Publication:
Geometric Representation Learning

dc.contributor.advisorAndrew McCallum
dc.contributor.authorVilnis, Luke
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2024-03-27T17:55:15.000
dc.date.accessioned2024-04-26T15:44:24Z
dc.date.available2024-04-26T15:44:24Z
dc.date.submittedFebruary
dc.date.submitted2021
dc.description.abstractVector embedding models are a cornerstone of modern machine learning methods for knowledge representation and reasoning. These methods aim to turn semantic questions into geometric questions by learning representations of concepts and other domain objects in a lower-dimensional vector space. In that spirit, this work advocates for density- and region-based representation learning. Embedding domain elements as geometric objects beyond a single point enables us to naturally represent breadth and polysemy, make asymmetric comparisons, answer complex queries, and provides a strong inductive bias when labeled data is scarce. We present a model for word representation using Gaussian densities, enabling asymmetric entailment judgments between concepts, and a probabilistic model for weighted transitive relations and multivariate discrete data based on a lattice of axis-aligned hyperrectangle representations (boxes). We explore the suitability of these embedding methods in different regimes of sparsity, edge weight, correlation, and independence structure, as well as extensions of the representation and different optimization strategies. We make a theoretical investigation of the representational power of the box lattice, and propose extensions to address shortcomings in modeling difficult distributions and graphs.
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentComputer Science
dc.identifier.doihttps://doi.org/10.7275/20638273
dc.identifier.orcidhttps://orcid.org/0000-0001-9220-012X
dc.identifier.urihttps://hdl.handle.net/20.500.14394/18443
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=3195&context=dissertations_2&unstamped=1
dc.source.statuspublished
dc.subjectApplied Statistics
dc.subjectArtificial Intelligence and Robotics
dc.subjectData Science
dc.titleGeometric Representation Learning
dc.typeopenaccess
dc.typearticle
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:lvilnis@gmail.com|institution:University of Massachusetts Amherst|Vilnis, Luke
digcom.identifierdissertations_2/2146
digcom.identifier.contextkey20638273
digcom.identifier.submissionpathdissertations_2/2146
dspace.entity.typePublication
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