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The treatment and covariates may be discrete or continuous in general spaces. Because of a decomposition property specific to the reproducing kernel Hilbert space, our estimators have simple closed-form solutions. We prove uniform consistency with finite sample rates via an original analysis of generalized kernel ridge regression. We extend our main results to counterfactual distributions and to causal functions identified by front and back door criteria. We achieve state-of-the-art performance in nonlinear simulations with many covariates, and conduct a policy evaluation of the US Job Corps training programme for disadvantaged youths.<\/jats:p>","DOI":"10.1093\/biomet\/asad042","type":"journal-article","created":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T20:24:16Z","timestamp":1688502256000},"page":"497-516","source":"Crossref","is-referenced-by-count":10,"title":["Kernel methods for causal functions: dose, heterogeneous and incremental response curves"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9732-5001","authenticated-orcid":false,"given":"R","family":"Singh","sequence":"first","affiliation":[{"name":"Department of Economics, Massachusetts Institute of Technology , 50 Memorial Drive, Cambridge, Massachusetts 02142, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L","family":"Xu","sequence":"additional","affiliation":[{"name":"Gatsby Computational Neuroscience Unit, University College London , 25 Howland Street , London W1T 4JG, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A","family":"Gretton","sequence":"additional","affiliation":[{"name":"Gatsby Computational Neuroscience Unit, University College London , 25 Howland Street , London W1T 4JG, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,7,5]]},"reference":[{"key":"2024051307572879700_asad042-B1","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1080\/07350015.2014.975555","article-title":"Estimating conditional average treatment effects","volume":"33","author":"Abrevaya","year":"2015","journal-title":"J. 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