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Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries. Symmetry estimation is carried out using hypothesis testing for invariance strategically over the subgroup lattice of a search group G acting on the feature space. We show that the estimation of the unique largest invariant subgroup of G generalizes useful tools from linear dimension reduction to a non-linear context. We show that the estimation is consistent when the subgroup lattice chosen is finite, even when some of the subgroups themselves are infinite. We demonstrate the performance of this estimator in synthetic settings and apply the methods to 2 data sets: satellite measurements of the Earth\u2019s magnetic field intensity and the distribution of sunspots.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf031","type":"journal-article","created":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T07:21:26Z","timestamp":1748848886000},"page":"1576-1618","source":"Crossref","is-referenced-by-count":2,"title":["Estimating maximal symmetries of regression functions via subgroup lattices"],"prefix":"10.1093","volume":"87","author":[{"given":"Louis G","family":"Christie","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge , Cambridge ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John A D","family":"Aston","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge , 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