Parameter estimation for stochastic hybrid models of biochemical reaction networks

Mikeev, Linar; Wolf, Verena

doi:10.1145/2185632.2185657

Cited by 13 publications

(10 citation statements)

References 16 publications

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“…The moment dynamics of this system are nonclosed and moment closure is required to approximate the information. We choose the parameters in this example such that it is possible to accurately approximate the entire probability distribution using finite state projection [Munsky and Khammash 2006]. Consequently, the true information can be computed up to a small error and we can evaluate the quality of our moment-closure-based approximate results.…”

Section: A Model Of Transient Gene Expressionmentioning

confidence: 99%

“…However, for most systems, the number of states that can be reached by the process is very large or even infinite, which often makes computing the time evolution of the probability distribution intractable. In such cases, approximate methods can sometimes be used (see, e.g., Munsky and Khammash [2006], , and Hjartarson et al [2013]). The idea of these methods is that the number of states that are likely to be reached by the process may be much smaller than the number of states that can theoretically be reached and thus the state space can be truncated.…”

Section: Introductionmentioning

confidence: 99%

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Moment-Based Methods for Parameter Inference and Experiment Design for Stochastic Biochemical Reaction Networks

Ruess

Lygeros

2015

ACM Trans. Model. Comput. Simul.

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Continuous-time Markov chains are commonly used in practice for modeling biochemical reaction networks in which the inherent randomness of the molecular interactions cannot be ignored. This has motivated recent research effort into methods for parameter inference and experiment design for such models. The major difficulty is that such methods usually require one to iteratively solve the chemical master equation that governs the time evolution of the probability distribution of the system. This, however, is rarely possible, and even approximation techniques remain limited to relatively small and simple systems. An alternative explored in this article is to base methods on only some low-order moments of the entire probability distribution. We summarize the theory behind such moment-based methods for parameter inference and experiment design and provide new case studies where we investigate their performance. ACM Reference Format:Jakob Ruess and John Lygeros. 2015. Moment-based methods for parameter inference and experiment design for stochastic biochemical reaction networks. ACM Trans. Model.

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Section: A Model Of Transient Gene Expressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Moment-Based Methods for Parameter Inference and Experiment Design for Stochastic Biochemical Reaction Networks

Ruess

Lygeros

2015

ACM Trans. Model. Comput. Simul.

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“…These methods have been used in a wide variety of application areas, e.g., [16], [25], [14], etc. In this paper, we minimize the relative squared error, defined as…”

Section: Crv2 Outbreak In July 2011mentioning

confidence: 99%

Fitting a code-red virus spread model: An account of putting theory into practice

Kolesnichenko

Haverkort

Remke

et al. 2016

2016 12th International Conference on the Design of Reliable Communication Networks (DRCN)

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This paper is about fitting a model for the spreading of a computer virus to measured data, contributing not only the fitted model, but equally important, an account of the process of getting there. Over the last years, there has been an increased interest in epidemic models to study the speed of virus spread. But parameterising such models is hard, because due to the unexpected nature of real outbreaks, there is not much solid measurement data available, and the data may often have imperfections. We propose a mean-field model for computer virus spread, and use parameter fitting techniques to set the model's parameter values based on measured data. We discuss a number of steps that had to be taken to make the fitting work, including preprocessing and interpreting the measurement data, and restructuring the model based on the available data. We show that the resulting parameterised model closely mimics real system behaviour, with a relative squared error of 0.7%.

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“…Parameter estimation techniques are widely used in application areas such as biochemical reactions [76], computer vision [106], cosmology [73], etc. In this thesis we combine a mean-field model of worm behaviour with parameter fitting techniques, and illustrate their combination on the case of the Code-Red worm.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…In general terms, there exist a number of parameter estimation techniques, such as, least squared error [1], maximum likelihood [78], generalized maximum spacing estimates [38], generalized method of moments [48], etc. These methods are widely used in application areas such as biochemical reactions [76], computer vision [106], cosmology [73], etc. We will use two well-known parameter estimation methods, namely, least squared error [1] and maximum likelihood [78] for this case-study.…”

Section: Motivationmentioning

confidence: 99%

Model-checking mean-field models : algorithms & applications

Kolesnichenko¹

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Large systems of interacting objects are highly prevalent in today's world. Such system usually consist of a large number of relatively simple identical objects, and can be observed in many different field as, e.g., physics (interactions of molecules in gas), chemistry (chemical reactions), epidemiology (spread of the infection), etc. In this thesis we primarily address large systems of interacting objects in computer science, namely, computer networks. Analysis of such large systems is made difficult by the state space explosion problem, i.e., the number of states of the model grows exponentially with the number of interacting objects. In this thesis we tackle the state-space explosion problem by applying meanfield approximation, which was originally developed for models in physics, like the interaction of molecules in a gas. The mean-field method works by not considering the state of each individual object separately, but only their average, i.e., what fraction of the objects are in each possible state at any time. It allows to compute the exact limiting behaviour of an infinite population of identical objects, and this limiting behaviour is a good approximation, even when the number of objects is not infinite but sufficiently large. In this thesis we provide the theoretical background necessary for applying the mean-field method and illustrate the approach by a peer-to-peer Botnet case study. This thesis aims at formulating and analysing advanced properties of large systems of interacting objects using fast, efficient, and accurate algorithms. We propose to apply model-checking techniques to mean-field models. This allows (i) defining advanced properties of mean-field models, such as survivability, steady-state availability, conditional instantaneous availability using logic; and (ii) automatically checking these properties using model-checking algorithms. Existing model-checking logics and algorithms can not directly be applied to mean-field models since the model consist of two layers: the local level, describing the behaviour of a randomly chosen individual object in a large system, and the global level, which addresses the overall system of all viii interacting objects. Therefore, we motivate and define two logics, called Mean Field Continuous Stochastic Logic (MF-CSL), and Mean-Field Logic (MFL), for describing properties of systems composed of many identical interacting objects, on both the local and the global level. We present model-checking algorithms for checking both MF-CSL and MFL properties, and illustrated these algorithms using an extensive example on virus propagation in a computer network. We discuss the differences in the expressiveness of these two logics as well as their possible combination. Additionally, we combine the mean-field method with parameter fitting techniques in order to model real-world large systems, and obtain a better understanding of the behaviour of such systems. We explain how to build a mean-field model of the system, and how to estimate the corresponding parameter valu...

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Parameter estimation for stochastic hybrid models of biochemical reaction networks

Cited by 13 publications

References 16 publications

Moment-Based Methods for Parameter Inference and Experiment Design for Stochastic Biochemical Reaction Networks

Moment-Based Methods for Parameter Inference and Experiment Design for Stochastic Biochemical Reaction Networks

Fitting a code-red virus spread model: An account of putting theory into practice

Model-checking mean-field models : algorithms & applications

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