dc.contributor.author Stokell, BG dc.contributor.author Shah, RD dc.date.accessioned 2022-06-29T19:46:34Z dc.date.available 2022-06-29T19:46:34Z dc.date.issued 2022 dc.date.submitted 2021-10-03 dc.identifier.issn 0960-3174 dc.identifier.other s11222-022-10110-5 dc.identifier.other 10110 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/338521 dc.description.abstract There are a variety of settings where vague prior information may be available on the importance of predictors in high-dimensional regression settings. Examples include ordering on the variables offered by their empirical variances (which is typically discarded through standardisation), the lag of predictors when fitting autoregressive models in time series settings, or the level of missingness of the variables. Whilst such orderings may not match the true importance of variables, we argue that there is little to be lost, and potentially much to be gained, by using them. We propose a simple scheme involving fitting a sequence of models indicated by the ordering. We show that the computational cost for fitting all models when ridge regression is used is no more than for a single fit of ridge regression, and describe a strategy for Lasso regression that makes use of previous fits to greatly speed up fitting the entire sequence of models. We propose to select a final estimator by cross-validation and provide a general result on the quality of the best performing estimator on a test set selected from among a number $M$ of competing estimators in a high-dimensional linear regression setting. Our result requires no sparsity assumptions and shows that only a $\log M$ price is incurred compared to the unknown best estimator. We demonstrate the effectiveness of our approach when applied to missing or corrupted data, and time series settings. An R package is available on github. dc.language en dc.publisher Springer Science and Business Media LLC dc.subject Article dc.subject High-dimensional data dc.subject Low variance filter dc.subject Lasso dc.subject Ridge regression dc.subject Missing data dc.subject Corrupted data dc.title High-dimensional regression with potential prior information on variable importance dc.type Article dc.date.updated 2022-06-29T19:46:34Z prism.issueIdentifier 3 prism.publicationName Statistics and Computing prism.volume 32 dc.identifier.doi 10.17863/CAM.85934 dcterms.dateAccepted 2022-05-16 rioxxterms.versionofrecord 10.1007/s11222-022-10110-5 rioxxterms.version VoR rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ dc.contributor.orcid Shah, RD [0000-0001-9073-3782] dc.identifier.eissn 1573-1375 pubs.funder-project-id Engineering and Physical Sciences Research Council (EP/N031938/1) cam.issuedOnline 2022-06-14
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