Inference in the Brain: Statistics Flowing in Redundant Population Codes

It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural ne...

Full description

Saved in:
Bibliographic Details
Published inNeuron (Cambridge, Mass.) Vol. 94; no. 5; pp. 943 - 953
Main Authors Pitkow, Xaq, Angelaki, Dora E.
Format Journal Article
LanguageEnglish
Published United States Elsevier Inc 07.06.2017
Elsevier Limited
Subjects
Online AccessGet full text
ISSN0896-6273
1097-4199
1097-4199
DOI10.1016/j.neuron.2017.05.028

Cover

Abstract It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural networks. We propose that these probabilistic computations function by a message-passing algorithm operating at the level of redundant neural populations. To explain this framework, we review its underlying concepts, including graphical models, sufficient statistics, and message-passing, and then describe how these concepts could be implemented by recurrently connected probabilistic population codes. The relevant information flow in these networks will be most interpretable at the population level, particularly for redundant neural codes. We therefore outline a general approach to identify the essential features of a neural message-passing algorithm. Finally, we argue that to reveal the most important aspects of these neural computations, we must study large-scale activity patterns during moderately complex, naturalistic behaviors. Pitkow and Angelaki speculate how the brain could perform inference by passing statistics between redundant, overlapping probabilistic population codes. They argue that neuroscience needs behavioral tasks that include uncertainty and nuisance variables to reveal these key computations.
AbstractList It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural networks. We propose that these probabilistic computations function by a message-passing algorithm operating at the level of redundant neural populations. To explain this framework, we review its underlying concepts, including graphical models, sufficient statistics, and message-passing, and then describe how these concepts could be implemented by recurrently connected probabilistic population codes. The relevant information flow in these networks will be most interpretable at the population level, particularly for redundant neural codes. We therefore outline a general approach to identify the essential features of a neural message-passing algorithm. Finally, we argue that to reveal the most important aspects of these neural computations, we must study large-scale activity patterns during moderately complex, naturalistic behaviors.
It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural networks. We propose that these probabilistic computations function by a message-passing algorithm operating at the level of redundant neural populations. To explain this framework, we review its underlying concepts, including graphical models, sufficient statistics, and message-passing, and then describe how these concepts could be implemented by recurrently connected probabilistic population codes. The relevant information flow in these networks will be most interpretable at the population level, particularly for redundant neural codes. We therefore outline a general approach to identify the essential features of a neural message-passing algorithm. Finally, we argue that to reveal the most important aspects of these neural computations, we must study large-scale activity patterns during moderately complex, naturalistic behaviors.It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural networks. We propose that these probabilistic computations function by a message-passing algorithm operating at the level of redundant neural populations. To explain this framework, we review its underlying concepts, including graphical models, sufficient statistics, and message-passing, and then describe how these concepts could be implemented by recurrently connected probabilistic population codes. The relevant information flow in these networks will be most interpretable at the population level, particularly for redundant neural codes. We therefore outline a general approach to identify the essential features of a neural message-passing algorithm. Finally, we argue that to reveal the most important aspects of these neural computations, we must study large-scale activity patterns during moderately complex, naturalistic behaviors.
It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural networks. We propose that these probabilistic computations function by a message-passing algorithm operating at the level of redundant neural populations. To explain this framework, we review its underlying concepts, including graphical models, sufficient statistics, and message-passing, and then describe how these concepts could be implemented by recurrently connected probabilistic population codes. The relevant information flow in these networks will be most interpretable at the population level, particularly for redundant neural codes. We therefore outline a general approach to identify the essential features of a neural message-passing algorithm. Finally, we argue that to reveal the most important aspects of these neural computations, we must study large-scale activity patterns during moderately complex, naturalistic behaviors. Pitkow and Angelaki speculate how the brain could perform inference by passing statistics between redundant, overlapping probabilistic population codes. They argue that neuroscience needs behavioral tasks that include uncertainty and nuisance variables to reveal these key computations.
Author Angelaki, Dora E.
Pitkow, Xaq
AuthorAffiliation 2 Department of Electrical and Computer Engineering, Rice University
1 Department of Neuroscience, Baylor College of Medicine
AuthorAffiliation_xml – name: 2 Department of Electrical and Computer Engineering, Rice University
– name: 1 Department of Neuroscience, Baylor College of Medicine
Author_xml – sequence: 1
  givenname: Xaq
  surname: Pitkow
  fullname: Pitkow, Xaq
  email: xaq@rice.edu
  organization: Department of Neuroscience, Baylor College of Medicine, Houston, TX 77030, USA
– sequence: 2
  givenname: Dora E.
  surname: Angelaki
  fullname: Angelaki, Dora E.
  organization: Department of Neuroscience, Baylor College of Medicine, Houston, TX 77030, USA
BackLink https://www.ncbi.nlm.nih.gov/pubmed/28595050$$D View this record in MEDLINE/PubMed
BookMark eNqNkk9v1DAQxS1URLeFb4BQJC5cEsZOnMQ9IMGK0kqVQPw5W1573HqVtRfbadVvT8KWlvZQ9TQH_97zzJs5IHs-eCTkNYWKAm3fryuPYwy-YkC7CngFrH9GFhREVzZUiD2ygF60Zcu6ep8cpLQGoA0X9AXZZz0XHDgsyMmptxjRayycL_IFFp-icv6o-JFVdik7nYrjIVw5fz4D39GM3iifi29hOw4TEnyxDAbTS_LcqiHhq5t6SH4df_65PCnPvn45XX48KzXnXS6pYco2vYbWKG4V19gLgcCgE2Bb3SITlvNVy6CtDQNrbL1ijLNe8d5OtT4kfOc7-q26vlLDILfRbVS8lhTknIxcy10yck5GApdTMpPuw063HVcbNBp9jupOG5ST91-8u5Dn4VJy3tStmD9-d2MQw-8RU5YblzQOg_IYxiSpAEE7BlBP6NsH6DqM0U-xzFRX076GuaM3_3d028q_5UxAswN0DClFtE-d9OiBTLv8d1PTXG54Ykw47fDSYZRJu_k8jIuoszTBPW7wBzq5zlg
CitedBy_id crossref_primary_10_1016_j_neuron_2020_02_023
crossref_primary_10_1016_j_neubiorev_2024_105623
crossref_primary_10_1038_s41467_021_26793_9
crossref_primary_10_1016_j_pneurobio_2021_101996
crossref_primary_10_1073_pnas_1912336117
crossref_primary_10_1021_acsaelm_3c01808
crossref_primary_10_1152_jn_00087_2019
crossref_primary_10_1080_13546783_2021_2022531
crossref_primary_10_1177_20416695211018720
crossref_primary_10_1103_PhysRevX_13_031028
crossref_primary_10_1038_s41398_020_01166_w
crossref_primary_10_1016_j_neubiorev_2022_104649
crossref_primary_10_1016_j_jneumeth_2019_01_019
crossref_primary_10_1016_j_cophys_2020_04_004
crossref_primary_10_1038_s41467_019_13472_z
crossref_primary_10_1126_sciadv_adk7214
crossref_primary_10_1162_neco_a_01166
crossref_primary_10_7554_eLife_64615
crossref_primary_10_34248_bsengineering_1516593
crossref_primary_10_1016_j_cub_2021_09_076
crossref_primary_10_1146_annurev_neuro_080317_061936
crossref_primary_10_1007_s00429_020_02188_2
crossref_primary_10_1038_s41467_023_37400_4
crossref_primary_10_1038_s41583_022_00582_9
crossref_primary_10_1103_PhysRevLett_125_178301
crossref_primary_10_7554_eLife_33334
crossref_primary_10_1038_s41583_023_00699_5
crossref_primary_10_7554_eLife_80280
crossref_primary_10_1016_j_neurobiolaging_2021_09_002
crossref_primary_10_1080_13854046_2018_1523465
crossref_primary_10_1016_j_neuron_2019_01_029
crossref_primary_10_1038_s41593_024_01575_w
crossref_primary_10_1523_JNEUROSCI_0674_21_2022
crossref_primary_10_1088_0253_6102_70_4_485
crossref_primary_10_1016_j_neuron_2018_05_040
crossref_primary_10_3390_e19090451
crossref_primary_10_1016_j_neubiorev_2022_104903
crossref_primary_10_3389_fams_2018_00011
crossref_primary_10_3389_fncom_2023_1092185
crossref_primary_10_3389_fncir_2018_00115
crossref_primary_10_1002_hbm_26257
crossref_primary_10_1016_j_biosystems_2022_104825
crossref_primary_10_1016_j_conb_2019_09_005
crossref_primary_10_1371_journal_pbio_2005239
crossref_primary_10_1038_s41583_024_00795_0
crossref_primary_10_1016_j_conb_2019_09_002
crossref_primary_10_1523_JNEUROSCI_1024_19_2019
crossref_primary_10_1016_j_conb_2018_04_004
crossref_primary_10_1126_sciadv_add4201
crossref_primary_10_2196_23777
crossref_primary_10_1038_s42003_024_06392_2
Cites_doi 10.1371/journal.pcbi.1002211
10.1016/j.neuron.2015.01.007
10.1073/pnas.1310416110
10.1038/381607a0
10.1073/pnas.1508738112
10.1038/nn.2735
10.1016/j.tics.2010.01.003
10.1016/j.neuron.2016.03.020
10.1371/journal.pcbi.1005268
10.1007/BF02551274
10.1523/JNEUROSCI.4522-12.2013
10.1038/nn1606
10.1038/nn1790
10.1016/j.neuron.2015.07.024
10.1038/nn.3309
10.1162/08997660460733976
10.1162/neco.1996.8.7.1341
10.1038/341052a0
10.1142/S0129065707001111
10.1038/nature12160
10.1038/nn.2191
10.1016/j.neuron.2013.09.006
10.1016/j.neuron.2013.09.007
10.1038/nature04766
10.1038/nn1691
10.1038/nn.3267
10.1016/j.neuron.2014.07.035
10.1037/a0021336
10.1038/370140a0
10.1016/0893-6080(91)90009-T
10.1038/nn.3807
10.1016/j.tics.2007.06.010
10.1038/nature13240
10.1038/nn.2983
10.1126/science.aac9462
10.1038/nature12742
10.1016/j.neuron.2008.08.007
10.1371/journal.pone.0015554
10.1016/j.conb.2015.04.003
10.1073/pnas.1101430108
10.1109/TPAMI.1984.4767596
10.1016/j.neuron.2016.09.038
10.1016/S0896-6273(04)00186-2
10.1523/JNEUROSCI.2837-13.2013
10.1523/JNEUROSCI.1706-11.2011
10.1364/JOSAA.20.001434
10.1016/j.neuron.2012.03.016
10.1073/pnas.0804451105
10.1016/j.neuron.2008.09.021
10.1038/nn1991
10.1523/JNEUROSCI.5179-08.2009
10.1016/j.neuron.2015.06.033
10.1073/pnas.1403112111
10.1561/2200000001
10.1126/science.1195870
10.1016/j.tics.2012.08.010
10.1017/S095252380000715X
ContentType Journal Article
Copyright 2017 Elsevier Inc.
Copyright © 2017 Elsevier Inc. All rights reserved.
2017. Elsevier Inc.
Copyright_xml – notice: 2017 Elsevier Inc.
– notice: Copyright © 2017 Elsevier Inc. All rights reserved.
– notice: 2017. Elsevier Inc.
DBID 6I.
AAFTH
AAYXX
CITATION
CGR
CUY
CVF
ECM
EIF
NPM
7QP
7QR
7TK
8FD
FR3
K9.
NAPCQ
P64
RC3
7X8
5PM
ADTOC
UNPAY
DOI 10.1016/j.neuron.2017.05.028
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
Medline
MEDLINE
MEDLINE (Ovid)
MEDLINE
MEDLINE
PubMed
Calcium & Calcified Tissue Abstracts
Chemoreception Abstracts
Neurosciences Abstracts
Technology Research Database
Engineering Research Database
ProQuest Health & Medical Complete (Alumni)
Nursing & Allied Health Premium
Biotechnology and BioEngineering Abstracts
Genetics Abstracts
MEDLINE - Academic
PubMed Central (Full Participant titles)
Unpaywall for CDI: Periodical Content
Unpaywall
DatabaseTitle CrossRef
MEDLINE
Medline Complete
MEDLINE with Full Text
PubMed
MEDLINE (Ovid)
Nursing & Allied Health Premium
Genetics Abstracts
Technology Research Database
ProQuest Health & Medical Complete (Alumni)
Chemoreception Abstracts
Engineering Research Database
Calcium & Calcified Tissue Abstracts
Neurosciences Abstracts
Biotechnology and BioEngineering Abstracts
MEDLINE - Academic
DatabaseTitleList
MEDLINE
MEDLINE - Academic
Nursing & Allied Health Premium

Database_xml – sequence: 1
  dbid: NPM
  name: PubMed
  url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed
  sourceTypes: Index Database
– sequence: 2
  dbid: EIF
  name: MEDLINE
  url: https://proxy.k.utb.cz/login?url=https://www.webofscience.com/wos/medline/basic-search
  sourceTypes: Index Database
– sequence: 3
  dbid: UNPAY
  name: Unpaywall
  url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/
  sourceTypes: Open Access Repository
DeliveryMethod fulltext_linktorsrc
Discipline Anatomy & Physiology
Biology
Statistics
EISSN 1097-4199
EndPage 953
ExternalDocumentID 10.1016/j.neuron.2017.05.028
PMC5543692
28595050
10_1016_j_neuron_2017_05_028
S089662731730466X
Genre Journal Article
Review
GrantInformation_xml – fundername: NINDS NIH HHS
  grantid: U01 NS094368
GroupedDBID ---
--K
-DZ
-~X
0R~
123
1RT
1~5
26-
2WC
3V.
4.4
457
4G.
53G
5RE
62-
6I.
7-5
7RV
7X7
8C1
8FE
8FH
AACTN
AAEDW
AAFTH
AAIAV
AAKRW
AAKUH
AALRI
AAUCE
AAVLU
AAXJY
AAXUO
ABJNI
ABMAC
ABMWF
ABVKL
ACGFO
ACGFS
ACIWK
ACNCT
ACPRK
ADBBV
ADEZE
ADFRT
ADJPV
AEFWE
AENEX
AEXQZ
AFKRA
AFTJW
AGKMS
AHHHB
AHMBA
AITUG
ALKID
ALMA_UNASSIGNED_HOLDINGS
AMRAJ
AQUVI
ASPBG
AVWKF
AZFZN
BAWUL
BBNVY
BENPR
BHPHI
BKEYQ
BKNYI
BPHCQ
BVXVI
CS3
DIK
DU5
E3Z
EBS
EJD
F5P
FCP
FDB
FEDTE
FIRID
HCIFZ
HVGLF
IAO
IHE
IHR
INH
IXB
J1W
JIG
K-O
KQ8
L7B
LK8
LX5
M0R
M0T
M2M
M2O
M3Z
M41
M7P
N9A
NCXOZ
O-L
O9-
OK1
P2P
P6G
PQQKQ
PROAC
RCE
RIG
ROL
RPZ
SCP
SDP
SES
SSZ
TR2
WOW
WQ6
ZA5
.55
.GJ
29N
3O-
5VS
AAEDT
AAFWJ
AAIKJ
AAMRU
AAQFI
AAQXK
AAYWO
AAYXX
ABDGV
ABWVN
ACRPL
ACVFH
ADCNI
ADMUD
ADNMO
ADVLN
AEUPX
AFPUW
AGHFR
AGQPQ
AIGII
AKAPO
AKBMS
AKRWK
AKYEP
APXCP
CITATION
EFKBS
FGOYB
G-2
HZ~
ITC
MVM
OZT
R2-
X7M
ZGI
ZKB
AGCQF
CGR
CUY
CVF
ECM
EIF
NPM
7QP
7QR
7TK
8FD
FR3
K9.
NAPCQ
P64
RC3
7X8
5PM
ADTOC
UNPAY
ID FETCH-LOGICAL-c557t-1d2af48c06da5fa5ce899e020790f6c6e29f55b62063d20fdf3b22528a58f2523
IEDL.DBID IXB
ISSN 0896-6273
1097-4199
IngestDate Sun Oct 26 03:30:21 EDT 2025
Tue Sep 30 15:36:35 EDT 2025
Thu Oct 02 11:33:09 EDT 2025
Tue Oct 07 06:38:10 EDT 2025
Mon Jul 21 05:48:42 EDT 2025
Thu Oct 16 04:43:17 EDT 2025
Thu Apr 24 23:10:26 EDT 2025
Fri Feb 23 02:22:45 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 5
Keywords coding
message-passing
population code
inference
nuisance
brain
nonlinear
theory
redundant
Language English
License This article is made available under the Elsevier license.
Copyright © 2017 Elsevier Inc. All rights reserved.
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c557t-1d2af48c06da5fa5ce899e020790f6c6e29f55b62063d20fdf3b22528a58f2523
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Review-3
content type line 23
OpenAccessLink https://www.sciencedirect.com/science/article/pii/S089662731730466X
PMID 28595050
PQID 1907318308
PQPubID 2031076
PageCount 11
ParticipantIDs unpaywall_primary_10_1016_j_neuron_2017_05_028
pubmedcentral_primary_oai_pubmedcentral_nih_gov_5543692
proquest_miscellaneous_1909172003
proquest_journals_1907318308
pubmed_primary_28595050
crossref_primary_10_1016_j_neuron_2017_05_028
crossref_citationtrail_10_1016_j_neuron_2017_05_028
elsevier_sciencedirect_doi_10_1016_j_neuron_2017_05_028
PublicationCentury 2000
PublicationDate 2017-06-07
PublicationDateYYYYMMDD 2017-06-07
PublicationDate_xml – month: 06
  year: 2017
  text: 2017-06-07
  day: 07
PublicationDecade 2010
PublicationPlace United States
PublicationPlace_xml – name: United States
– name: Cambridge
PublicationTitle Neuron (Cambridge, Mass.)
PublicationTitleAlternate Neuron
PublicationYear 2017
Publisher Elsevier Inc
Elsevier Limited
Publisher_xml – name: Elsevier Inc
– name: Elsevier Limited
References Berkes, Orbán, Lengyel, Fiser (bib6) 2011; 331
DiCarlo, Cox (bib18) 2007; 11
Raju, Pitkow (bib66) 2016; 29
Chen, Deangelis, Angelaki (bib10) 2013; 33
Geman, Geman (bib24) 1984; 6
Sutton, Barto (bib73) 1998
Liu, Gu, DeAngelis, Angelaki (bib47) 2013; 16
Cohen, Newsome (bib13) 2008; 60
Kriegeskorte, Mur, Bandettini (bib41) 2008; 2
Schäfer, Zimmermann (bib72) 2007; 17
Koller, Friedman (bib40) 2009
Beck, Ma, Kiani, Hanks, Churchland, Roitman, Shadlen, Latham, Pouget (bib2) 2008; 60
Pitkow, Liu, Angelaki, DeAngelis, Pouget (bib65) 2015; 87
Chen, Deangelis, Angelaki (bib11) 2013; 80
Daunizeau, den Ouden, Pessiglione, Kiebel, Stephan, Friston (bib16) 2010; 5
Minka (bib53) 2001
Babadi, Sompolinsky (bib1) 2014; 83
Cybenko (bib15) 1989; 2
Cohen, Newsome (bib14) 2009; 29
Montúfar, Pascanu, Cho, Bengio (bib54) 2014; 27
Krizhevsky, Sutskever, Hinton (bib42) 2012; 25
Zeiler, Fergus (bib79) 2014
Haefner, Berkes, Fiser (bib28) 2016; 90
Helmholtz (bib30) 1925; Volume III
Marr (bib52) 1982
Gao, Ganguli (bib23) 2015; 32
Pitkow (bib63) 2010; 10
Kanitscheider, Coen-Cagli, Pouget (bib37) 2015; 112
Moreno-Bote, Beck, Kanitscheider, Pitkow, Latham, Pouget (bib56) 2014; 17
Lee, Mumford (bib45) 2003; 20
Lakshminarasimhan, Pouget, DeAngelis, Angelaki, Pitkow (bib43) 2017
Fetsch, Pouget, DeAngelis, Angelaki (bib20) 2011; 15
Beck, Ma, Pitkow, Latham, Pouget (bib4) 2012; 74
Heinemann, Globerson (bib29) 2011
Moreno-Bote, Knill, Pouget (bib55) 2011; 108
Rust, Movshon (bib69) 2005; 8
Saez, Rigotti, Ostojic, Fusi, Salzman (bib70) 2015; 87
Uka, DeAngelis (bib74) 2004; 42
Jazayeri, Movshon (bib34) 2006; 9
Buesing, Bill, Nessler, Maass (bib9) 2011; 7
Hornik (bib32) 1991; 4
Hinton, G.E., and Sejnowski, T.J. (1983). Optimal perceptual inference. Proceedings of the IEEE conference on Computer Vision and Pattern Recognition. pp. 448–453.
Rigotti, Barak, Warden, Wang, Daw, Miller, Fusi (bib68) 2013; 497
Kira, Yang, Shadlen (bib39) 2015; 85
Laplace (bib44) 1812
Rao (bib67) 2004; 16
Savin, Denève (bib71) 2014; 27
Britten, Newsome, Shadlen, Celebrini, Movshon (bib8) 1996; 13
Ma, Beck, Latham, Pouget (bib49) 2006; 9
Pitkow, Ahmadian, Miller (bib64) 2011; 24
Ganguli, Huh, Sompolinsky (bib22) 2008; 105
Jonas, Körding (bib36) 2017; 13
Ng, A.Y., and Russell, S.J. (2000). Algorithms for inverse reinforcement learning. In Proceedings of ICML.
Chen, DeAngelis, Angelaki (bib12) 2013; 33
Jiang, Shen, Cadwell, Berens, Sinz, Ecker, Patel, Tolias (bib35) 2015; 350
Kim, Greene, Zlateski, Lee, Richardson, Turaga, Purcaro, Balkam, Robinson, Behabadi (bib38) 2014; 509
Goodman, Ullman, Tenenbaum (bib25) 2011; 118
Ma (bib48) 2012; 16
Yamins, Hong, Cadieu, Solomon, Seibert, DiCarlo (bib78) 2014; 111
Hoyer, Hyvärinen (bib33) 2003; 15
Haefner, Gerwinn, Macke, Bethge (bib27) 2013; 16
Newsome, Britten, Movshon (bib57) 1989; 341
Zohary, Shadlen, Newsome (bib80) 1994; 370
Wainwright, Jordan (bib75) 2008; 1
Bellman (bib5) 1957
Orbán, Berkes, Fiser, Lengyel (bib61) 2016; 92
Pearl (bib62) 1988
Mante, Sussillo, Shenoy, Newsome (bib50) 2013; 503
Bondy, Cumming (bib7) 2016
Dolan, Dayan (bib19) 2013; 80
Fiser, Berkes, Orbán, Lengyel (bib21) 2010; 14
Liu, Dickman, Newlands, DeAngelis, Angelaki (bib46) 2013; 110
Daw, O’Doherty, Dayan, Seymour, Dolan (bib17) 2006; 441
Nienborg, Cumming (bib59) 2007; 10
Wainwright, Simoncelli (bib76) 2000; 12
Wolpert (bib77) 1996; 8
Beck, Latham, Pouget (bib3) 2011; 31
Marder, Taylor (bib51) 2011; 14
Gu, Angelaki, Deangelis (bib26) 2008; 11
Olshausen, Field (bib60) 1996; 381
Gu (10.1016/j.neuron.2017.05.028_bib26) 2008; 11
Goodman (10.1016/j.neuron.2017.05.028_bib25) 2011; 118
10.1016/j.neuron.2017.05.028_bib31
Moreno-Bote (10.1016/j.neuron.2017.05.028_bib56) 2014; 17
Raju (10.1016/j.neuron.2017.05.028_bib66) 2016; 29
Beck (10.1016/j.neuron.2017.05.028_bib3) 2011; 31
Mante (10.1016/j.neuron.2017.05.028_bib50) 2013; 503
Zohary (10.1016/j.neuron.2017.05.028_bib80) 1994; 370
Liu (10.1016/j.neuron.2017.05.028_bib47) 2013; 16
Bondy (10.1016/j.neuron.2017.05.028_bib7) 2016
Rao (10.1016/j.neuron.2017.05.028_bib67) 2004; 16
Fetsch (10.1016/j.neuron.2017.05.028_bib20) 2011; 15
Kriegeskorte (10.1016/j.neuron.2017.05.028_bib41) 2008; 2
Ganguli (10.1016/j.neuron.2017.05.028_bib22) 2008; 105
Jonas (10.1016/j.neuron.2017.05.028_bib36) 2017; 13
Krizhevsky (10.1016/j.neuron.2017.05.028_bib42) 2012; 25
Kim (10.1016/j.neuron.2017.05.028_bib38) 2014; 509
Nienborg (10.1016/j.neuron.2017.05.028_bib59) 2007; 10
Fiser (10.1016/j.neuron.2017.05.028_bib21) 2010; 14
Hoyer (10.1016/j.neuron.2017.05.028_bib33) 2003; 15
Lakshminarasimhan (10.1016/j.neuron.2017.05.028_bib43) 2017
Chen (10.1016/j.neuron.2017.05.028_bib12) 2013; 33
Bellman (10.1016/j.neuron.2017.05.028_bib5) 1957
Yamins (10.1016/j.neuron.2017.05.028_bib78) 2014; 111
Dolan (10.1016/j.neuron.2017.05.028_bib19) 2013; 80
Rigotti (10.1016/j.neuron.2017.05.028_bib68) 2013; 497
Babadi (10.1016/j.neuron.2017.05.028_bib1) 2014; 83
Cybenko (10.1016/j.neuron.2017.05.028_bib15) 1989; 2
Liu (10.1016/j.neuron.2017.05.028_bib46) 2013; 110
DiCarlo (10.1016/j.neuron.2017.05.028_bib18) 2007; 11
Wolpert (10.1016/j.neuron.2017.05.028_bib77) 1996; 8
Marr (10.1016/j.neuron.2017.05.028_bib52) 1982
Kira (10.1016/j.neuron.2017.05.028_bib39) 2015; 85
Rust (10.1016/j.neuron.2017.05.028_bib69) 2005; 8
Olshausen (10.1016/j.neuron.2017.05.028_bib60) 1996; 381
Schäfer (10.1016/j.neuron.2017.05.028_bib72) 2007; 17
Newsome (10.1016/j.neuron.2017.05.028_bib57) 1989; 341
Marder (10.1016/j.neuron.2017.05.028_bib51) 2011; 14
Kanitscheider (10.1016/j.neuron.2017.05.028_bib37) 2015; 112
Pitkow (10.1016/j.neuron.2017.05.028_bib65) 2015; 87
Hornik (10.1016/j.neuron.2017.05.028_bib32) 1991; 4
Saez (10.1016/j.neuron.2017.05.028_bib70) 2015; 87
Cohen (10.1016/j.neuron.2017.05.028_bib13) 2008; 60
Pitkow (10.1016/j.neuron.2017.05.028_bib63) 2010; 10
Ma (10.1016/j.neuron.2017.05.028_bib48) 2012; 16
Chen (10.1016/j.neuron.2017.05.028_bib10) 2013; 33
Haefner (10.1016/j.neuron.2017.05.028_bib28) 2016; 90
Wainwright (10.1016/j.neuron.2017.05.028_bib75) 2008; 1
Gao (10.1016/j.neuron.2017.05.028_bib23) 2015; 32
Geman (10.1016/j.neuron.2017.05.028_bib24) 1984; 6
Helmholtz (10.1016/j.neuron.2017.05.028_bib30) 1925; Volume III
10.1016/j.neuron.2017.05.028_bib58
Lee (10.1016/j.neuron.2017.05.028_bib45) 2003; 20
Orbán (10.1016/j.neuron.2017.05.028_bib61) 2016; 92
Minka (10.1016/j.neuron.2017.05.028_bib53) 2001
Beck (10.1016/j.neuron.2017.05.028_bib2) 2008; 60
Montúfar (10.1016/j.neuron.2017.05.028_bib54) 2014; 27
Chen (10.1016/j.neuron.2017.05.028_bib11) 2013; 80
Uka (10.1016/j.neuron.2017.05.028_bib74) 2004; 42
Jiang (10.1016/j.neuron.2017.05.028_bib35) 2015; 350
Pitkow (10.1016/j.neuron.2017.05.028_bib64) 2011; 24
Laplace (10.1016/j.neuron.2017.05.028_bib44) 1812
Zeiler (10.1016/j.neuron.2017.05.028_bib79) 2014
Koller (10.1016/j.neuron.2017.05.028_bib40) 2009
Jazayeri (10.1016/j.neuron.2017.05.028_bib34) 2006; 9
Britten (10.1016/j.neuron.2017.05.028_bib8) 1996; 13
Moreno-Bote (10.1016/j.neuron.2017.05.028_bib55) 2011; 108
Ma (10.1016/j.neuron.2017.05.028_bib49) 2006; 9
Daw (10.1016/j.neuron.2017.05.028_bib17) 2006; 441
Berkes (10.1016/j.neuron.2017.05.028_bib6) 2011; 331
Haefner (10.1016/j.neuron.2017.05.028_bib27) 2013; 16
Wainwright (10.1016/j.neuron.2017.05.028_bib76) 2000; 12
Sutton (10.1016/j.neuron.2017.05.028_bib73) 1998
Daunizeau (10.1016/j.neuron.2017.05.028_bib16) 2010; 5
Buesing (10.1016/j.neuron.2017.05.028_bib9) 2011; 7
Heinemann (10.1016/j.neuron.2017.05.028_bib29) 2011
Pearl (10.1016/j.neuron.2017.05.028_bib62) 1988
Savin (10.1016/j.neuron.2017.05.028_bib71) 2014; 27
Beck (10.1016/j.neuron.2017.05.028_bib4) 2012; 74
Cohen (10.1016/j.neuron.2017.05.028_bib14) 2009; 29
References_xml – volume: 9
  start-page: 690
  year: 2006
  end-page: 696
  ident: bib34
  article-title: Optimal representation of sensory information by neural populations
  publication-title: Nat. Neurosci.
– volume: 25
  start-page: 1106
  year: 2012
  end-page: 1114
  ident: bib42
  article-title: ImageNet classification with deep convolutional neural networks
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 1
  start-page: 1
  year: 2008
  end-page: 305
  ident: bib75
  article-title: Graphical models, exponential families, and variational inference
  publication-title: Found. Trends Mach. Learn.
– volume: 17
  start-page: 1410
  year: 2014
  end-page: 1417
  ident: bib56
  article-title: Information-limiting correlations
  publication-title: Nat. Neurosci.
– volume: 5
  start-page: e15554
  year: 2010
  ident: bib16
  article-title: Observing the observer (I): meta-bayesian models of learning and decision-making
  publication-title: PLoS ONE
– volume: 13
  start-page: 87
  year: 1996
  end-page: 100
  ident: bib8
  article-title: A relationship between behavioral choice and the visual responses of neurons in macaque MT
  publication-title: Vis. Neurosci.
– volume: Volume III
  year: 1925
  ident: bib30
  publication-title: Treatise on Physiological Optics
– volume: 32
  start-page: 148
  year: 2015
  end-page: 155
  ident: bib23
  article-title: On simplicity and complexity in the brave new world of large-scale neuroscience
  publication-title: Curr. Opin. Neurobiol.
– volume: 10
  start-page: 1608
  year: 2007
  end-page: 1614
  ident: bib59
  article-title: Psychophysically measured task strategy for disparity discrimination is reflected in V2 neurons
  publication-title: Nat. Neurosci.
– start-page: 319
  year: 2011
  end-page: 326
  ident: bib29
  article-title: What cannot be learned with Bethe approximations
  publication-title: Uncertainty in Artificial Intelligence
– volume: 80
  start-page: 1310
  year: 2013
  end-page: 1321
  ident: bib11
  article-title: Diverse spatial reference frames of vestibular signals in parietal cortex
  publication-title: Neuron
– volume: 60
  start-page: 1142
  year: 2008
  end-page: 1152
  ident: bib2
  article-title: Probabilistic population codes for Bayesian decision making
  publication-title: Neuron
– volume: 441
  start-page: 876
  year: 2006
  end-page: 879
  ident: bib17
  article-title: Cortical substrates for exploratory decisions in humans
  publication-title: Nature
– volume: 29
  start-page: 1
  year: 2016
  end-page: 9
  ident: bib66
  article-title: Inference by reparameterization in neural population codes
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 110
  start-page: 17999
  year: 2013
  end-page: 18004
  ident: bib46
  article-title: Reduced choice-related activity and correlated noise accompany perceptual deficits following unilateral vestibular lesion
  publication-title: Proc. Natl. Acad. Sci. USA
– volume: 2
  start-page: 4
  year: 2008
  ident: bib41
  article-title: Representational similarity analysis—connecting the branches of systems neuroscience
  publication-title: Front. Syst. Neurosci.
– year: 1988
  ident: bib62
  article-title: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
– volume: 509
  start-page: 331
  year: 2014
  end-page: 336
  ident: bib38
  article-title: Space-time wiring specificity supports direction selectivity in the retina
  publication-title: Nature
– volume: 16
  start-page: 511
  year: 2012
  end-page: 518
  ident: bib48
  article-title: Organizing probabilistic models of perception
  publication-title: Trends Cogn. Sci.
– volume: 27
  start-page: 2924
  year: 2014
  end-page: 2932
  ident: bib54
  article-title: On the number of linear regions of deep neural networks
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 17
  start-page: 253
  year: 2007
  end-page: 263
  ident: bib72
  article-title: Recurrent neural networks are universal approximators
  publication-title: Int. J. Neural Syst.
– year: 2009
  ident: bib40
  article-title: Probabilistic Graphical Models: Principles and Techniques
– volume: 8
  start-page: 1341
  year: 1996
  end-page: 1390
  ident: bib77
  article-title: The lack of a priori distinctions between learning algorithms
  publication-title: Neural Comput.
– volume: 20
  start-page: 1434
  year: 2003
  end-page: 1448
  ident: bib45
  article-title: Hierarchical Bayesian inference in the visual cortex
  publication-title: J. Opt. Soc. Am. A Opt. Image Sci. Vis.
– volume: 13
  start-page: e1005268
  year: 2017
  ident: bib36
  article-title: Could a neuroscientist understand a microprocessor?
  publication-title: PLoS Comput. Biol.
– volume: 60
  start-page: 162
  year: 2008
  end-page: 173
  ident: bib13
  article-title: Context-dependent changes in functional circuitry in visual area MT
  publication-title: Neuron
– volume: 497
  start-page: 585
  year: 2013
  end-page: 590
  ident: bib68
  article-title: The importance of mixed selectivity in complex cognitive tasks
  publication-title: Nature
– year: 2016
  ident: bib7
  article-title: Feedback dynamics determine the structure of spike-count correlation in visual cortex
  publication-title: bioRxiv
– start-page: 818
  year: 2014
  end-page: 833
  ident: bib79
  article-title: Visualizing and understanding convolutional networks
  publication-title: European conference on computer vision
– volume: 14
  start-page: 119
  year: 2010
  end-page: 130
  ident: bib21
  article-title: Statistically optimal perception and learning: from behavior to neural representations
  publication-title: Trends Cogn. Sci.
– volume: 83
  start-page: 1213
  year: 2014
  end-page: 1226
  ident: bib1
  article-title: Sparseness and expansion in sensory representations
  publication-title: Neuron
– year: 1998
  ident: bib73
  article-title: Reinforcement Learning: An Introduction
– volume: 4
  start-page: 251
  year: 1991
  end-page: 257
  ident: bib32
  article-title: Approximation capabilities of multilayer feedforward networks
  publication-title: Neural Netw.
– start-page: 362
  year: 2001
  end-page: 369
  ident: bib53
  article-title: Expectation propagation for approximate Bayesian inference
  publication-title: Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI)
– volume: 74
  start-page: 30
  year: 2012
  end-page: 39
  ident: bib4
  article-title: Not noisy, just wrong: the role of suboptimal inference in behavioral variability
  publication-title: Neuron
– volume: 112
  start-page: E6973
  year: 2015
  end-page: E6982
  ident: bib37
  article-title: Origin of information-limiting noise correlations
  publication-title: Proc. Natl. Acad. Sci. USA
– volume: 12
  start-page: 855
  year: 2000
  end-page: 861
  ident: bib76
  article-title: Scale mixtures of Gaussians and the statistics of natural images
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 16
  start-page: 235
  year: 2013
  end-page: 242
  ident: bib27
  article-title: Inferring decoding strategies from choice probabilities in the presence of correlated variability
  publication-title: Nat. Neurosci.
– year: 2017
  ident: bib43
  article-title: Inferring decoding strategies for multiple correlated neural populations
  publication-title: bioRxiv
– volume: 80
  start-page: 312
  year: 2013
  end-page: 325
  ident: bib19
  article-title: Goals and habits in the brain
  publication-title: Neuron
– volume: 6
  start-page: 721
  year: 1984
  end-page: 741
  ident: bib24
  article-title: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images
  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
– volume: 42
  start-page: 297
  year: 2004
  end-page: 310
  ident: bib74
  article-title: Contribution of area MT to stereoscopic depth perception: choice-related response modulations reflect task strategy
  publication-title: Neuron
– volume: 108
  start-page: 12491
  year: 2011
  end-page: 12496
  ident: bib55
  article-title: Bayesian sampling in visual perception
  publication-title: Proc. Natl. Acad. Sci. USA
– reference: Hinton, G.E., and Sejnowski, T.J. (1983). Optimal perceptual inference. Proceedings of the IEEE conference on Computer Vision and Pattern Recognition. pp. 448–453.
– year: 1812
  ident: bib44
  article-title: Théorie Analytique des Probabilités
– volume: 87
  start-page: 411
  year: 2015
  end-page: 423
  ident: bib65
  article-title: How can single sensory neurons predict behavior?
  publication-title: Neuron
– volume: 7
  start-page: e1002211
  year: 2011
  ident: bib9
  article-title: Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons
  publication-title: PLoS Comput. Biol.
– volume: 11
  start-page: 1201
  year: 2008
  end-page: 1210
  ident: bib26
  article-title: Neural correlates of multisensory cue integration in macaque MSTd
  publication-title: Nat. Neurosci.
– volume: 14
  start-page: 133
  year: 2011
  end-page: 138
  ident: bib51
  article-title: Multiple models to capture the variability in biological neurons and networks
  publication-title: Nat. Neurosci.
– year: 1982
  ident: bib52
  article-title: Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
– volume: 15
  start-page: 277
  year: 2003
  end-page: 284
  ident: bib33
  article-title: Interpreting neural response variability as Monte Carlo sampling of the posterior
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 350
  start-page: aac9462
  year: 2015
  ident: bib35
  article-title: Principles of connectivity among morphologically defined cell types in adult neocortex
  publication-title: Science
– volume: 31
  start-page: 15310
  year: 2011
  end-page: 15319
  ident: bib3
  article-title: Marginalization in neural circuits with divisive normalization
  publication-title: J. Neurosci.
– volume: 87
  start-page: 869
  year: 2015
  end-page: 881
  ident: bib70
  article-title: Abstract context representations in primate amygdala and prefrontal cortex
  publication-title: Neuron
– volume: 118
  start-page: 110
  year: 2011
  end-page: 119
  ident: bib25
  article-title: Learning a theory of causality
  publication-title: Psychol. Rev.
– volume: 92
  start-page: 530
  year: 2016
  end-page: 543
  ident: bib61
  article-title: Neural variability and sampling-based probabilistic representations in the visual cortex
  publication-title: Neuron
– volume: 2
  start-page: 303
  year: 1989
  end-page: 314
  ident: bib15
  article-title: Approximation by superpositions of a sigmoidal function
  publication-title: Math. Contr. Signals Syst.
– volume: 33
  start-page: 18574
  year: 2013
  end-page: 18582
  ident: bib12
  article-title: Eye-centered representation of optic flow tuning in the ventral intraparietal area
  publication-title: J. Neurosci.
– volume: 331
  start-page: 83
  year: 2011
  end-page: 87
  ident: bib6
  article-title: Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment
  publication-title: Science
– volume: 27
  start-page: 1
  year: 2014
  end-page: 6
  ident: bib71
  article-title: Spatio-temporal representations of uncertainty in spiking neural networks
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 11
  start-page: 333
  year: 2007
  end-page: 341
  ident: bib18
  article-title: Untangling invariant object recognition
  publication-title: Trends Cogn. Sci.
– volume: 16
  start-page: 89
  year: 2013
  end-page: 97
  ident: bib47
  article-title: Choice-related activity and correlated noise in subcortical vestibular neurons
  publication-title: Nat. Neurosci.
– volume: 15
  start-page: 146
  year: 2011
  end-page: 154
  ident: bib20
  article-title: Neural correlates of reliability-based cue weighting during multisensory integration
  publication-title: Nat. Neurosci.
– volume: 29
  start-page: 6635
  year: 2009
  end-page: 6648
  ident: bib14
  article-title: Estimates of the contribution of single neurons to perception depend on timescale and noise correlation
  publication-title: J. Neurosci.
– volume: 503
  start-page: 78
  year: 2013
  end-page: 84
  ident: bib50
  article-title: Context-dependent computation by recurrent dynamics in prefrontal cortex
  publication-title: Nature
– year: 1957
  ident: bib5
  article-title: Dynamic Programming
– volume: 111
  start-page: 8619
  year: 2014
  end-page: 8624
  ident: bib78
  article-title: Performance-optimized hierarchical models predict neural responses in higher visual cortex
  publication-title: Proc. Natl. Acad. Sci. USA
– volume: 370
  start-page: 140
  year: 1994
  end-page: 143
  ident: bib80
  article-title: Correlated neuronal discharge rate and its implications for psychophysical performance
  publication-title: Nature
– volume: 85
  start-page: 861
  year: 2015
  end-page: 873
  ident: bib39
  article-title: A neural implementation of Wald’s sequential probability ratio test
  publication-title: Neuron
– reference: Ng, A.Y., and Russell, S.J. (2000). Algorithms for inverse reinforcement learning. In Proceedings of ICML.
– volume: 10
  start-page: 1
  year: 2010
  end-page: 20
  ident: bib63
  article-title: Exact feature probabilities in images with occlusion
  publication-title: J. Vis.
– volume: 105
  start-page: 18970
  year: 2008
  end-page: 18975
  ident: bib22
  article-title: Memory traces in dynamical systems
  publication-title: Proc. Natl. Acad. Sci. USA
– volume: 33
  start-page: 3567
  year: 2013
  end-page: 3581
  ident: bib10
  article-title: Functional specializations of the ventral intraparietal area for multisensory heading discrimination
  publication-title: J. Neurosci.
– volume: 8
  start-page: 1647
  year: 2005
  end-page: 1650
  ident: bib69
  article-title: In praise of artifice
  publication-title: Nat. Neurosci.
– volume: 90
  start-page: 649
  year: 2016
  end-page: 660
  ident: bib28
  article-title: Perceptual decision-making as probabilistic inference by neural sampling
  publication-title: Neuron
– volume: 9
  start-page: 1432
  year: 2006
  end-page: 1438
  ident: bib49
  article-title: Bayesian inference with probabilistic population codes
  publication-title: Nat. Neurosci.
– volume: 24
  start-page: 738
  year: 2011
  end-page: 746
  ident: bib64
  article-title: Learning unbelievable probabilities
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 16
  start-page: 1
  year: 2004
  end-page: 38
  ident: bib67
  article-title: Bayesian computation in recurrent neural circuits
  publication-title: Neural Comput.
– volume: 341
  start-page: 52
  year: 1989
  end-page: 54
  ident: bib57
  article-title: Neuronal correlates of a perceptual decision
  publication-title: Nature
– volume: 381
  start-page: 607
  year: 1996
  end-page: 609
  ident: bib60
  article-title: Emergence of simple-cell receptive field properties by learning a sparse code for natural images
  publication-title: Nature
– volume: 7
  start-page: e1002211
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib9
  article-title: Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons
  publication-title: PLoS Comput. Biol.
  doi: 10.1371/journal.pcbi.1002211
– volume: 85
  start-page: 861
  year: 2015
  ident: 10.1016/j.neuron.2017.05.028_bib39
  article-title: A neural implementation of Wald’s sequential probability ratio test
  publication-title: Neuron
  doi: 10.1016/j.neuron.2015.01.007
– volume: 110
  start-page: 17999
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib46
  article-title: Reduced choice-related activity and correlated noise accompany perceptual deficits following unilateral vestibular lesion
  publication-title: Proc. Natl. Acad. Sci. USA
  doi: 10.1073/pnas.1310416110
– year: 1988
  ident: 10.1016/j.neuron.2017.05.028_bib62
– start-page: 362
  year: 2001
  ident: 10.1016/j.neuron.2017.05.028_bib53
  article-title: Expectation propagation for approximate Bayesian inference
– volume: 381
  start-page: 607
  year: 1996
  ident: 10.1016/j.neuron.2017.05.028_bib60
  article-title: Emergence of simple-cell receptive field properties by learning a sparse code for natural images
  publication-title: Nature
  doi: 10.1038/381607a0
– volume: 112
  start-page: E6973
  year: 2015
  ident: 10.1016/j.neuron.2017.05.028_bib37
  article-title: Origin of information-limiting noise correlations
  publication-title: Proc. Natl. Acad. Sci. USA
  doi: 10.1073/pnas.1508738112
– volume: 14
  start-page: 133
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib51
  article-title: Multiple models to capture the variability in biological neurons and networks
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn.2735
– volume: 14
  start-page: 119
  year: 2010
  ident: 10.1016/j.neuron.2017.05.028_bib21
  article-title: Statistically optimal perception and learning: from behavior to neural representations
  publication-title: Trends Cogn. Sci.
  doi: 10.1016/j.tics.2010.01.003
– volume: 90
  start-page: 649
  year: 2016
  ident: 10.1016/j.neuron.2017.05.028_bib28
  article-title: Perceptual decision-making as probabilistic inference by neural sampling
  publication-title: Neuron
  doi: 10.1016/j.neuron.2016.03.020
– volume: 13
  start-page: e1005268
  year: 2017
  ident: 10.1016/j.neuron.2017.05.028_bib36
  article-title: Could a neuroscientist understand a microprocessor?
  publication-title: PLoS Comput. Biol.
  doi: 10.1371/journal.pcbi.1005268
– volume: 27
  start-page: 2924
  year: 2014
  ident: 10.1016/j.neuron.2017.05.028_bib54
  article-title: On the number of linear regions of deep neural networks
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 2
  start-page: 303
  year: 1989
  ident: 10.1016/j.neuron.2017.05.028_bib15
  article-title: Approximation by superpositions of a sigmoidal function
  publication-title: Math. Contr. Signals Syst.
  doi: 10.1007/BF02551274
– volume: 33
  start-page: 3567
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib10
  article-title: Functional specializations of the ventral intraparietal area for multisensory heading discrimination
  publication-title: J. Neurosci.
  doi: 10.1523/JNEUROSCI.4522-12.2013
– volume: 8
  start-page: 1647
  year: 2005
  ident: 10.1016/j.neuron.2017.05.028_bib69
  article-title: In praise of artifice
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn1606
– start-page: 319
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib29
  article-title: What cannot be learned with Bethe approximations
– volume: 9
  start-page: 1432
  year: 2006
  ident: 10.1016/j.neuron.2017.05.028_bib49
  article-title: Bayesian inference with probabilistic population codes
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn1790
– volume: 87
  start-page: 869
  year: 2015
  ident: 10.1016/j.neuron.2017.05.028_bib70
  article-title: Abstract context representations in primate amygdala and prefrontal cortex
  publication-title: Neuron
  doi: 10.1016/j.neuron.2015.07.024
– volume: 2
  start-page: 4
  year: 2008
  ident: 10.1016/j.neuron.2017.05.028_bib41
  article-title: Representational similarity analysis—connecting the branches of systems neuroscience
  publication-title: Front. Syst. Neurosci.
– volume: 16
  start-page: 235
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib27
  article-title: Inferring decoding strategies from choice probabilities in the presence of correlated variability
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn.3309
– year: 2016
  ident: 10.1016/j.neuron.2017.05.028_bib7
  article-title: Feedback dynamics determine the structure of spike-count correlation in visual cortex
  publication-title: bioRxiv
– volume: 12
  start-page: 855
  year: 2000
  ident: 10.1016/j.neuron.2017.05.028_bib76
  article-title: Scale mixtures of Gaussians and the statistics of natural images
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 16
  start-page: 1
  year: 2004
  ident: 10.1016/j.neuron.2017.05.028_bib67
  article-title: Bayesian computation in recurrent neural circuits
  publication-title: Neural Comput.
  doi: 10.1162/08997660460733976
– year: 1812
  ident: 10.1016/j.neuron.2017.05.028_bib44
– volume: 8
  start-page: 1341
  year: 1996
  ident: 10.1016/j.neuron.2017.05.028_bib77
  article-title: The lack of a priori distinctions between learning algorithms
  publication-title: Neural Comput.
  doi: 10.1162/neco.1996.8.7.1341
– volume: 341
  start-page: 52
  year: 1989
  ident: 10.1016/j.neuron.2017.05.028_bib57
  article-title: Neuronal correlates of a perceptual decision
  publication-title: Nature
  doi: 10.1038/341052a0
– start-page: 818
  year: 2014
  ident: 10.1016/j.neuron.2017.05.028_bib79
  article-title: Visualizing and understanding convolutional networks
– volume: 29
  start-page: 1
  year: 2016
  ident: 10.1016/j.neuron.2017.05.028_bib66
  article-title: Inference by reparameterization in neural population codes
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 17
  start-page: 253
  year: 2007
  ident: 10.1016/j.neuron.2017.05.028_bib72
  article-title: Recurrent neural networks are universal approximators
  publication-title: Int. J. Neural Syst.
  doi: 10.1142/S0129065707001111
– volume: 24
  start-page: 738
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib64
  article-title: Learning unbelievable probabilities
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 497
  start-page: 585
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib68
  article-title: The importance of mixed selectivity in complex cognitive tasks
  publication-title: Nature
  doi: 10.1038/nature12160
– year: 1998
  ident: 10.1016/j.neuron.2017.05.028_bib73
– volume: 11
  start-page: 1201
  year: 2008
  ident: 10.1016/j.neuron.2017.05.028_bib26
  article-title: Neural correlates of multisensory cue integration in macaque MSTd
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn.2191
– ident: 10.1016/j.neuron.2017.05.028_bib58
– volume: 80
  start-page: 1310
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib11
  article-title: Diverse spatial reference frames of vestibular signals in parietal cortex
  publication-title: Neuron
  doi: 10.1016/j.neuron.2013.09.006
– volume: 80
  start-page: 312
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib19
  article-title: Goals and habits in the brain
  publication-title: Neuron
  doi: 10.1016/j.neuron.2013.09.007
– volume: 15
  start-page: 277
  year: 2003
  ident: 10.1016/j.neuron.2017.05.028_bib33
  article-title: Interpreting neural response variability as Monte Carlo sampling of the posterior
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 441
  start-page: 876
  year: 2006
  ident: 10.1016/j.neuron.2017.05.028_bib17
  article-title: Cortical substrates for exploratory decisions in humans
  publication-title: Nature
  doi: 10.1038/nature04766
– volume: 9
  start-page: 690
  year: 2006
  ident: 10.1016/j.neuron.2017.05.028_bib34
  article-title: Optimal representation of sensory information by neural populations
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn1691
– volume: 16
  start-page: 89
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib47
  article-title: Choice-related activity and correlated noise in subcortical vestibular neurons
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn.3267
– volume: 83
  start-page: 1213
  year: 2014
  ident: 10.1016/j.neuron.2017.05.028_bib1
  article-title: Sparseness and expansion in sensory representations
  publication-title: Neuron
  doi: 10.1016/j.neuron.2014.07.035
– volume: 118
  start-page: 110
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib25
  article-title: Learning a theory of causality
  publication-title: Psychol. Rev.
  doi: 10.1037/a0021336
– volume: 370
  start-page: 140
  year: 1994
  ident: 10.1016/j.neuron.2017.05.028_bib80
  article-title: Correlated neuronal discharge rate and its implications for psychophysical performance
  publication-title: Nature
  doi: 10.1038/370140a0
– volume: Volume III
  year: 1925
  ident: 10.1016/j.neuron.2017.05.028_bib30
– volume: 4
  start-page: 251
  year: 1991
  ident: 10.1016/j.neuron.2017.05.028_bib32
  article-title: Approximation capabilities of multilayer feedforward networks
  publication-title: Neural Netw.
  doi: 10.1016/0893-6080(91)90009-T
– volume: 17
  start-page: 1410
  year: 2014
  ident: 10.1016/j.neuron.2017.05.028_bib56
  article-title: Information-limiting correlations
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn.3807
– volume: 11
  start-page: 333
  year: 2007
  ident: 10.1016/j.neuron.2017.05.028_bib18
  article-title: Untangling invariant object recognition
  publication-title: Trends Cogn. Sci.
  doi: 10.1016/j.tics.2007.06.010
– volume: 509
  start-page: 331
  year: 2014
  ident: 10.1016/j.neuron.2017.05.028_bib38
  article-title: Space-time wiring specificity supports direction selectivity in the retina
  publication-title: Nature
  doi: 10.1038/nature13240
– volume: 15
  start-page: 146
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib20
  article-title: Neural correlates of reliability-based cue weighting during multisensory integration
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn.2983
– year: 2009
  ident: 10.1016/j.neuron.2017.05.028_bib40
– volume: 350
  start-page: aac9462
  year: 2015
  ident: 10.1016/j.neuron.2017.05.028_bib35
  article-title: Principles of connectivity among morphologically defined cell types in adult neocortex
  publication-title: Science
  doi: 10.1126/science.aac9462
– volume: 503
  start-page: 78
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib50
  article-title: Context-dependent computation by recurrent dynamics in prefrontal cortex
  publication-title: Nature
  doi: 10.1038/nature12742
– volume: 60
  start-page: 162
  year: 2008
  ident: 10.1016/j.neuron.2017.05.028_bib13
  article-title: Context-dependent changes in functional circuitry in visual area MT
  publication-title: Neuron
  doi: 10.1016/j.neuron.2008.08.007
– volume: 5
  start-page: e15554
  year: 2010
  ident: 10.1016/j.neuron.2017.05.028_bib16
  article-title: Observing the observer (I): meta-bayesian models of learning and decision-making
  publication-title: PLoS ONE
  doi: 10.1371/journal.pone.0015554
– volume: 32
  start-page: 148
  year: 2015
  ident: 10.1016/j.neuron.2017.05.028_bib23
  article-title: On simplicity and complexity in the brave new world of large-scale neuroscience
  publication-title: Curr. Opin. Neurobiol.
  doi: 10.1016/j.conb.2015.04.003
– year: 2017
  ident: 10.1016/j.neuron.2017.05.028_bib43
  article-title: Inferring decoding strategies for multiple correlated neural populations
  publication-title: bioRxiv
– volume: 108
  start-page: 12491
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib55
  article-title: Bayesian sampling in visual perception
  publication-title: Proc. Natl. Acad. Sci. USA
  doi: 10.1073/pnas.1101430108
– volume: 27
  start-page: 1
  year: 2014
  ident: 10.1016/j.neuron.2017.05.028_bib71
  article-title: Spatio-temporal representations of uncertainty in spiking neural networks
  publication-title: Adv. Neural Inf. Process. Syst.
– year: 1982
  ident: 10.1016/j.neuron.2017.05.028_bib52
– volume: 6
  start-page: 721
  year: 1984
  ident: 10.1016/j.neuron.2017.05.028_bib24
  article-title: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images
  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
  doi: 10.1109/TPAMI.1984.4767596
– volume: 92
  start-page: 530
  year: 2016
  ident: 10.1016/j.neuron.2017.05.028_bib61
  article-title: Neural variability and sampling-based probabilistic representations in the visual cortex
  publication-title: Neuron
  doi: 10.1016/j.neuron.2016.09.038
– volume: 25
  start-page: 1106
  year: 2012
  ident: 10.1016/j.neuron.2017.05.028_bib42
  article-title: ImageNet classification with deep convolutional neural networks
  publication-title: Adv. Neural Inf. Process. Syst.
– volume: 10
  start-page: 1
  year: 2010
  ident: 10.1016/j.neuron.2017.05.028_bib63
  article-title: Exact feature probabilities in images with occlusion
  publication-title: J. Vis.
– volume: 42
  start-page: 297
  year: 2004
  ident: 10.1016/j.neuron.2017.05.028_bib74
  article-title: Contribution of area MT to stereoscopic depth perception: choice-related response modulations reflect task strategy
  publication-title: Neuron
  doi: 10.1016/S0896-6273(04)00186-2
– volume: 33
  start-page: 18574
  year: 2013
  ident: 10.1016/j.neuron.2017.05.028_bib12
  article-title: Eye-centered representation of optic flow tuning in the ventral intraparietal area
  publication-title: J. Neurosci.
  doi: 10.1523/JNEUROSCI.2837-13.2013
– ident: 10.1016/j.neuron.2017.05.028_bib31
– volume: 31
  start-page: 15310
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib3
  article-title: Marginalization in neural circuits with divisive normalization
  publication-title: J. Neurosci.
  doi: 10.1523/JNEUROSCI.1706-11.2011
– volume: 20
  start-page: 1434
  year: 2003
  ident: 10.1016/j.neuron.2017.05.028_bib45
  article-title: Hierarchical Bayesian inference in the visual cortex
  publication-title: J. Opt. Soc. Am. A Opt. Image Sci. Vis.
  doi: 10.1364/JOSAA.20.001434
– volume: 74
  start-page: 30
  year: 2012
  ident: 10.1016/j.neuron.2017.05.028_bib4
  article-title: Not noisy, just wrong: the role of suboptimal inference in behavioral variability
  publication-title: Neuron
  doi: 10.1016/j.neuron.2012.03.016
– volume: 105
  start-page: 18970
  year: 2008
  ident: 10.1016/j.neuron.2017.05.028_bib22
  article-title: Memory traces in dynamical systems
  publication-title: Proc. Natl. Acad. Sci. USA
  doi: 10.1073/pnas.0804451105
– volume: 60
  start-page: 1142
  year: 2008
  ident: 10.1016/j.neuron.2017.05.028_bib2
  article-title: Probabilistic population codes for Bayesian decision making
  publication-title: Neuron
  doi: 10.1016/j.neuron.2008.09.021
– volume: 10
  start-page: 1608
  year: 2007
  ident: 10.1016/j.neuron.2017.05.028_bib59
  article-title: Psychophysically measured task strategy for disparity discrimination is reflected in V2 neurons
  publication-title: Nat. Neurosci.
  doi: 10.1038/nn1991
– year: 1957
  ident: 10.1016/j.neuron.2017.05.028_bib5
– volume: 29
  start-page: 6635
  year: 2009
  ident: 10.1016/j.neuron.2017.05.028_bib14
  article-title: Estimates of the contribution of single neurons to perception depend on timescale and noise correlation
  publication-title: J. Neurosci.
  doi: 10.1523/JNEUROSCI.5179-08.2009
– volume: 87
  start-page: 411
  year: 2015
  ident: 10.1016/j.neuron.2017.05.028_bib65
  article-title: How can single sensory neurons predict behavior?
  publication-title: Neuron
  doi: 10.1016/j.neuron.2015.06.033
– volume: 111
  start-page: 8619
  year: 2014
  ident: 10.1016/j.neuron.2017.05.028_bib78
  article-title: Performance-optimized hierarchical models predict neural responses in higher visual cortex
  publication-title: Proc. Natl. Acad. Sci. USA
  doi: 10.1073/pnas.1403112111
– volume: 1
  start-page: 1
  year: 2008
  ident: 10.1016/j.neuron.2017.05.028_bib75
  article-title: Graphical models, exponential families, and variational inference
  publication-title: Found. Trends Mach. Learn.
  doi: 10.1561/2200000001
– volume: 331
  start-page: 83
  year: 2011
  ident: 10.1016/j.neuron.2017.05.028_bib6
  article-title: Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment
  publication-title: Science
  doi: 10.1126/science.1195870
– volume: 16
  start-page: 511
  year: 2012
  ident: 10.1016/j.neuron.2017.05.028_bib48
  article-title: Organizing probabilistic models of perception
  publication-title: Trends Cogn. Sci.
  doi: 10.1016/j.tics.2012.08.010
– volume: 13
  start-page: 87
  year: 1996
  ident: 10.1016/j.neuron.2017.05.028_bib8
  article-title: A relationship between behavioral choice and the visual responses of neurons in macaque MT
  publication-title: Vis. Neurosci.
  doi: 10.1017/S095252380000715X
SSID ssj0014591
Score 2.492624
SecondaryResourceType review_article
Snippet It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To...
SourceID unpaywall
pubmedcentral
proquest
pubmed
crossref
elsevier
SourceType Open Access Repository
Aggregation Database
Index Database
Enrichment Source
Publisher
StartPage 943
SubjectTerms Activity patterns
Algorithms
Animals
Brain
Brain - physiology
Codes
coding
Decision Making
Humans
Hypotheses
inference
Logic
message-passing
Models, Neurological
Nerve Net - physiology
Neural networks
Neurons
Neurosciences
nonlinear
Nonlinear Dynamics
nuisance
Perception - physiology
Population
population code
Probability
redundant
Reviews
Statistical analysis
Statistics
theory
SummonAdditionalLinks – databaseName: Unpaywall
  dbid: UNPAY
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3db9MwED-NToi98LHBKAxkJMRbujSOnYS3MlEVJKZpUKk8WY4_xKCkFWs1lb-eO-dDTEXaeKoin6U0d_H9HP_udwCvjfbc22EaldyIKM1EGmnhXISprORcOEwKVI386VROpunHmZjtQNu4kFiV9MU6rNHNszv-HOcF6ZRjqqNzPDk7Xlp_B3alQPjdg93p6dnoa0CLhYzILpxwFhmdcBZtuVzgdAWNSFI9HdZ6ndSD_d_paBtubrMm762rpd5c6fn8r5Q0fgDnbWFPzUT5MVivyoH5va3zePt_-xDuNwCVjWq7R7Djqn04GFW4Of-5YW9YoIyGb_H7cLfuZLk5gMmHtnCQXVQMQSV7R70n3jICs7UWNBvPF1eYKMng3FHxGjqVnXUNxNjJwrrLxzAdv_9yMomaJg2RESJbRUObaJ_mJpZWC6-FcbiDcwhCsyL20kiXFF6IUiaIhWwSe-t5iWtIkmuRe_zlT6BXLSr3lFhWZW50YnMtOZ36kzieMD7PbKplzl0feOsrZRoFc2qkMVctVe27qj2syMMqFgo93Ieom7WsFTxusM_aMFANCqnRhcIkc8PMozZqVLMSXCoEXBmtmzEOv-qG8R0mx-vKLdbBBnfNRBPsw2EdZN2tksAgotQYb-ta-HUGpA9-faS6-BZ0whEpclkkfRh0gXqrJ_Dsfyc8hz26Cgy67Ah6q19r9wKx2qp82bydfwBzPTsZ
  priority: 102
  providerName: Unpaywall
Title Inference in the Brain: Statistics Flowing in Redundant Population Codes
URI https://dx.doi.org/10.1016/j.neuron.2017.05.028
https://www.ncbi.nlm.nih.gov/pubmed/28595050
https://www.proquest.com/docview/1907318308
https://www.proquest.com/docview/1909172003
https://pubmed.ncbi.nlm.nih.gov/PMC5543692
http://www.cell.com/article/S089662731730466X/pdf
UnpaywallVersion publishedVersion
Volume 94
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAFT
  databaseName: Open Access Digital Library
  customDbUrl:
  eissn: 1097-4199
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0014591
  issn: 0896-6273
  databaseCode: KQ8
  dateStart: 19950201
  isFulltext: true
  titleUrlDefault: http://grweb.coalliance.org/oadl/oadl.html
  providerName: Colorado Alliance of Research Libraries
– providerCode: PRVESC
  databaseName: Elsevier Free Content
  customDbUrl:
  eissn: 1097-4199
  dateEnd: 20241102
  omitProxy: true
  ssIdentifier: ssj0014591
  issn: 0896-6273
  databaseCode: IXB
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVBFR
  databaseName: Free Medical Journals
  customDbUrl:
  eissn: 1097-4199
  dateEnd: 20241102
  omitProxy: true
  ssIdentifier: ssj0014591
  issn: 0896-6273
  databaseCode: DIK
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: http://www.freemedicaljournals.com
  providerName: Flying Publisher
– providerCode: PRVLSH
  databaseName: Elsevier Journals
  customDbUrl:
  mediaType: online
  eissn: 1097-4199
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0014591
  issn: 0896-6273
  databaseCode: AKRWK
  dateStart: 19880301
  isFulltext: true
  providerName: Library Specific Holdings
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fa9swEBalY2wvY2v3I1tbNBh70-JYlqz0LQ0N6cpK6RaWPQlZlmhG5oQ1oeS_351km4UWOvZkZJ1B6KS7T9bdd4R8sMZzX_YyVnArWJaLjBnhHANXVnAuHDgFzEb-ciHHk-zzVEx3yLDJhcGwytr2R5serHX9plvPZnc5m3W_JqqP7OXgAPF2T07BDvNMYfmGs-lJe5OQiVg1D4QZSjfpcyHGK3BGIgtqL_J3Yk32-93TXfh5N4ryybpams2tmc__clGj5-RZjS3pIA7_Bdlx1R7ZH1Rwrv61oR9piPYMv9H3yONYhHKzT8ZnTc4fnVUU8CA9wbIRxxRxaKRxpqP54hZ8HApcOcw7A33Qy7b2Fx0uSnfzkkxGp9-GY1bXV2BWiHzFemVqfKZsIksjvBHWweHLAX7M-4mXVrq074UoZAowpkwTX3pewPZPlRHKw5O_IrvVonJvMECqUNakpTKS44U98toJ61VeZkYq7jqEN9OqbU0-jjUw5rqJMvupozI0KkMnQoMyOoS1Xy0j-cYD8nmjMb21iDT4hwe-PGgUrOtNfKMBK-Vo8hLoft92w_bDOxVTucU6yMCBFyP8OuR1XA_tUJEbEABmAsPaWimtAFJ7b_dUs-tA8Q0gj8t-2iGf2jX1TzPw9r9n4B15iq0QBZcfkN3V77U7BLy1Ko7Io8H51ffzo7CxoDW5uBz8-AN4tyx0
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fb9MwED6NITReEGz8KAwwEuLNNI1jJ-Vtq6g62CYEm9Q3y3FsUVTSirWa-t9zZycR1ZCGeIoUXyTL57v7HN99B_DWGi98Nch4KazkWS4zbqRzHENZKYR0GBSoGvnsXE0us09TOd2BUVsLQ2mVje-PPj146-ZNv1nN_nI2639LiiGxl2MApNs9Nb0DdzOJ6ISq-KbH3VVCJmPbPJTmJN7Wz4Ukr0AaSTSog0jgSU3Z_x6fbuLPm2mUe-t6aTbXZj7_I0aNH8KDBlyyozj_R7Dj6n04OKrxYP1zw96xkO4Z_qPvw73YhXJzAJOTtuiPzWqGgJAdU9-ID4yAaORxZuP54hqDHAl8dVR4hgphX7rmX2y0qNzVY7gcf7wYTXjTYIFbKfMVH1Sp8VlhE1UZ6Y20Dk9fDgFkPky8ssqlQy9lqVLEMVWa-MqLEu0_LYwsPD7FE9itF7V7RhlSZWFNWhVGCbqxJ2I7aX2RV5lRhXA9EO2yatuwj1MTjLlu08x-6KgMTcrQidSojB7w7qtlZN-4RT5vNaa3dpHGAHHLl4etgnVjxVcawVJOPi_B4TfdMNofXaqY2i3WQQZPvJTi14OncT90UyVyQESYCU5ra6d0AsTtvT1Sz74Hjm9EeUIN0x687_bUP63A8_9egdewN7k4O9WnJ-efX8B9Ggkpcfkh7K5-rd1LBF-r8lUwrt_KOSxH
linkToUnpaywall http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3db9MwED-NToi98LHBKAxkJMRbujSOnYS3MlEVJKZpUKk8WY4_xKCkFWs1lb-eO-dDTEXaeKoin6U0d_H9HP_udwCvjfbc22EaldyIKM1EGmnhXISprORcOEwKVI386VROpunHmZjtQNu4kFiV9MU6rNHNszv-HOcF6ZRjqqNzPDk7Xlp_B3alQPjdg93p6dnoa0CLhYzILpxwFhmdcBZtuVzgdAWNSFI9HdZ6ndSD_d_paBtubrMm762rpd5c6fn8r5Q0fgDnbWFPzUT5MVivyoH5va3zePt_-xDuNwCVjWq7R7Djqn04GFW4Of-5YW9YoIyGb_H7cLfuZLk5gMmHtnCQXVQMQSV7R70n3jICs7UWNBvPF1eYKMng3FHxGjqVnXUNxNjJwrrLxzAdv_9yMomaJg2RESJbRUObaJ_mJpZWC6-FcbiDcwhCsyL20kiXFF6IUiaIhWwSe-t5iWtIkmuRe_zlT6BXLSr3lFhWZW50YnMtOZ36kzieMD7PbKplzl0feOsrZRoFc2qkMVctVe27qj2syMMqFgo93Ieom7WsFTxusM_aMFANCqnRhcIkc8PMozZqVLMSXCoEXBmtmzEOv-qG8R0mx-vKLdbBBnfNRBPsw2EdZN2tksAgotQYb-ta-HUGpA9-faS6-BZ0whEpclkkfRh0gXqrJ_Dsfyc8hz26Cgy67Ah6q19r9wKx2qp82bydfwBzPTsZ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Inference+in+the+Brain%3A+Statistics+Flowing+in+Redundant+Population+Codes&rft.jtitle=Neuron+%28Cambridge%2C+Mass.%29&rft.au=Pitkow%2C+Xaq&rft.au=Angelaki%2C+Dora+E&rft.date=2017-06-07&rft.issn=1097-4199&rft.eissn=1097-4199&rft.volume=94&rft.issue=5&rft.spage=943&rft_id=info:doi/10.1016%2Fj.neuron.2017.05.028&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0896-6273&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0896-6273&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0896-6273&client=summon