The Identity of Information
Standard
The Identity of Information : How Deterministic Dependencies Constrain Information Synergy and Redundancy. / Chicharro, Daniel; Pica, Giuseppe; Panzeri, Stefano.
In: ENTROPY-SWITZ, Vol. 20, No. 3, 05.03.2018.Research output: SCORING: Contribution to journal › SCORING: Journal article › Research › peer-review
Harvard
APA
Vancouver
Bibtex
}
RIS
TY - JOUR
T1 - The Identity of Information
T2 - How Deterministic Dependencies Constrain Information Synergy and Redundancy
AU - Chicharro, Daniel
AU - Pica, Giuseppe
AU - Panzeri, Stefano
PY - 2018/3/5
Y1 - 2018/3/5
N2 - Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (2010) proposed a partial information decomposition (PID) that separates the mutual information that a set of sources contains about a set of targets into nonnegative terms interpretable as these pieces. Quantifying redundancy requires assigning an identity to different information pieces, to assess when information is common across sources. Harder et al. (2013) proposed an identity axiom that imposes necessary conditions to quantify qualitatively common information. However, Bertschinger et al. (2012) showed that, in a counterexample with deterministic target-source dependencies, the identity axiom is incompatible with ensuring PID nonnegativity. Here, we study systematically the consequences of information identity criteria that assign identity based on associations between target and source variables resulting from deterministic dependencies. We show how these criteria are related to the identity axiom and to previously proposed redundancy measures, and we characterize how they lead to negative PID terms. This constitutes a further step to more explicitly address the role of information identity in the quantification of redundancy. The implications for studying neural coding are discussed.
AB - Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (2010) proposed a partial information decomposition (PID) that separates the mutual information that a set of sources contains about a set of targets into nonnegative terms interpretable as these pieces. Quantifying redundancy requires assigning an identity to different information pieces, to assess when information is common across sources. Harder et al. (2013) proposed an identity axiom that imposes necessary conditions to quantify qualitatively common information. However, Bertschinger et al. (2012) showed that, in a counterexample with deterministic target-source dependencies, the identity axiom is incompatible with ensuring PID nonnegativity. Here, we study systematically the consequences of information identity criteria that assign identity based on associations between target and source variables resulting from deterministic dependencies. We show how these criteria are related to the identity axiom and to previously proposed redundancy measures, and we characterize how they lead to negative PID terms. This constitutes a further step to more explicitly address the role of information identity in the quantification of redundancy. The implications for studying neural coding are discussed.
U2 - 10.3390/e20030169
DO - 10.3390/e20030169
M3 - SCORING: Journal article
C2 - 33265260
VL - 20
JO - ENTROPY-SWITZ
JF - ENTROPY-SWITZ
SN - 1099-4300
IS - 3
ER -