{"ID":2887039,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.02585","arxiv_id":"2508.02585","title":"Variational Bernstein-von Mises theorem with increasing parameter dimension","abstract":"Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings or specific models. To address this limitation, this paper develops a finite-sample theory for VB in a broad class of parametric models with latent variables. We establish theoretical properties of the VB posterior, including a non-asymptotic variational Bernstein--von Mises theorem. Furthermore, we derive consistency and asymptotic normality of the VB estimator. An application to multivariate Gaussian mixture models is presented for illustration.","short_abstract":"Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings or specific models. To address this limitation, this paper develops a finite-samp...","url_abs":"https://arxiv.org/abs/2508.02585","url_pdf":"https://arxiv.org/pdf/2508.02585v1","authors":"[\"Jiawei Yan\",\"Peirong Xu\",\"Tao Wang\"]","published":"2025-08-04T16:40:33Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}