Approximate MMAP by Marginal Search
  We present a heuristic strategy for marginal MAP (MMAP) queries in graphical
models. The algorithm is based on a reduction of the task to a polynomial
number of marginal inference computations. Given an input evidence, the
marginals mass functions of the variables to be explained are computed.
Marginal information gain is used to decide the variables to be explained
first, and their most probable marginal states are consequently moved to the
evidence. The sequential iteration of this procedure leads to a MMAP
explanation and the minimum information gain obtained during the process can be
regarded as a confidence measure for the explanation. Preliminary experiments
show that the proposed confidence measure is properly detecting instances for
which the algorithm is accurate and, for sufficiently high confidence levels,
the algorithm gives the exact solution or an approximation whose Hamming
distance from the exact one is small.
