The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous timescales . In this work we focus on rounding procedures based on building an ellipsoid that closely matches the sampling space, that can be used to define an efficient Hit-and-Run markov chain Monte Carlo. In this way the uniformity of the sampling  is rigorously guaranteed  at odds with procedures based on non-markovian dynamics . We analyze and compare three rounding methods in order to sample the feasible steady states of a model of the metabolism of the bacterium E. Coli. The first is based on principal component analysis (PCA), the second on linear programming (LP) and finally we employ the Lovazs ellipsoid method (LEM). Our results show that a rounding procedure is mandatory for such inference problems and suggest that a combination of LEM or LP with a subsequent PCA seems to perform the best  .
The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous time scales . In this work we focus on rounding procedures based on building an ellipsoid that closely matches the sampling space, that can be used to define an efficient hit-and-run (HR) Markov Chain Monte Carlo. In this way the uniformity of the sampling of the convex space of interest is rigorously guaranteed , at odds with non markovian methods . We analyze and compare three rounding methods in order to sample the feasible steady states of metabolic networks of three models of growing size up to genomic scale. The first is based on principal component analysis (PCA), the second on linear programming (LP) and finally we employ the lovasz ellipsoid method (LEM). Our results show that a rounding procedure is mandatory for the application of the HR in these inference problem and suggest that a combination of LEM or LP with a subsequent PCA perform the best . We finally compare the distributions of the HR with that of two heuristics based on the Artificially Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good agreement with the results of the HR for the small network, while on genome scale models present inconsistencies .
R
timescales
time scales
R
Hit-and-Run markov chain
hit-and-run (HR) Markov Chain
A
of the convex space of interest
A
,
R
procedures based on non-markovian dynamics
non markovian methods
R
a model of the metabolism of the bacterium E. Coli.
metabolic networks of three models of growing size up to genomic scale.
R
Lovazs
lovasz
R
such inference problems
the application of the HR in these inference problem
D
seems to
A
. We finally compare the distributions of the HR with that of two heuristics based on the Artificially Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good agreement with the results of the HR for the small network, while on genome scale models present inconsistencies