{"ID":2872899,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.07439","arxiv_id":"2509.07439","title":"Bayesian inference with Besov-Laplace priors for spatially inhomogeneous binary classification surfaces","abstract":"In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with Besov-Laplace priors, which are prior distributions on function spaces routinely used in imaging and inverse problems in view of their useful edge-preserving and sparsity-promoting properties. Building on a recent line of work in the literature, we investigate the theoretical asymptotic recovery properties of the associated posterior distributions, and show that suitably tuned Besov-Laplace priors lead to minimax-optimal posterior contraction rates as the sample size increases, under the frequentist assumption that the data have been generated by a spatially inhomogeneous ground truth belonging to a Besov space.","short_abstract":"In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with Besov-Laplace priors, which are prior distributions on function spaces routinely used in i...","url_abs":"https://arxiv.org/abs/2509.07439","url_pdf":"https://arxiv.org/pdf/2509.07439v1","authors":"[\"Matteo Giordano\"]","published":"2025-09-09T06:54:08Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}