Learning probability distributions is a fundamental inferential task in statistics but challenging if a data distribution of our interest is complicated and high-dimensional. Addressing this challenging problem is the main topic of this thesis, and mainly discussed herein are two types of new tree-based methods: a single-tree method and an ensemble method. The new single tree method, the main topic of Chapter 2, is introduced by constructing a generalized Polya tree process, that is, a new Bayesian nonparametric model, equipped with a new flexible tree prior. With this new prior we can find trees that represent the distributional structures well, and the tree space is efficiently explored with a new sequential Monte Carlo algorithm. The new ensemble method discussed in Chapter 3 is proposed under a new addition rule defined for probability distributions. The new rule based on cumulative distribution functions and their generalizations enables us to smoothly introduce a new efficient boosting algorithm, inheriting the important notions such as \"residuals\" and \"zeros\"..The thesis is closed by Chapter 4 which provides concluding remarks.
","abstract_html":"<p>Learning probability distributions is a fundamental inferential task in statistics but challenging if a data distribution of our interest is complicated and high-dimensional. Addressing this challenging problem is the main topic of this thesis, and mainly discussed herein are two types of new tree-based methods: a single-tree method and an ensemble method. The new single tree method, the main topic of Chapter 2, is introduced by constructing a generalized Polya tree process, that is, a new Bayesian nonparametric model, equipped with a new flexible tree prior. With this new prior we can find trees that represent the distributional structures well, and the tree space is efficiently explored with a new sequential Monte Carlo algorithm. The new ensemble method discussed in Chapter 3 is proposed under a new addition rule defined for probability distributions. The new rule based on cumulative distribution functions and their generalizations enables us to smoothly introduce a new efficient boosting algorithm, inheriting the important notions such as "residuals" and "zeros"..The thesis is closed by Chapter 4 which provides concluding remarks.</p>","abstract_has_math":false,"creators":["Awaya, Naoki"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Ma, Li"],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022","date_published":"2022","updated_at":"2026-07-24T02:07:21Z","subjects":["Statistics","Bayes statistics","Boosting","High-dimensional data analysis","Monte Carlo","Nonparametrics","Tree-based method"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10161/25822","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ma, Li"]},{"key":"dc:creator","label":"Author","values":["Awaya, Naoki"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-09-21T13:55:06Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-09-21T13:55:06Z"]},{"key":"dc:date.issued","label":"Date","values":["2022"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Statistics","Bayes statistics","Boosting","High-dimensional data analysis","Monte Carlo","Nonparametrics","Tree-based method"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10161/25822"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Learning probability distributions is a fundamental inferential task in statistics but challenging if a data distribution of our interest is complicated and high-dimensional. Addressing this challenging problem is the main topic of this thesis, and mainly discussed herein are two types of new tree-based methods: a single-tree method and an ensemble method. The new single tree method, the main topic of Chapter 2, is introduced by constructing a generalized Polya tree process, that is, a new Bayesian nonparametric model, equipped with a new flexible tree prior. With this new prior we can find trees that represent the distributional structures well, and the tree space is efficiently explored with a new sequential Monte Carlo algorithm. The new ensemble method discussed in Chapter 3 is proposed under a new addition rule defined for probability distributions. The new rule based on cumulative distribution functions and their generalizations enables us to smoothly introduce a new efficient boosting algorithm, inheriting the important notions such as \"residuals\" and \"zeros\"..The thesis is closed by Chapter 4 which provides concluding remarks.
"]},{"key":"dc:title","label":"Title","values":["Tree-based Methods for Learning Probability Distributions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Ma, Li"],"dc:creator":["Awaya, Naoki"],"dc:date.accessioned":["2022-09-21T13:55:06Z"],"dc:date.available":["2022-09-21T13:55:06Z"],"dc:date.issued":["2022"],"dc:description.abstract":["Learning probability distributions is a fundamental inferential task in statistics but challenging if a data distribution of our interest is complicated and high-dimensional. Addressing this challenging problem is the main topic of this thesis, and mainly discussed herein are two types of new tree-based methods: a single-tree method and an ensemble method. The new single tree method, the main topic of Chapter 2, is introduced by constructing a generalized Polya tree process, that is, a new Bayesian nonparametric model, equipped with a new flexible tree prior. With this new prior we can find trees that represent the distributional structures well, and the tree space is efficiently explored with a new sequential Monte Carlo algorithm. The new ensemble method discussed in Chapter 3 is proposed under a new addition rule defined for probability distributions. The new rule based on cumulative distribution functions and their generalizations enables us to smoothly introduce a new efficient boosting algorithm, inheriting the important notions such as \"residuals\" and \"zeros\"..The thesis is closed by Chapter 4 which provides concluding remarks.
"],"dc:identifier.uri":["https://hdl.handle.net/10161/25822"],"dc:subject":["Statistics","Bayes statistics","Boosting","High-dimensional data analysis","Monte Carlo","Nonparametrics","Tree-based method"],"dc:title":["Tree-based Methods for Learning Probability Distributions"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:07:21Z"}