The uniform sampling of convex polytopes is an interesting computational problem with many applications , in particular in the field of metabolic network analysis , but the performances of sampling algorithms can be affected by high condition numbers in real instances . In this work we define a procedure in order to reduce the condition number based on building an ellipsoid that closely matches the sampling space . This defines an affine transformation that renders the space homogeneous and suited to an efficient sampling by means of an Hit-and-Run Montecarlo markov chain . In this way the uniformity of the sampling is rigorously guaranteed at odds with procedures based on non-markovian dynamics. We propose two methods in order to build the ellipsoid: one based on principal component analysis and the other on linear programming . We show its performances on highly heterogeneous hyper-rectangles and apply it to a model of the metabolism of the bacterium E.Coli .
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 .
R
, in particular in the field of metabolic network analysis
in inference from linear constraints
R
high condition numbers in real instances
ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous timescales
R
define a procedure in order to reduce the condition number
focus on rounding procedures
R
. This defines an affine transformation that renders the space homogeneous and suited to an efficient sampling by means of an
, that can be used to define an efficient
R
Montecarlo markov chain
markov chain Monte Carlo
R
propose two
analyze and compare three rounding
R
build the ellipsoid: one
sample the feasible steady states of a model of the metabolism of the bacterium E.Coli. The first is
R
and the other
(PCA), the second
R
. We show its performances on highly heterogeneous hyper-rectangles and apply it to a model of the metabolism of the bacterium E.Coli
(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