Sampling bias corrections for discrete and Gaussian partial information decompositions
9 affiliations
- 1Institute for Neural Information Processing, Center for Molecular Neurobiology, University Medical Center Hamburg-Eppendorf (UKE), 20251 Hamburg, Germany
- 2Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf (UKE), 20246 Hamburg, Germany
- 3Picower Institute for Learning and Memory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- 4Department of Psychology, University of Torino, 10124 Turin, Italy
- 5Optical Approaches to Brain Function Laboratory, Istituto Italiano di Tecnologia, 16163 Genova, Italy
- 6Department of Cognitive Neuroscience, Bielefeld University, 33501 Bielefeld, Germany
- 7Department of Psychiatry, University of Oxford, Oxford OX3 7JX, UK
- 8Division of Information Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
- 9St. John's College, University of Cambridge, Cambridge CB2 1TP, UK
Abstract
Shannon Information theory has long been a tool of choice to measure empirically how populations of neurons in the brain encode information about cognitive variables. Recently, Partial Information Decomposition (PID) has emerged as principled way to break down this information into components identifying not only the unique information carried by each neuron, but also whether relationships between neurons generate synergistic or redundant information. While it has been long recognized that Shannon information measures on neural activity suffer from a (mostly upward) limited sampling estimation bias, this issue has largely been ignored in the burgeoning field of PID analysis of neural activity. We used simulations to investigate the limited sampling bias of PID computed from discrete probabilities (suited to describe neural spiking activity). We found that PID suffers from a large bias that is uneven across components, with synergy by far the most biased. Using approximate analytical expansions, we found that the bias of synergy increases quadratically with the number of discrete responses of each neuron, whereas the bias of unique and redundant information increase only linearly or sub-linearly. Based on the understanding of the PID bias properties, we developed simple yet effective procedures that correct for the bias effectively, and that improve greatly the PID estimation with respect to current state-of-the-art procedures. We apply these PID bias correction procedures to datasets of 53117 pairs neurons in auditory cortex, posterior parietal cortex and hippocampus of mice performing cognitive tasks, deriving precise estimates and bounds of how synergy and redundancy vary across these brain regions.
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BibTeX
@article{lorenz2026sampling,
title = {{Sampling bias corrections for discrete and Gaussian partial information decompositions}},
author = {Gabriel Matías Lorenz and Nicola Marie Engel and Loren Koçillari and Marco Celotto and Davide Orsenigo and Sebastiano Curreli and Simone Blanco Malerba and Andreas Karl Engel and Christoph Kayser and Tommaso Fellin and Andrea I. Luppi and Stefano Panzeri},
journal = {Patterns},
year = {2026},
month = jul,
doi = {10.1016/j.patter.2026.101619},
url = {https://doi.org/10.1016/j.patter.2026.101619},
note = {CC BY},
}
RIS
TY - JOUR
TI - Sampling bias corrections for discrete and Gaussian partial information decompositions
AU - Gabriel Matías Lorenz
AU - Nicola Marie Engel
AU - Loren Koçillari
AU - Marco Celotto
AU - Davide Orsenigo
AU - Sebastiano Curreli
AU - Simone Blanco Malerba
AU - Andreas Karl Engel
AU - Christoph Kayser
AU - Tommaso Fellin
AU - Andrea I. Luppi
AU - Stefano Panzeri
PY - 2026
DA - 2026/07/23
JO - Patterns
DO - 10.1016/j.patter.2026.101619
UR - https://doi.org/10.1016/j.patter.2026.101619
AB - Shannon Information theory has long been a tool of choice to measure empirically how populations of neurons in the brain encode information about cognitive variables. Recently, Partial Information Decomposition (PID) has emerged as principled way to break down this information into components identifying not only the unique information carried by each neuron, but also whether relationships between neurons generate synergistic or redundant information. While it has been long recognized that Shannon information measures on neural activity suffer from a (mostly upward) limited sampling estimation bias, this issue has largely been ignored in the burgeoning field of PID analysis of neural activity. We used simulations to investigate the limited sampling bias of PID computed from discrete probabilities (suited to describe neural spiking activity). We found that PID suffers from a large bias that is uneven across components, with synergy by far the most biased. Using approximate analytical expansions, we found that the bias of synergy increases quadratically with the number of discrete responses of each neuron, whereas the bias of unique and redundant information increase only linearly or sub-linearly. Based on the understanding of the PID bias properties, we developed simple yet effective procedures that correct for the bias effectively, and that improve greatly the PID estimation with respect to current state-of-the-art procedures. We apply these PID bias correction procedures to datasets of 53117 pairs neurons in auditory cortex, posterior parietal cortex and hippocampus of mice performing cognitive tasks, deriving precise estimates and bounds of how synergy and redundancy vary across these brain regions.
SN - 2666-3899
ER -