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

复杂的高维数据出现在许多重要的生物实验中，并且由于分子信息生成技术的快速发展，复杂性继续呈指数级增长。例如，生成大规模的单核苷酸多态性（SNP）数据（目前在50万至100万的数量级）以研究遗传标记与复杂性状和疾病的潜在关联现在已经成为常规。另一个例子是在DNA基因表达微阵列中产生的大规模数据，通常在相对较少的受试者上测量。虽然这些实验的数据量很大，但重要的信号通常很少，而且在“大海捞针”中找到这些信号带来了许多分析和实践挑战。

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.