{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/152656"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/152656","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Empirical Bayes via ERM and Rademacher complexities: the Poisson model","abstract":"We consider the problem of empirical Bayes estimation for (multivariate) Poisson means. Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have several shortcomings. For example, the classical Robbins estimator does not retain the monotonicity property of the Bayes estimator and performs poorly under moderate sample size. Estimators based on the minimum distance and non-parametric maximum likelihood (NPMLE) methods correct these issues, but are computationally expensive with complexity growing exponentially with dimension. Extending the approach of Barbehenn and Zhao (2022), in this work we construct monotone estimators based on empirical risk minimization (ERM) that retain similar theoretical guarantees and can be computed much more efficiently. Adapting the idea of offset Rademacher complexity Liang et. al (2015) to the non-standard loss and function class in empirical Bayes, we show that the shape-constrained ERM estimator attains the minimax regret within constant factors in one dimension and within logarithmic factors in multiple dimensions.","abstract_html":"We consider the problem of empirical Bayes estimation for (multivariate) Poisson means. Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have several shortcomings. For example, the classical Robbins estimator does not retain the monotonicity property of the Bayes estimator and performs poorly under moderate sample size. Estimators based on the minimum distance and non-parametric maximum likelihood (NPMLE) methods correct these issues, but are computationally expensive with complexity growing exponentially with dimension. Extending the approach of Barbehenn and Zhao (2022), in this work we construct monotone estimators based on empirical risk minimization (ERM) that retain similar theoretical guarantees and can be computed much more efficiently. Adapting the idea of offset Rademacher complexity Liang et. al (2015) to the non-standard loss and function class in empirical Bayes, we show that the shape-constrained ERM estimator attains the minimax regret within constant factors in one dimension and within logarithmic factors in multiple dimensions.","abstract_has_math":false,"creators":["Teh, Anzo Zhao Yang"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science","school":null,"contributors":[],"advisors":["Polyanskiy, Yury"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-09","date_published":"2023-09","updated_at":"2026-07-22T22:22:22Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"rights_urls":["https://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/152656","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Polyanskiy, Yury"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have several shortcomings. For example, the classical Robbins estimator does not retain the monotonicity property of the Bayes estimator and performs poorly under moderate sample size. Estimators based on the minimum distance and non-parametric maximum likelihood (NPMLE) methods correct these issues, but are computationally expensive with complexity growing exponentially with dimension. Extending the approach of Barbehenn and Zhao (2022), in this work we construct monotone estimators based on empirical risk minimization (ERM) that retain similar theoretical guarantees and can be computed much more efficiently. Adapting the idea of offset Rademacher complexity Liang et. al (2015) to the non-standard loss and function class in empirical Bayes, we show that the shape-constrained ERM estimator attains the minimax regret within constant factors in one dimension and within logarithmic factors in multiple dimensions."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Empirical Bayes via ERM and Rademacher complexities: the Poisson model"]}]}],"canonical_facts":{"dc:contributor.advisor":["Polyanskiy, Yury"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Teh, Anzo Zhao Yang"],"dc:date.accessioned":["2023-11-02T20:06:17Z"],"dc:date.available":["2023-11-02T20:06:17Z"],"dc:date.issued":["2023-09"],"dc:description.abstract":["We consider the problem of empirical Bayes estimation for (multivariate) Poisson means. Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have several shortcomings. For example, the classical Robbins estimator does not retain the monotonicity property of the Bayes estimator and performs poorly under moderate sample size. Estimators based on the minimum distance and non-parametric maximum likelihood (NPMLE) methods correct these issues, but are computationally expensive with complexity growing exponentially with dimension. Extending the approach of Barbehenn and Zhao (2022), in this work we construct monotone estimators based on empirical risk minimization (ERM) that retain similar theoretical guarantees and can be computed much more efficiently. Adapting the idea of offset Rademacher complexity Liang et. al (2015) to the non-standard loss and function class in empirical Bayes, we show that the shape-constrained ERM estimator attains the minimax regret within constant factors in one dimension and within logarithmic factors in multiple dimensions."],"dc:description.degree":["S.M."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/152656"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Empirical Bayes via ERM and Rademacher complexities: the Poisson model"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Science in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:22Z"}