I will describe the problem of multiparametric generation (which is #P-complete) and a relaxation of this problem (multiparametric Boltzmann sampling) for which we construct a fully polynomial algorithm. Our algorithm relies on the convex optimisation techniques, namely on the Exponential Conic Solver (ECOS) constructed in 2013 by Domahidi, Chu and Boyd.
The implementation of our algorithm is available on github. As a practical benchmark, we perform the tuning of regular grammars with over 1k tuning parameters, 19k states and 357k transitions in about 2 hours (the previously known algorithm was exponential in the number of parameters).
In order to give impression of the numerous applications of multiparametric sampling, I will present six different examples:
I. Software testing and code generation using lambda calculus;
II. Non-uniform sparse random graphs;
III. Belief propagation in tree decomposition for RNA design (Ponty, Will, Hammer);
IV. Bose-Einstein condensate in quantum harmonic oscillator represented by integer partitions;
V. Multiclass queuing networks (Buši? , Bouillard, Rovetta);
VI. Combinatorial Learning problems and connection with Maximum Likelihood approach.
