{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T10:53:27Z","timestamp":1767178407521,"version":"build-2238731810"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012969","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T00:00:00Z","timestamp":1746489600000}}],"reference-count":22,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T00:00:00Z","timestamp":1744329600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Throughout the brain information is coded in the activity of multiple neurons at once, so called population codes. Population codes are a robust and accurate way of coding information. One can evaluate the quality of population coding by trying to read out the code with a decoder, and estimate the encoded stimulus. In particular when neurons are noisy, coding accuracy has extensively been evaluated in terms of the trial-to-trial variation in the estimate. While most decoders yield unbiased estimators if many neurons are actived, when only a few neurons are active, biases readily emerge. That is, even after averaging, a systematic difference between the true stimulus and its estimate remains. We characterize the shape of this bias for different encoding models (rectified cosine tuning and von Mises functions) and show that it can be both attractive or repulsive for different stimulus values. Biases appear for maximum likelihood and Bayesian decoders. The biases have a non-trivial dependence on noise. We also introduce a technique to estimate the bias and variance of Bayesian least square decoders. The work is of interest to those studying neural populations with a few active neurons.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012969","type":"journal-article","created":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T16:01:12Z","timestamp":1744387272000},"page":"e1012969","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Biases in neural population codes with a few active neurons"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5043-6724","authenticated-orcid":true,"given":"Sander W.","family":"Keemink","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6525-6814","authenticated-orcid":true,"given":"Mark C.W.","family":"van Rossum","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,4,11]]},"reference":[{"issue":"2","key":"pcbi.1012969.ref001","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1038\/35039062","article-title":"Information processing with population codes","volume":"1","author":"A Pouget","year":"2000","journal-title":"Nat Rev Neurosci"},{"key":"pcbi.1012969.ref002","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF00363954","article-title":"A theory for the use of visual orientation information which exploits the columnar structure of striate cortex","volume":"58","author":"MA Paradiso","year":"1988","journal-title":"Biol Cybern"},{"key":"pcbi.1012969.ref003","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1162\/089976699300016827","article-title":"The effect of correlated variability on the accuracy of a population code","volume":"11","author":"LF Abbott","year":"1999","journal-title":"Neural Comput"},{"key":"pcbi.1012969.ref004","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1162\/089976602753633367","article-title":"Population coding and decoding in a neural field: a computational study","volume":"14","author":"S Wu","year":"2002","journal-title":"Neural Comput"},{"issue":"2","key":"pcbi.1012969.ref005","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1162\/NECO_a_00227","article-title":"Transmission of population-coded information","volume":"24","author":"A Renart","year":"2012","journal-title":"Neural Comput"},{"key":"pcbi.1012969.ref006","article-title":"Fundamentals of statistical signal processing: Estimation theory","author":"SM Kay","year":"1993"},{"key":"pcbi.1012969.ref007","doi-asserted-by":"crossref","first-page":"3271","DOI":"10.1162\/neco.2009.09-08-869","article-title":"Is the homunculus \u201caware\u201d of sensory adaptation?","volume":"21","author":"P Seri\u00e8s","year":"2009","journal-title":"Neural Comput"},{"issue":"4","key":"pcbi.1012969.ref008","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1023\/B:PRIT.0000011274.44405.9b","article-title":"On some singularities in parameter estimation problems","volume":"39","author":"Si Amari","year":"2003","journal-title":"Probl Inf Transm"},{"key":"pcbi.1012969.ref009","first-page":"1","article-title":"Unconscious biases in neural populations coding multiple stimuli","author":"SW Keemink","year":"2018","journal-title":"Neural computation"},{"issue":"10","key":"pcbi.1012969.ref010","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1038\/nn.4105","article-title":"A Bayesian observer model constrained by efficient coding can explain\u2019anti-Bayesian\u2019percepts","volume":"18","author":"XX Wei","year":"2015","journal-title":"Nat Neurosci"},{"issue":"5","key":"pcbi.1012969.ref011","first-page":"1680","article-title":"Representation of sensory information in the cricket cercal sensory system","volume":"66","author":"JP Miller","year":"1991","journal-title":"I. Response properties of the primary interneurons. J Neurophysiol"},{"issue":"5","key":"pcbi.1012969.ref012","first-page":"1690","article-title":"Representation of sensory information in the cricket cercal sensory system","volume":"66","author":"FE Theunissen","year":"1991","journal-title":"II. Information theoretic calculation of system accuracy and optimal tuning-curve widths of four primary interneurons. J Neurophysiol"},{"key":"pcbi.1012969.ref013","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF00962720","article-title":"Vector reconstruction from firing rates","volume":"1","author":"E Salinas","year":"1994","journal-title":"J Comput Neurosci"},{"key":"pcbi.1012969.ref014","article-title":"Theoretical neuroscience: computational and mathematical modeling of neural systems. Cambridge","author":"P Dayan","year":"2001"},{"key":"pcbi.1012969.ref015","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1162\/neco.1996.8.3.511","article-title":"Parameter extraction from population codes: a critical assessment","volume":"8","author":"HP Snippe","year":"1996","journal-title":"Neural Comput"},{"issue":"3","key":"pcbi.1012969.ref016","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1152\/jn.00864.2017","article-title":"Effects of V1 surround modulation tuning on visual saliency and the tilt illusion","volume":"120","author":"SW Keemink","year":"2018","journal-title":"J Neurophysiol"},{"issue":"7","key":"pcbi.1012969.ref017","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1162\/NECO_a_00292","article-title":"Fisher and Shannon information in finite neural populations","volume":"24","author":"S Yarrow","year":"2012","journal-title":"Neural Comput"},{"key":"pcbi.1012969.ref018","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1088\/0954-898X_13_4_302","article-title":"Threshold behaviour of the maximum likelihood method in population decoding","volume":"13","author":"X Xie","year":"2002","journal-title":"Network"},{"issue":"5","key":"pcbi.1012969.ref019","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.preteyeres.2012.05.001","article-title":"Optical superresolution and visual hyperacuity","volume":"31","author":"G Westheimer","year":"2012","journal-title":"Prog Retin Eye Res"},{"key":"pcbi.1012969.ref020","doi-asserted-by":"crossref","first-page":"10749","DOI":"10.1073\/pnas.90.22.10749","article-title":"Simple models for reading neuronal population codes","volume":"90","author":"HS Seung","year":"1993","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1012969.ref021","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1162\/089976699300016809","article-title":"Neuronal Tuning: to sharpen or to broaden?","volume":"11","author":"K Zhang","year":"1999","journal-title":"Neural Comp"},{"key":"pcbi.1012969.ref022","article-title":"GNU Octave version 9.2.0 manual: a high-level interactive language for numerical computations","author":"JW Eaton","year":"2024"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1012969","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T00:00:00Z","timestamp":1746489600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012969","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T13:59:50Z","timestamp":1746539990000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012969"}},"subtitle":[],"editor":[{"given":"Stefano","family":"Panzeri","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,4,11]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1012969","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,11]]}}}