{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/139223"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/139223","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Approximating the Log-Partition Function","abstract":"Graphical Models are used to represent structural information on a high-dimensional joint probability distribution. Their expressiveness offers simple reductions from a large number of NP-hard problems to inference tasks such as computing the partition function (exact inference) or approximating the log-partition function (approximate inference). In this master thesis, we will motivate the need for a general constant-factor approximations of the log-partition function and prove that a variant of the well studied tree-reweighted algorithm [1] achieves constant factor guarantees. We will express the corresponding approximation ratio 𝜅(𝐺) solely as a function of the graph structure 𝐺.","abstract_html":"Graphical Models are used to represent structural information on a high-dimensional joint probability distribution. Their expressiveness offers simple reductions from a large number of NP-hard problems to inference tasks such as computing the partition function (exact inference) or approximating the log-partition function (approximate inference). In this master thesis, we will motivate the need for a general constant-factor approximations of the log-partition function and prove that a variant of the well studied tree-reweighted algorithm [1] achieves constant factor guarantees. We will express the corresponding approximation ratio 𝜅(𝐺) solely as a function of the graph structure 𝐺.","abstract_has_math":false,"creators":["Cosson, Romain"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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Their expressiveness offers simple reductions from a large number of NP-hard problems to inference tasks such as computing the partition function (exact inference) or approximating the log-partition function (approximate inference). In this master thesis, we will motivate the need for a general constant-factor approximations of the log-partition function and prove that a variant of the well studied tree-reweighted algorithm [1] achieves constant factor guarantees. We will express the corresponding approximation ratio 𝜅(𝐺) solely as a function of the graph structure 𝐺."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Approximating the Log-Partition Function"]}]}],"canonical_facts":{"dc:contributor.advisor":["Shah, Devavrat"],"dc:contributor.department":["Massachusetts Institute of Technology. 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We will express the corresponding approximation ratio 𝜅(𝐺) solely as a function of the graph structure 𝐺."],"dc:description.degree":["S.M."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/139223"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Approximating the Log-Partition Function"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Science in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:11Z"}