Geometric Decomposition of Statistical Inference through Gradient Flow and Co-Monotonicity Measures

• URL: http://arxiv.org/abs/2511.04599v2
• Date: Mon, 10 Nov 2025 10:18:16 GMT
• Title: Geometric Decomposition of Statistical Inference through Gradient Flow and Co-Monotonicity Measures
• Authors: Pawel Gajer, Jacques Ravel,
• Abstract summary: We develop a geometric decomposition framework offering two strategies for partitioning inference problems into regional analyses.<n>We use path-monotonicity-validated discrete Morse theory to partition samples into gradient flow cells where outcomes exhibit monotonic behavior.<n>Co-monotonicity decomposition leverages association structure, defining embeddings of samples into association space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 leverages association structure: vertex-level coefficients measuring directional concordance between outcome and features, or between feature pairs, define 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.

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