  Second-generation sequencing technologies have replaced array-based
technologies and become the default method for genomics and epigenomics
analysis. Second-generation sequencing technologies sequence tens of millions
of 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 the
genome. Effective extraction of signals in these short read counts is the key
to the success of sequencing technologies. Nonparametric methods, in particular
smoothing splines, have been used extensively for modeling and processing
single sequencing samples. However, nonparametric joint modeling of multiple
second-generation sequencing samples is still lacking due to computational
cost. In this article, we develop an adaptive basis selection method for
efficient computation of exponential family smoothing splines for modeling
multiple second-generation sequencing samples. Our adaptive basis selection
gives a sparse approximation of smoothing splines, yielding a lower-dimensional
effective model space for a more scalable computation. The asymptotic analysis
shows that the effective model space is rich enough to retain essential
features of the data. Moreover, exponential family smoothing spline models
computed via adaptive basis selection are shown to have good statistical
properties, e.g., convergence at the same rate as that of full basis
exponential family smoothing splines. The empirical performance is demonstrated
through simulation studies and two second-generation sequencing data examples.
