Matrix and tensor factorization methods decompose the observed matrix and tensor data into a set of factor matrices. They provide a useful way to extract latent factors or features from complex data, and also to predict missing data. Matrix and tensor factorization has drawn significant attentions in a wide variety of applications, such as topic modeling, recommender system, and learning from social network and knowledge base. However, developing factorization methods for massive and sparse observations remains a challenge, especially when the data are binary or count-valued (which is true of most real-world data). In this thesis, we present a set of scalable Bayesian factorization models for low rank approximation of massive matrix or tensors with binary and count-valued observations. The proposed models enjoy the following properties: (1) The inference complexity scales linearly in the number of non-zeros in the data; (2) The side-information along a certain dimension, such as pairwise relationships (e.g., an adjacency network) between entities, can be easily leveraged to handle issues such as data sparsity, and the cold-start problem; (3) The proposed models have full local conjugacy, leading to simple, closed-form batch inference as well as online inference; (4) In contrast to many existing matrix and tensor factorization methods, in which factor matrices are usually assumed to be real-valued, we assume non-negativity on factor matrices. The non-negative factor matrices in our model provide easy interpretability; (5) For tensor factorization, the number of \"topics\", or in other words, the rank of tensor, can be inferred from the data. In this thesis, we evaluate the proposed models on a variety of real-world data sets, from diverse domains, such as analyzing scholarly text data, political science data, large-scale market transaction data and knowledge-graphs, etc.
","abstract_html":"<p>Matrix and tensor factorization methods decompose the observed matrix and tensor data into a set of factor matrices. They provide a useful way to extract latent factors or features from complex data, and also to predict missing data. Matrix and tensor factorization has drawn significant attentions in a wide variety of applications, such as topic modeling, recommender system, and learning from social network and knowledge base. However, developing factorization methods for massive and sparse observations remains a challenge, especially when the data are binary or count-valued (which is true of most real-world data). In this thesis, we present a set of scalable Bayesian factorization models for low rank approximation of massive matrix or tensors with binary and count-valued observations. The proposed models enjoy the following properties: (1) The inference complexity scales linearly in the number of non-zeros in the data; (2) The side-information along a certain dimension, such as pairwise relationships (e.g., an adjacency network) between entities, can be easily leveraged to handle issues such as data sparsity, and the cold-start problem; (3) The proposed models have full local conjugacy, leading to simple, closed-form batch inference as well as online inference; (4) In contrast to many existing matrix and tensor factorization methods, in which factor matrices are usually assumed to be real-valued, we assume non-negativity on factor matrices. The non-negative factor matrices in our model provide easy interpretability; (5) For tensor factorization, the number of "topics", or in other words, the rank of tensor, can be inferred from the data. In this thesis, we evaluate the proposed models on a variety of real-world data sets, from diverse domains, such as analyzing scholarly text data, political science data, large-scale market transaction data and knowledge-graphs, etc.</p>","abstract_has_math":false,"creators":["Hu, Changwei"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Carin, Lawrence"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-24T02:07:07Z","subjects":["Statistics","Computer science","Artificial intelligence"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10161/14383","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Carin, Lawrence"]},{"key":"dc:creator","label":"Author","values":["Hu, Changwei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-05-16T17:27:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-05-16T17:27:26Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Statistics","Computer science","Artificial intelligence"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10161/14383"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Matrix and tensor factorization methods decompose the observed matrix and tensor data into a set of factor matrices. They provide a useful way to extract latent factors or features from complex data, and also to predict missing data. Matrix and tensor factorization has drawn significant attentions in a wide variety of applications, such as topic modeling, recommender system, and learning from social network and knowledge base. However, developing factorization methods for massive and sparse observations remains a challenge, especially when the data are binary or count-valued (which is true of most real-world data). In this thesis, we present a set of scalable Bayesian factorization models for low rank approximation of massive matrix or tensors with binary and count-valued observations. The proposed models enjoy the following properties: (1) The inference complexity scales linearly in the number of non-zeros in the data; (2) The side-information along a certain dimension, such as pairwise relationships (e.g., an adjacency network) between entities, can be easily leveraged to handle issues such as data sparsity, and the cold-start problem; (3) The proposed models have full local conjugacy, leading to simple, closed-form batch inference as well as online inference; (4) In contrast to many existing matrix and tensor factorization methods, in which factor matrices are usually assumed to be real-valued, we assume non-negativity on factor matrices. The non-negative factor matrices in our model provide easy interpretability; (5) For tensor factorization, the number of \"topics\", or in other words, the rank of tensor, can be inferred from the data. In this thesis, we evaluate the proposed models on a variety of real-world data sets, from diverse domains, such as analyzing scholarly text data, political science data, large-scale market transaction data and knowledge-graphs, etc.
"]},{"key":"dc:title","label":"Title","values":["Scalable Bayesian Matrix and Tensor Factorization for Discrete Data"]}]}],"canonical_facts":{"dc:contributor.advisor":["Carin, Lawrence"],"dc:creator":["Hu, Changwei"],"dc:date.accessioned":["2017-05-16T17:27:26Z"],"dc:date.available":["2017-05-16T17:27:26Z"],"dc:date.issued":["2017"],"dc:description.abstract":["Matrix and tensor factorization methods decompose the observed matrix and tensor data into a set of factor matrices. They provide a useful way to extract latent factors or features from complex data, and also to predict missing data. Matrix and tensor factorization has drawn significant attentions in a wide variety of applications, such as topic modeling, recommender system, and learning from social network and knowledge base. However, developing factorization methods for massive and sparse observations remains a challenge, especially when the data are binary or count-valued (which is true of most real-world data). In this thesis, we present a set of scalable Bayesian factorization models for low rank approximation of massive matrix or tensors with binary and count-valued observations. The proposed models enjoy the following properties: (1) The inference complexity scales linearly in the number of non-zeros in the data; (2) The side-information along a certain dimension, such as pairwise relationships (e.g., an adjacency network) between entities, can be easily leveraged to handle issues such as data sparsity, and the cold-start problem; (3) The proposed models have full local conjugacy, leading to simple, closed-form batch inference as well as online inference; (4) In contrast to many existing matrix and tensor factorization methods, in which factor matrices are usually assumed to be real-valued, we assume non-negativity on factor matrices. The non-negative factor matrices in our model provide easy interpretability; (5) For tensor factorization, the number of \"topics\", or in other words, the rank of tensor, can be inferred from the data. In this thesis, we evaluate the proposed models on a variety of real-world data sets, from diverse domains, such as analyzing scholarly text data, political science data, large-scale market transaction data and knowledge-graphs, etc.
"],"dc:identifier.uri":["https://hdl.handle.net/10161/14383"],"dc:subject":["Statistics","Computer science","Artificial intelligence"],"dc:title":["Scalable Bayesian Matrix and Tensor Factorization for Discrete Data"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:07:07Z"}