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One of the objectives of designing feature selection learning algorithms isto obtain classifiers that depend on a small number of attributes and haveverifiable future performance guarantees. There are few, if any, approachesthat successfully address the two goals simultaneously. Performance guaranteesbecome crucial for tasks such as microarray data analysis due to very smallsample sizes resulting in limited empirical evaluation. To the best of ourknowledge, such algorithms that give theoretical bounds on the futureperformance have not been proposed so far in the context of the classificationof gene expression data. In this work, we investigate the premise of learning aconjunction (or disjunction) of decision stumps in Occam's Razor, SampleCompression, and PAC-Bayes learning settings for identifying a small subset ofattributes that can be used to perform reliable classification tasks. We applythe proposed approaches for gene identification from DNA microarray data andcompare our results to those of well known successful approaches proposed forthe task. We show that our algorithm not only finds hypotheses with muchsmaller number of genes while giving competitive classification accuracy butalso have tight risk guarantees on future performance unlike other approaches.The proposed approaches are general and extensible in terms of both designingnovel algorithms and application to other domains.

Feature Selection with Conjunctions of Decision Stumps and Learning from Microarray Data