Statistical methods for investigating linear and non-linear relationships in sparse high-dimensional data

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Complex high-dimensional data arise in many important biological experiments, and the complexity continues to grow exponentially due to rapid advances in technology on how molecular information is generated. For example, it has now become routine to generate large-scale Single Nucleotide Polymorphism (SNP) data, currently in the order of 500,000 to 1 million, to study potential association of genetic markers with complex traits and diseases. Another example, is large scale data arising in DNA gene expression microarrays, often measured on relatively few subjects. Although the volume of data from such experiments is large, important signals are typically few in number and finding the "needles in the haystacks" poses numerous analytical and practical challenges.