{"ID":2825233,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.05273","arxiv_id":"2601.05273","title":"Bayesian Recovery for Probabilistic Coalition Structures","abstract":"Probabilistic Coalition Structure Generation (PCSG) is NP-hard and can be recast as an $l_0$-type sparse recovery problem by representing coalition structures as sparse coefficient vectors over a coalition-incidence design. A natural question is whether standard sparse methods, such as $l_1$ relaxations and greedy pursuits, can reliably recover the optimal coalition structure in this setting. We show that the answer is negative in a PCSG-inspired regime where overlapping coalitions generate highly coherent, near-duplicate columns: the irrepresentable condition fails for the design, and $k$-step Orthogonal Matching Pursuit (OMP) exhibits a nonvanishing probability of irreversible mis-selection. In contrast, we prove that Sparse Bayesian Learning (SBL) with a Gaussian-Gamma hierarchy is support consistent under the same structural assumptions. The concave sparsity penalty induced by SBL suppresses spurious near-duplicates and recovers the true coalition support with probability tending to one. This establishes a rigorous separation between convex, greedy, and Bayesian sparse approaches for PCSG.","short_abstract":"Probabilistic Coalition Structure Generation (PCSG) is NP-hard and can be recast as an $l_0$-type sparse recovery problem by representing coalition structures as sparse coefficient vectors over a coalition-incidence design. A natural question is whether standard sparse methods, such as $l_1$ relaxations and greedy purs...","url_abs":"https://arxiv.org/abs/2601.05273","url_pdf":"https://arxiv.org/pdf/2601.05273v1","authors":"[\"Angshul Majumdar\"]","published":"2025-12-25T13:03:07Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"cs.AI\"]","methods":"[]","has_code":false}