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