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Our error analysis relies on a Hermite series expansion of the log posterior whose first terms are precisely cancelled out by the first order optimality conditions associated to the Gaussian VI optimization problem.<\/jats:p>","DOI":"10.1214\/24-aos2393","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T01:48:23Z","timestamp":1728006503000},"page":"1384-1409","source":"Crossref","is-referenced-by-count":15,"title":["On the approximation accuracy of Gaussian variational inference"],"prefix":"10.1214","volume":"52","author":[{"given":"Anya","family":"Katsevich","sequence":"first","affiliation":[{"name":"Department of Mathematics, Massachusetts Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philippe","family":"Rigollet","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Massachusetts Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"6","doi-asserted-by":"publisher","unstructured":"<small>Bishop, C. 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