Inference of the sparse kinetic Ising model using the decimation method

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the $\ell_1$-optimization based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done automatically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudo-likelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that on various topologies and with different distribution of couplings, the decimation method outperforms the widely-used $\ell _1$-optimization based methods.Comment: 11 pages, 5 figure

A generic approach to behaviour-driven biochemical model construction

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Modelling of biochemical systems has received considerable attention over the last decade from bioengineering, biochemistry, computer science, and mathematics. This thesis investigates the applications of computational techniques to computational systems biology, for the construction of biochemical models in terms of topology and kinetic rates. Due to the complexity of biochemical systems, it is natural to construct models representing the biochemical systems incrementally in a piecewise manner. Syntax and semantics of two patterns are defined for the instantiation of components which are extendable, reusable and fundamental building blocks for models composition. We propose and implement a set of genetic operators and composition rules to tackle issues of piecewise composing models from scratch. Quantitative Petri nets are evolved by the genetic operators, and evolutionary process of modelling are guided by the composition rules. Metaheuristic algorithms are widely applied in BioModel Engineering to support intelligent and heuristic analysis of biochemical systems in terms of structure and kinetic rates. We illustrate parameters of biochemical models based on Biochemical Systems Theory, and then the topology and kinetic rates of the models are manipulated by employing evolution strategy and simulated annealing respectively. A new hybrid modelling framework is proposed and implemented for the models construction. Two heuristic algorithms are performed on two embedded layers in the hybrid framework: an outer layer for topology mutation and an inner layer for rates optimization. Moreover, variants of the hybrid piecewise modelling framework are investigated. Regarding flexibility of these variants, various combinations of evolutionary operators, evaluation criteria and design principles can be taken into account. We examine performance of five sets of the variants on specific aspects of modelling. The comparison of variants is not to explicitly show that one variant clearly outperforms the others, but it provides an indication of considering important features for various aspects of the modelling. Because of the very heavy computational demands, the process of modelling is paralleled by employing a grid environment, GridGain. Application of the GridGain and heuristic algorithms to analyze biological processes can support modelling of biochemical systems in a computational manner, which can also benefit mathematical modelling in computer science and bioengineering. We apply our proposed modelling framework to model biochemical systems in a hybrid piecewise manner. Modelling variants of the framework are comparatively studied on specific aims of modelling. Simulation results show that our modelling framework can compose synthetic models exhibiting similar species behaviour, generate models with alternative topologies and obtain general knowledge about key modelling features