  The shuffled linear regression problem aims to recover linear relationships
in datasets where the correspondence between input and output is unknown. This
problem arises in a wide range of applications including survey data, in which
one needs to decide whether the anonymity of the responses can be preserved
while uncovering significant statistical connections. In this work, we propose
a novel optimization algorithm for shuffled linear regression based on a
posterior-maximizing objective function assuming Gaussian noise prior. We
compare and contrast our approach with existing methods on synthetic and real
data. We show that our approach performs competitively while achieving
empirical running-time improvements. Furthermore, we demonstrate that our
algorithm is able to utilize the side information in the form of seeds, which
recently came to prominence in related problems.
