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→EI and Integrated Information Theory
=EI and Other Related Topics=
=EI and Other Related Topics=
==EI and Integrated Information Theory==
==EI and Integrated Information Theory==
The concept of Effective Information (EI) was first introduced in a paper <ref name="tononi_2003">{{cite journal |last1=Tononi|first1=G.|last2=Sporns|first2=O.|title=Measuring information integration|journal=BMC Neuroscience|volume=4 |issue=31 |year=2003|url=https://doi.org/10.1186/1471-2202-4-31}}</ref> by Tononi et al. (2003) In this article, the authors defined the indicator of the [[Integrated Information Ability]] and established the [[Integrated Information Theory (IIT)]], which later evolved into an important branch of consciousness theory. The definition of the indicator of the [[Integrated Information Ability]] is based on effective information.
The concept of Effective Information (EI) was first introduced in a paper <ref name="tononi_2003">{{cite journal |last1=Tononi|first1=G.|last2=Sporns|first2=O.|title=Measuring information integration|journal=BMC Neuroscience|volume=4 |issue=31 |year=2003|url=https://doi.org/10.1186/1471-2202-4-31}}</ref> by Tononi et al. (2003) In this article, the authors defined the indicator of the [[Integrated Information Capability]] and established the [[Integrated Information Theory (IIT)]], which later evolved into an important branch of consciousness theory. The definition of the indicator of the [[Integrated Information Capability]] is based on effective information.
===EI and Φ===
===EI and Φ===
The integrated information (or the degree of integration) <math>\Phi</math>, can be defined as the minimum value of EI between any two bipartitions of a system. Suppose the system is 𝑋, and 𝑆 is a subset of 𝑋, that is partitioned into two parts, 𝐴 and 𝐵. There are causal interactions between 𝐴, 𝐵, and the rest of 𝑋. [[文件:OriginalEI.png|350x350px|The Division in Integrated Information Theory|替代=|缩略图|链接=https://wiki.swarma.org/index.php/%E6%96%87%E4%BB%B6:OriginalEI.png]] In this scenario, we can measure the strength of these causal interactions. First, we calculate the EI from 𝐴 to 𝐵, i.e., we intervene on 𝐴 such that it follows the maximum entropy distribution, then measure the mutual information between 𝐴 and 𝐵:
The integrated information (or the degree of integration) <math>\Phi</math>, can be defined as the minimum value of EI between any two bipartitions of a system. Suppose the system is 𝑋, and 𝑆 is a subset of 𝑋, that is partitioned into two parts, 𝐴 and 𝐵. There are causal interactions between 𝐴, 𝐵, and the rest of 𝑋. [[文件:OriginalEI.png|350x350px|The Division in Integrated Information Theory|替代=|缩略图|链接=https://wiki.swarma.org/index.php/%E6%96%87%E4%BB%B6:OriginalEI.png]] In this scenario, we can measure the strength of these causal interactions. First, we calculate the EI from 𝐴 to 𝐵, i.e., we intervene on 𝐴 such that it follows the maximum entropy distribution, then measure the mutual information between 𝐴 and 𝐵:
</math>
</math>
This defines the relationship between [[Integrated Information Ability]] and EI.
This defines the relationship between [[Integrated Information Capability]] and EI.
===Distinction===
===Distinction===
It is important to note that unlike EI calculations for Markov chains, the EI here measures the causal connections between two parts of the system, rather than the strength of causal connections across two different time points in the same system.
It is important to note that unlike EI calculations for Markov chains, the EI here measures the causal connections between two parts of the system, rather than the strength of causal connections across two different time points in the same system.
==EI and Other Causal Metrics==
==EI and Other Causal Metrics==
EI is a metric used to measure the strength of causal effects in a causal mechanism. Before the introduction of EI, several causal metrics had already been proposed. So, what is the relationship between EI and these causal measures? As Comolatti and Hoel pointed out in their 2022 paper, many causal metrics, including EI, can be expressed as combinations of two basic elements <ref name=":0">Comolatti, R., & Hoel, E. (2022). Causal emergence is widespread across measures of causation. ''arXiv preprint arXiv:2202.01854''.</ref>. These two basic elements are called "Causal Primitives", which represent '''Sufficiency''' and '''Necessity''' and in causal relationships.
EI is a metric used to measure the strength of causal effects in a causal mechanism. Before the introduction of EI, several causal metrics had already been proposed. So, what is the relationship between EI and these causal measures? As Comolatti and Hoel pointed out in their 2022 paper, many causal metrics, including EI, can be expressed as combinations of two basic elements <ref name=":0">Comolatti, R., & Hoel, E. (2022). Causal emergence is widespread across measures of causation. ''arXiv preprint arXiv:2202.01854''.</ref>. These two basic elements are called "Causal Primitives", which represent '''Sufficiency''' and '''Necessity''' and in causal relationships.