Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes
This work addresses the need for joint network estimation and inference in multi-experiment point process data, such as in neuroscience, offering improved statistical power and flexibility, though it is incremental as it builds on existing multivariate point process methods.
The authors tackled the problem of jointly estimating networks from high-dimensional point process data across multiple conditions, where similarity between networks is unknown, by proposing a method that adaptively encourages similarity and includes a hierarchical multiple testing procedure for edges. Their approach reduces the number of tests, improves power while controlling error rates, and is validated through simulations and neuronal spike train data.
Modern high-dimensional point process data, especially those from neuroscience experiments, often involve observations from multiple conditions and/or experiments. Networks of interactions corresponding to these conditions are expected to share many edges, but also exhibit unique, condition-specific ones. However, the degree of similarity among the networks from different conditions is generally unknown. Existing approaches for multivariate point processes do not take these structures into account and do not provide inference for jointly estimated networks. To address these needs, we propose a joint estimation procedure for networks of high-dimensional point processes that incorporates easy-to-compute weights in order to data-adaptively encourage similarity between the estimated networks. We also propose a powerful hierarchical multiple testing procedure for edges of all estimated networks, which takes into account the data-driven similarity structure of the multi-experiment networks. Compared to conventional multiple testing procedures, our proposed procedure greatly reduces the number of tests and results in improved power, while tightly controlling the family-wise error rate. Unlike existing procedures, our method is also free of assumptions on dependency between tests, offers flexibility on p-values calculated along the hierarchy, and is robust to misspecification of the hierarchical structure. We verify our theoretical results via simulation studies and demonstrate the application of the proposed procedure using neuronal spike train data.