Beyond independent component analysis: identifiability and algorithms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918157077184512 |
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| author | Ribot, Alvaro Seigal, Anna Zwiernik, Piotr |
| author_facet | Ribot, Alvaro Seigal, Anna Zwiernik, Piotr |
| contents | Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero structure generalizes diagonality. These models have been the subject of recent work in non-independent component analysis. We show that pairwise mean independence answers the question of how much one can relax independence: it is identifiable, any weaker notion is non-identifiable, and it contains the models previously studied as special cases. Our results apply to distributions with the required zero pattern at any cumulant tensor. We propose an algebraic recovery algorithm based on least-squares optimization over the orthogonal group. Simulations highlight robustness: enforcing full independence can harm estimation, while pairwise mean independence enables more stable recovery. These findings extend the classical ICA framework and provide a rigorous basis for blind source separation beyond independence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond independent component analysis: identifiability and algorithms Ribot, Alvaro Seigal, Anna Zwiernik, Piotr Statistics Theory Machine Learning 62H12, 62R01, 62E10, 15A69 Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero structure generalizes diagonality. These models have been the subject of recent work in non-independent component analysis. We show that pairwise mean independence answers the question of how much one can relax independence: it is identifiable, any weaker notion is non-identifiable, and it contains the models previously studied as special cases. Our results apply to distributions with the required zero pattern at any cumulant tensor. We propose an algebraic recovery algorithm based on least-squares optimization over the orthogonal group. Simulations highlight robustness: enforcing full independence can harm estimation, while pairwise mean independence enables more stable recovery. These findings extend the classical ICA framework and provide a rigorous basis for blind source separation beyond independence. |
| title | Beyond independent component analysis: identifiability and algorithms |
| topic | Statistics Theory Machine Learning 62H12, 62R01, 62E10, 15A69 |
| url | https://arxiv.org/abs/2510.07525 |