Sampling bias corrections for discrete and Gaussian partial information decompositions

Partial information decomposition (PID) has emerged as a principled way to decompose the information carried by neural activity into components identifying whether interactions among neurons or brain areas generate synergistic or redundant information. Here, we demonstrate that empirical measures of synergy and redundancy based on either Gaussian or discrete probability estimators suffer from a substantial limited-sampling estimation bias. This bias is much larger for synergy than for redundancy. The gap between them increases with the number of parameters specifying the probability distributions. We develop procedures that effectively correct for the bias and provide rules of thumb for the sample sizes required to obtain unbiased estimates. We show that, when used on empirical brain datasets, they successfully remove large synergy biases across species, recording modalities, and experimental designs. Our bias corrections extend the range of neuroscience questions and experimental designs addressable with PID and allow accurate comparisons between synergy and redundancy.