Fast inference of ill-posed problems within a convex space. (21st July 2016)

• Record Type: Journal Article
• Authors: Fernandez-de-Cossio-Diaz, J; Mulet, R
• Is Part Of: Journal of statistical mechanics. (2016:Jul.)
• Publication Date: 2016-07-21
• Subjects: Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/07/073207
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem ill-defined: the model is consistent with the data for many values of its parameters. The objective is to find the probability distribution of parameter values consistent with the data, a problem that can be cast as the exploration of a high dimensional convex polytope. In this work we introduce a novel algorithm to solve this problem efficiently. It provides results that are statistically indistinguishable from currently used numerical techniques while its running time scales linearly with the system size. We show that the algorithm performs robustly in many abstract and practical applications. As working examples we simulate the effects of restricting reaction fluxes on the space of feasible phenotypes of a genome scale Escherichia coli metabolic network and infer the traffic flow between origin and destination nodes in a real communication network.