Closed-Form Gaussian Estimators for Multi-Source Partial Information Decomposition
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917479665631232 |
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| author | Lyu, Aobo Clark, Andrew Raviv, Netanel |
| author_facet | Lyu, Aobo Clark, Andrew Raviv, Netanel |
| contents | Computing multi-source partial information decomposition (PID) for continuous data is hard: existing closed-form Gaussian estimators are restricted to two source variables, while continuous arbitrary-source estimators are typically learning-based and do not provide closed-form expressions. To address this, we develop closed-form Gaussian estimators for multi-source PID. We provide two-source redundancy, multi-source unique information, the K-th order synergistic effect from source subsets of size K, and the total synergistic effect. The estimators are derived from the conditional-independence-based information measures introduced in our earlier work, under which every quantity reduces to a log-determinant expression in covariance blocks of the system. The resulting estimator is plug-in consistent, affine invariant, source-permutation symmetric, and additive over independent systems. We validate it on a controlled Gaussian benchmark, evaluate its computational efficiency against baselines, and confirm its numerical stability in finite-sample regimes. To our knowledge, this is the first covariance-based closed-form estimator that provides multi-source continuous PID measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Closed-Form Gaussian Estimators for Multi-Source Partial Information Decomposition Lyu, Aobo Clark, Andrew Raviv, Netanel Information Theory Computing multi-source partial information decomposition (PID) for continuous data is hard: existing closed-form Gaussian estimators are restricted to two source variables, while continuous arbitrary-source estimators are typically learning-based and do not provide closed-form expressions. To address this, we develop closed-form Gaussian estimators for multi-source PID. We provide two-source redundancy, multi-source unique information, the K-th order synergistic effect from source subsets of size K, and the total synergistic effect. The estimators are derived from the conditional-independence-based information measures introduced in our earlier work, under which every quantity reduces to a log-determinant expression in covariance blocks of the system. The resulting estimator is plug-in consistent, affine invariant, source-permutation symmetric, and additive over independent systems. We validate it on a controlled Gaussian benchmark, evaluate its computational efficiency against baselines, and confirm its numerical stability in finite-sample regimes. To our knowledge, this is the first covariance-based closed-form estimator that provides multi-source continuous PID measures. |
| title | Closed-Form Gaussian Estimators for Multi-Source Partial Information Decomposition |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.09919 |