  Convolution trees, loopy belief propagation, and fast numerical p-convolution
are combined for the first time to efficiently solve networks with several
additive constraints between random variables. An implementation of this
"convolution forest" approach is constructed from scratch, including an
improved trimmed convolution tree algorithm and engineering details that permit
fast inference in practice, and improve the ability of scientists to prototype
models with additive relationships between discrete variables. The utility of
this approach is demonstrated using several examples: these include
illustrations on special cases of some classic NP-complete problems (subset sum
and knapsack), identification of GC-rich genomic regions with a large hidden
Markov model, inference of molecular composition from summary statistics of the
intact molecule, and estimation of elemental abundance in the presence of
overlapping isotope peaks.
