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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.15844 |
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| _version_ | 1866913201584603136 |
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| author | Bhattacharya, Sagnik Narayan, Prakash |
| author_facet | Bhattacharya, Sagnik Narayan, Prakash |
| contents | Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. The Markov chain on a tree is shown to possess a global Markov property based on graph separation; this property plays a key role in our proofs. When the underlying joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15844 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shared Information for a Markov Chain on a Tree Bhattacharya, Sagnik Narayan, Prakash Information Theory Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. The Markov chain on a tree is shown to possess a global Markov property based on graph separation; this property plays a key role in our proofs. When the underlying joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance. |
| title | Shared Information for a Markov Chain on a Tree |
| topic | Information Theory |
| url | https://arxiv.org/abs/2307.15844 |