Genomic Similarity and Kernel Methods II: Methods for Genomic Information

Measures of genomic similarity are often the basis of flexible statistical analyses, and when based on kernel methods, they provide a powerful platform to take advantage of a broad and deep statistical theory, and a wide range of existing software; see the companion paper for a review of this material [1]. The kernel method converts information - perhaps complex or high-dimensional information - for a pair of subjects to a quantitative value representing either similarity or dissimilarity, with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This approach provides enormous opportunities to enhance genetic analyses by including a wide range of publically-available data as structured kernel 'prior' information. Kernel methods are appealing for their generality, yet this generality can make it challenging to formulate measures of similarity that directly address a specific scientific aim, or that are most powerful to detect a specific genetic mechanism. Although it is difficult to create a cook book of kernels for genetic studies, useful guidelines can be gleaned from a variety of novel published approaches. We review some novel developments of kernels for specific analyses and speculate on how to build kernels for complex genomic attributes based on publically available data. The creativity of analysts, with rigorous evaluations by applications to real and simulated data, will ultimately provide a much stronger array of kernel 'tools' for genetic analyses.