A Gaussian Tree Approximation for Integer Least-Squares
Jacob Goldberger and Amir Leshem
In: NIPS 2009, 6-8 DEC 2009, Vancover, Canada.
This paper proposes a new algorithm for the linear least squares
problem where the unknown variables are constrained to be in a
finite set. The factor graph that corresponds to this problem is
very loopy; in fact, it is a complete graph. Hence, applying the
Belief Propagation (BP) algorithm yields very poor results. The
algorithm described here is based on an optimal tree approximation of the Gaussian density of the unconstrained linear system. It is shown that even though the approximation
is not directly applied to the exact discrete distribution,
applying the BP algorithm to the modified factor graph
outperforms current methods in terms of both performance and complexity. The improved performance of the proposed
algorithm is demonstrated on the problem of MIMO detection.