Decomposing and Tracing Mutual Information by Quantifying Reachable Decision Regions
The idea of a partial information decomposition (PID) gained significant attention for attributing the components of mutual information from multiple variables about a target to being unique, redundant/shared or synergetic. Since the original measure for this analysis was criticized, several alterna...
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| Published in: | Entropy (Basel, Switzerland) Vol. 25; no. 7; p. 1014 |
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| Abstract | The idea of a partial information decomposition (PID) gained significant attention for attributing the components of mutual information from multiple variables about a target to being unique, redundant/shared or synergetic. Since the original measure for this analysis was criticized, several alternatives have been proposed but have failed to satisfy the desired axioms, an inclusion–exclusion principle or have resulted in negative partial information components. For constructing a measure, we interpret the achievable type I/II error pairs for predicting each state of a target variable (reachable decision regions) as notions of pointwise uncertainty. For this representation of uncertainty, we construct a distributive lattice with mutual information as consistent valuation and obtain an algebra for the constructed measure. The resulting definition satisfies the original axioms, an inclusion–exclusion principle and provides a non-negative decomposition for an arbitrary number of variables. We demonstrate practical applications of this approach by tracing the flow of information through Markov chains. This can be used to model and analyze the flow of information in communication networks or data processing systems. |
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| AbstractList | The idea of a partial information decomposition (PID) gained significant attention for attributing the components of mutual information from multiple variables about a target to being unique, redundant/shared or synergetic. Since the original measure for this analysis was criticized, several alternatives have been proposed but have failed to satisfy the desired axioms, an inclusion–exclusion principle or have resulted in negative partial information components. For constructing a measure, we interpret the achievable type I/II error pairs for predicting each state of a target variable (reachable decision regions) as notions of pointwise uncertainty. For this representation of uncertainty, we construct a distributive lattice with mutual information as consistent valuation and obtain an algebra for the constructed measure. The resulting definition satisfies the original axioms, an inclusion–exclusion principle and provides a non-negative decomposition for an arbitrary number of variables. We demonstrate practical applications of this approach by tracing the flow of information through Markov chains. This can be used to model and analyze the flow of information in communication networks or data processing systems. The idea of a partial information decomposition (PID) gained significant attention for attributing the components of mutual information from multiple variables about a target to being unique, redundant/shared or synergetic. Since the original measure for this analysis was criticized, several alternatives have been proposed but have failed to satisfy the desired axioms, an inclusion-exclusion principle or have resulted in negative partial information components. For constructing a measure, we interpret the achievable type I/II error pairs for predicting each state of a target variable (reachable decision regions) as notions of pointwise uncertainty. For this representation of uncertainty, we construct a distributive lattice with mutual information as consistent valuation and obtain an algebra for the constructed measure. The resulting definition satisfies the original axioms, an inclusion-exclusion principle and provides a non-negative decomposition for an arbitrary number of variables. We demonstrate practical applications of this approach by tracing the flow of information through Markov chains. This can be used to model and analyze the flow of information in communication networks or data processing systems.The idea of a partial information decomposition (PID) gained significant attention for attributing the components of mutual information from multiple variables about a target to being unique, redundant/shared or synergetic. Since the original measure for this analysis was criticized, several alternatives have been proposed but have failed to satisfy the desired axioms, an inclusion-exclusion principle or have resulted in negative partial information components. For constructing a measure, we interpret the achievable type I/II error pairs for predicting each state of a target variable (reachable decision regions) as notions of pointwise uncertainty. For this representation of uncertainty, we construct a distributive lattice with mutual information as consistent valuation and obtain an algebra for the constructed measure. The resulting definition satisfies the original axioms, an inclusion-exclusion principle and provides a non-negative decomposition for an arbitrary number of variables. We demonstrate practical applications of this approach by tracing the flow of information through Markov chains. This can be used to model and analyze the flow of information in communication networks or data processing systems. The idea of a partial information decomposition (PID) gained significant attention for attributing the components of mutual information from multiple variables about a target to being unique, redundant/shared or synergetic. Since the original measure for this analysis was criticized, several alternatives have been proposed but have failed to satisfy the desired axioms, an inclusion–exclusion principle or have resulted in negative partial information components. For constructing a measure, we interpret the achievable type I/II error pairs for predicting each state of a target variable (reachable decision regions) as notions of pointwise uncertainty. For this representation of uncertainty, we construct a distributive lattice with mutual information as consistent valuation and obtain an algebra for the constructed measure. The resulting definition satisfies the original axioms, an inclusion–exclusion principle and provides a non-negative decomposition for an arbitrary number of variables. We demonstrate practical applications of this approach by tracing the flow of information through Markov chains. This can be used to model and analyze the flow of information in communication networks or data processing systems. |
| Audience | Academic |
| Author | Mages, Tobias Rohner, Christian |
| AuthorAffiliation | Department of Information Technology, Uppsala University, 752 36 Uppsala, Sweden; christian.rohner@it.uu.se |
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| References | Knuth (ref_13) 2019; 531 Harder (ref_8) 2013; 87 Rosas (ref_4) 2020; 53 Bertschinger (ref_10) 2014; 16 Schechtman (ref_16) 2019; 77 ref_14 Rassouli (ref_3) 2020; 15 ref_12 ref_23 ref_11 ref_22 Griffith (ref_6) 2014; 16 Neyman (ref_17) 1933; 231 ref_21 ref_20 ref_1 Fawcett (ref_15) 2006; 27 ref_2 ref_19 ref_18 ref_9 James (ref_24) 2018; 3 ref_5 ref_7 |
| References_xml | – ident: ref_7 doi: 10.1007/978-3-319-00395-5 – volume: 231 start-page: 289 year: 1933 ident: ref_17 article-title: IX. On the Problem of the Most Efficient Tests of Statistical Hypotheses publication-title: Philos. Trans. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character – ident: ref_2 doi: 10.3390/e19090494 – ident: ref_9 – ident: ref_5 – volume: 16 start-page: 2161 year: 2014 ident: ref_10 article-title: Quantifying Unique Information publication-title: Entropy doi: 10.3390/e16042161 – ident: ref_12 doi: 10.1109/ISIT.2014.6875280 – ident: ref_11 – volume: 27 start-page: 861 year: 2006 ident: ref_15 article-title: An introduction to ROC analysis publication-title: Pattern Recognit. Lett. doi: 10.1016/j.patrec.2005.10.010 – ident: ref_21 doi: 10.3390/e24030403 – volume: 531 start-page: 1700370 year: 2019 ident: ref_13 article-title: Lattices and Their Consistent Quantification publication-title: Ann. Der Phys. doi: 10.1002/andp.201700370 – volume: 3 start-page: 738 year: 2018 ident: ref_24 article-title: dit: A Python package for discrete information theory publication-title: J. Open Source Softw. doi: 10.21105/joss.00738 – volume: 15 start-page: 2012 year: 2020 ident: ref_3 article-title: Data Disclosure Under Perfect Sample Privacy publication-title: IEEE Trans. Inf. Forensics Secur. doi: 10.1109/TIFS.2019.2954652 – volume: 87 start-page: 012130 year: 2013 ident: ref_8 article-title: Bivariate measure of redundant information publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.87.012130 – ident: ref_23 doi: 10.1109/ISIT.2014.6875230 – volume: 77 start-page: 171 year: 2019 ident: ref_16 article-title: The relationship between Gini terminology and the ROC curve publication-title: Metron doi: 10.1007/s40300-019-00160-7 – ident: ref_14 – ident: ref_18 – ident: ref_20 doi: 10.3390/e20040297 – volume: 16 start-page: 1985 year: 2014 ident: ref_6 article-title: Intersection Information Based on Common Randomness publication-title: Entropy doi: 10.3390/e16041985 – volume: 53 start-page: 485001 year: 2020 ident: ref_4 article-title: An operational information decomposition via synergistic disclosure publication-title: J. Phys. Math. Theor. doi: 10.1088/1751-8121/abb723 – ident: ref_19 doi: 10.1109/CDC45484.2021.9683569 – ident: ref_22 doi: 10.3390/e19020071 – ident: ref_1 doi: 10.3390/e20040307 |
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| SubjectTerms | Algebra Axioms Communication networks Computer Science with specialization in Computer Communication Data processing Datavetenskap med inriktning mot datorkommunikation Decomposition Information flow information flow analysis Information management Markov chains Markov processes partial information decomposition redundancy synergy Tracing Uncertainty Valuation Variables |
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| Title | Decomposing and Tracing Mutual Information by Quantifying Reachable Decision Regions |
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