Adaptive Basis Selection for Exponential Family Smoothing Splines with Application in Joint Modeling of Multiple Sequencing Samples

摘要

Second-generation sequencing technologies have replaced array-basedtechnologies and become the default method for genomics and epigenomicsanalysis. Second-generation sequencing technologies sequence tens of millionsof DNA/cDNA fragments in parallel. After the resulting sequences (short reads)are mapped to the genome, one gets a sequence of short read counts along thegenome. Effective extraction of signals in these short read counts is the keyto the success of sequencing technologies. Nonparametric methods, in particularsmoothing splines, have been used extensively for modeling and processingsingle sequencing samples. However, nonparametric joint modeling of multiplesecond-generation sequencing samples is still lacking due to computationalcost. In this article, we develop an adaptive basis selection method forefficient computation of exponential family smoothing splines for modelingmultiple second-generation sequencing samples. Our adaptive basis selectiongives a sparse approximation of smoothing splines, yielding a lower-dimensionaleffective model space for a more scalable computation. The asymptotic analysisshows that the effective model space is rich enough to retain essentialfeatures of the data. Moreover, exponential family smoothing spline modelscomputed via adaptive basis selection are shown to have good statisticalproperties, e.g., convergence at the same rate as that of full basisexponential family smoothing splines. The empirical performance is demonstratedthrough simulation studies and two second-generation sequencing data examples.