Random projections as regularizers: learning a linear discriminant from fewer observations than dimensions

We prove theoretical guarantees for an averaging-ensemble of randomly projected Fisher Linear Discriminant classifiers, focusing on the case when 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 s...

• Type: Journal
• Year: 2015
• Where: ML
• Authors: Robert J. Durrant, Ata Kabán
• Keywords: Machine Learning, ML 2015