Conservative Significance Testing of Tripartite Interactions in Multivariate Neural Data

Abstract An important goal in systems neuroscience is to understand the structure of neuronal interactions, frequently approached by studying functional relations between recorded neuronal signals. Commonly used pairwise metrics (e.g. correlation coefficient) offer limited insight, neither addressing the specificity of estimated neuronal interactions nor potential synergistic coupling between neuronal signals. Tripartite metrics, such as partial correlation, variance partitioning, and partial information decomposition, address these questions by disentangling functional relations into interpretable information atoms (unique, redundant and synergistic). Here, we apply these tripartite metrics to simulated neuronal recordings to investigate their sensitivity to impurities (like noise or other unexplained variance) in the data. We find that all considered metrics are accurate and specific for pure signals but experience significant bias for impure signals. We show that permutation-testing of such metrics results in high false positive rates even for small impurities and large data sizes. We present a conservative null hypothesis for significance testing of tripartite metrics, which significantly decreases false positive rate at a tolerable expense of increasing false negative rate. We hope our study raises awareness about the potential pitfalls of significance testing and of interpretation of functional relations, offering both conceptual and practical advice. Author Summary Tripartite functional relation metrics enable the study of interesting effects in neural recordings, such as redundancy, functional connection specificity and synergistic coupling. However, common estimators of such relations are designed for pure (e.g. non-noisy) signals rare for such recordings. We study the performance of tripartite estimators using simulated impure neural signals. We demonstrate that permutation-testing is not a robust procedure for inferring ground truth interactions from studied estimators. We develop an adjusted conservative testing procedure, reducing false positive rate of studied estimators for impure data. Besides addressing significance testing, our results should aid in accurate interpretation of tripartite functional relations and functional connectivity.