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dc.contributor.authorDurrant, Robert J.
dc.contributor.authorKabán, Ata
dc.date.accessioned2014-12-15T22:09:57Z
dc.date.available2014-08-19
dc.date.available2014-12-15T22:09:57Z
dc.date.issued2014-08-19
dc.identifier.citationDurrant, R. J., & Kabán, A. (2014). Random projections as regularizers: learning a linear discriminant from fewer observations than dimensions. Machine Learning, 99(2), 257–286. http://doi.org/10.1007/s10994-014-5466-8en
dc.identifier.issn1573-0565
dc.identifier.urihttps://hdl.handle.net/10289/8971
dc.description.abstractWe prove theoretical guarantees for an averaging-ensemble of randomly projected Fisher linear discriminant classifiers, focusing on the casewhen there are fewer training observations than data dimensions. The specific form and simplicity of this ensemble permits a direct and much more detailed analysis than existing generic tools in previous works. In particular, we are able to derive the exact form of the generalization error of our ensemble, conditional on the training set, and based on this we give theoretical guarantees which directly link the performance of the ensemble to that of the corresponding linear discriminant learned in the full data space. To the best of our knowledge these are the first theoretical results to prove such an explicit link for any classifier and classifier ensemble pair. Furthermore we show that the randomly projected ensemble is equivalent to implementing a sophisticated regularization scheme to the linear discriminant learned in the original data space and this prevents overfitting in conditions of small sample size where pseudo-inverse FLD learned in the data space is provably poor. Our ensemble is learned from a set of randomly projected representations of the original high dimensional data and therefore for this approach data can be collected, stored and processed in such a compressed form. We confirm our theoretical findings with experiments, and demonstrate the utility of our approach on several datasets from the bioinformatics domain and one very high dimensional dataset from the drug discovery domain, both settings in which fewer observations than dimensions are the norm.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherSpringer Verlag
dc.rightsThis is an author’s accepted version of an article published in the journal: Machine Learning. © 2014 Springer.
dc.subjectrandom projections
dc.subjectensemble learning
dc.subjectlinear discriminant analysis
dc.subjectcompressed learning
dc.subjectlearning theory
dc.titleRandom projections as regularizers: learning a linear discriminant from fewer observations than dimensions
dc.typeJournal Article
dc.identifier.doi10.1007/s10994-014-5466-8
dc.relation.isPartOfMachine Learning
pubs.begin-page257
pubs.elements-id85345
pubs.end-page286
pubs.issue2
pubs.organisational-group/Waikato
pubs.organisational-group/Waikato/FCMS
pubs.organisational-group/Waikato/FCMS/Statistics
pubs.publication-statusPublished
pubs.volume99


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