Principal Inertia Components and Applications
© 1963-2012 IEEE. We explore properties and applications of the principal inertia components (PICs) between two discrete random variables $X$ and $Y$. The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between $X$ and $Y$...
| Main Authors: | , , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers (IEEE)
2021
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| Online Access: | https://hdl.handle.net/1721.1/134996 |
| _version_ | 1811080819203112960 |
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| author | Calmon, Flavio du Pin Makhdoumi, Ali Medard, Muriel Varia, Mayank Christiansen, Mark Duffy, Ken R |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Calmon, Flavio du Pin Makhdoumi, Ali Medard, Muriel Varia, Mayank Christiansen, Mark Duffy, Ken R |
| author_sort | Calmon, Flavio du Pin |
| collection | MIT |
| description | © 1963-2012 IEEE. We explore properties and applications of the principal inertia components (PICs) between two discrete random variables $X$ and $Y$. The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between $X$ and $Y$. Moreover, the PICs describe which functions of $X$ can or cannot be reliably inferred (in terms of MMSE), given an observation of $Y$. We demonstrate that the PICs play an important role in information theory, and they can be used to characterize information-theoretic limits of certain estimation problems. In privacy settings, we prove that the PICs are related to the fundamental limits of perfect privacy. |
| first_indexed | 2024-09-23T11:37:22Z |
| format | Article |
| id | mit-1721.1/134996 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:37:22Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1349962023-12-22T20:39:37Z Principal Inertia Components and Applications Calmon, Flavio du Pin Makhdoumi, Ali Medard, Muriel Varia, Mayank Christiansen, Mark Duffy, Ken R Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science © 1963-2012 IEEE. We explore properties and applications of the principal inertia components (PICs) between two discrete random variables $X$ and $Y$. The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between $X$ and $Y$. Moreover, the PICs describe which functions of $X$ can or cannot be reliably inferred (in terms of MMSE), given an observation of $Y$. We demonstrate that the PICs play an important role in information theory, and they can be used to characterize information-theoretic limits of certain estimation problems. In privacy settings, we prove that the PICs are related to the fundamental limits of perfect privacy. 2021-10-27T20:10:14Z 2021-10-27T20:10:14Z 2017 2019-06-20T18:28:16Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134996 en 10.1109/TIT.2017.2700857 IEEE Transactions on Information Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Calmon, Flavio du Pin Makhdoumi, Ali Medard, Muriel Varia, Mayank Christiansen, Mark Duffy, Ken R Principal Inertia Components and Applications |
| title | Principal Inertia Components and Applications |
| title_full | Principal Inertia Components and Applications |
| title_fullStr | Principal Inertia Components and Applications |
| title_full_unstemmed | Principal Inertia Components and Applications |
| title_short | Principal Inertia Components and Applications |
| title_sort | principal inertia components and applications |
| url | https://hdl.handle.net/1721.1/134996 |
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