  Pairwise alignment of DNA sequencing data is a ubiquitous task in
bioinformatics and typically represents a heavy computational burden.
State-of-the-art approaches to speed up this task use hashing to identify short
segments (k-mers) that are shared by pairs of reads, which can then be used to
estimate alignment scores. However, when the number of reads is large,
accurately estimating alignment scores for all pairs is still very costly.
Moreover, in practice, one is only interested in identifying pairs of reads
with large alignment scores. In this work, we propose a new approach to
pairwise alignment estimation based on two key new ingredients. The first
ingredient is to cast the problem of pairwise alignment estimation under a
general framework of rank-one crowdsourcing models, where the workers'
responses correspond to k-mer hash collisions. These models can be accurately
solved via a spectral decomposition of the response matrix. The second
ingredient is to utilise a multi-armed bandit algorithm to adaptively refine
this spectral estimator only for read pairs that are likely to have large
alignments. The resulting algorithm iteratively performs a spectral
decomposition of the response matrix for adaptively chosen subsets of the read
pairs.
