Improved Moves for Truncated Convex Models
Mudigonda Pawan Kumar and Philip Torr
In: NIPS 22, Neural Information Processing Conference,(2008).
We consider the problem of obtaining the approximate maximum a posteriori estimate
of a discrete random field characterized by pairwise potentials that form a
truncated convex model. For this problem, we propose an improved st-MINCUT
based move making algorithm. Unlike previous move making approaches, which
either provide a loose bound or no bound on the quality of the solution (in terms
of the corresponding Gibbs energy), our algorithm achieves the same guarantees
as the standard linear programming (LP) relaxation. Compared to previous
approaches based on the LP relaxation, e.g. interior-point algorithms or treereweighted
message passing (TRW), our method is faster as it uses only the efficient
st-MINCUT algorithm in its design. Furthermore, it directly provides us with
a primal solution (unlike TRW and other related methods which solve the dual
of the LP). We demonstrate the effectiveness of the proposed approach on both
synthetic and standard real data problems.
Our analysis also opens up an interesting question regarding the relationship between
move making algorithms (such as alpha-expansion and the algorithms presented
in this paper) and the randomized rounding schemes used with convex relaxations.
We believe that further explorations in this direction would help design
efficient algorithms for more complex relaxations.