysis (IVA) is an ongoing area of research which jointly decomposes multiple datasets to recover latent sources. Since it is formulated within the maximum likelihood (ML) framework, IVA benefits from the exploitation of prior knowledge -- forms of diversity -- in the estimation of its probability density function (PDF). In recent years, application of IVA has grown by the imposition of constraints due to various forms of diversity. By taking advantage of prior information, which is usually known beforehand, the IVA solution improves in performance. An important form of diversity is sparsity. In real-world situations, it is common for latent variables to confound relationships between covariates and impede source recovery, allowing for sparsity assumptions to be made in the IVA solution. If applied to the IVA solution, leveraging known sparsity can reduce the effects of confounding variables, isolating the most important relationships in the observed data. As such, an algorithm which imposes sparsity in the IVA solution is attractive as it may improve separation performance. The challenges we face are determining how to manipulate IVA to impose sparsity and which algorithm to use for sparse estimation. In this thesis, we begin with the background and derivation of IVA and we discuss the way in which we may impose sparsity constraints through the inverse covariance matrix to manipulate the IVA solution. Next, we review three competing techniques for sparse inverse covariance estimation, simulating their performance under varying parameters and demonstrating their strengths and weaknesses. Finally, we impart our accumulated research onto a mathematical framework which allows us to impose sparsity on the IVA solution and develop the IVA-SPICE algorithm whose flagship feature is the graphical lasso algorithm for sparse inverse covariance estimation. Using simulated data, we show that by incorporating sparsity as a form of diversity in IVA, we increase its success when underlying data is sparse, thereby expanding its application in real-world problems.