Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces

Cross-channel unlabeled sensing addresses the problem of recovering a multi-channel signal from measurements that were shuffled across channels. This work expands the cross-channel unlabeled sensing framework to signals that lie in a union of subspaces. The extension allows for handling more complex signal structures and broadens the framework to tasks like compressed sensing. These mismatches between samples and channels often arise in applications such as whole-brain calcium imaging of freely moving organisms or multi-target tracking. We improve over previous models by deriving tighter bounds on the required number of samples for unique reconstruction, while supporting more general signal types. The approach is validated through an application in whole-brain calcium imaging, where organism movements disrupt sample-to-neuron mappings. This demonstrates the utility of our framework in real-world settings with imprecise sample-channel associations, achieving accurate signal reconstruction.

False Discovery Rate Control for Gaussian Graphical Models via Neighborhood Screening

Gaussian graphical models emerge in a wide range of fields. They model the statistical relationships between variables as a graph, where an edge between two variables indicates conditional dependence. Unfortunately, well-established estimators, such as the graphical lasso or neighborhood selection, are known to be susceptible to a high prevalence of false edge detections. False detections may encourage inaccurate or even incorrect scientific interpretations, with major implications in applications, such as biomedicine or healthcare. In this paper, we introduce a nodewise variable selection approach to graph learning and provably control the false discovery rate of the selected edge set at a self-estimated level. A novel fusion method of the individual neighborhoods outputs an undirected graph estimate. The proposed method is parameter-free and does not require tuning by the user. Benchmarks against competing false discovery rate controlling methods in numerical experiments considering different graph topologies show a significant gain in performance.

Reconstruction of Multivariate Sparse Signals from Mismatched Samples

Erroneous correspondences between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To systematically address this fundamental problem, we pose it as a signal reconstruction problem where we have lost correspondences between the samples and their respective channels. We show that under the assumption that the signals of interest admit a sparse representation over an overcomplete dictionary, unique signal recovery is possible. Our derivations reveal that the problem is equivalent to a structured unlabeled sensing problem without precise knowledge of the sensing matrix. Unfortunately, existing methods are neither robust to errors in the regressors nor do they exploit the structure of the problem. Therefore, we propose a novel robust two-step approach for the reconstruction of shuffled sparse signals. The performance and robustness of the proposed approach is illustrated in an application of whole-brain calcium imaging in computational neuroscience. The proposed framework can be generalized to sparse signal representations other than the ones considered in this work to be applied in a variety of real-world problems with imprecise measurement or channel assignment.