From Global to Local Correlation: Geometric Decomposition of Statistical Inference
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918208765689856 |
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| author | Gajer, Pawel Ravel, Jacques |
| author_facet | Gajer, Pawel Ravel, Jacques |
| contents | Understanding feature-outcome associations in high-dimensional data remains
challenging when relationships vary across subpopulations, yet standard
methods assuming global associations miss context-dependent patterns, reducing
statistical power and interpretability. We develop a geometric decomposition
framework offering two strategies for partitioning inference problems into
regional analyses on data-derived Riemannian graphs. Gradient flow
decomposition uses path-monotonicity-validated discrete Morse theory to
partition samples into gradient flow cells where outcomes exhibit monotonic
behavior. Co-monotonicity decomposition utilizes vertex-level coefficients
that provide context-dependent versions of the classical Pearson correlation:
these coefficients measure edge-based directional concordance between outcome
and features, or between feature pairs, defining embeddings of samples into
association space. These embeddings induce Riemannian k-NN graphs on which
biclustering identifies co-monotonicity cells (coherent regions) and feature
modules. This extends naturally to multi-modal integration across multiple
feature sets. Both strategies apply independently or jointly, with Bayesian
posterior sampling providing credible intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Global to Local Correlation: Geometric Decomposition of Statistical Inference Gajer, Pawel Ravel, Jacques Methodology Statistics Theory Machine Learning 62G08, 62H30, 58E05 Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical power and interpretability. We develop a geometric decomposition framework offering two strategies for partitioning inference problems into regional analyses on data-derived Riemannian graphs. Gradient flow decomposition uses path-monotonicity-validated discrete Morse theory to partition samples into gradient flow cells where outcomes exhibit monotonic behavior. Co-monotonicity decomposition utilizes vertex-level coefficients that provide context-dependent versions of the classical Pearson correlation: these coefficients measure edge-based directional concordance between outcome and features, or between feature pairs, defining embeddings of samples into association space. These embeddings induce Riemannian k-NN graphs on which biclustering identifies co-monotonicity cells (coherent regions) and feature modules. This extends naturally to multi-modal integration across multiple feature sets. Both strategies apply independently or jointly, with Bayesian posterior sampling providing credible intervals. |
| title | From Global to Local Correlation: Geometric Decomposition of Statistical Inference |
| topic | Methodology Statistics Theory Machine Learning 62G08, 62H30, 58E05 |
| url | https://arxiv.org/abs/2511.04599 |