{"ID":2870126,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.12584","arxiv_id":"2509.12584","title":"Sharp mean-field analysis of permutation mixtures and permutation-invariant decisions","abstract":"We develop sharp bounds on the statistical distance between high-dimensional permutation mixtures and their i.i.d. counterparts. Our approach establishes a new geometric link between the spectrum of a complex channel overlap matrix and the information geometry of the channel, yielding tight dimension-independent bounds that close gaps left by previous work. Within this geometric framework, we also derive dimension-dependent bounds that uncover phase transitions in dimensionality for Gaussian and Poisson families. Applied to compound decision problems, this refined control of permutation mixtures enables sharper mean-field analyses of permutation-invariant decision rules, yielding strong non-asymptotic equivalence results between two notions of compound regret in Gaussian and Poisson models.","short_abstract":"We develop sharp bounds on the statistical distance between high-dimensional permutation mixtures and their i.i.d. counterparts. Our approach establishes a new geometric link between the spectrum of a complex channel overlap matrix and the information geometry of the channel, yielding tight dimension-independent bounds...","url_abs":"https://arxiv.org/abs/2509.12584","url_pdf":"https://arxiv.org/pdf/2509.12584v1","authors":"[\"Yiguo Liang\",\"Yanjun Han\"]","published":"2025-09-16T02:22:47Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.IT\"]","methods":"[]","has_code":false}