Approximate maximum likelihood estimation for stochastic chemical kinetics

Lecture Notes in Computer Science

2013

Abstract. Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are qualitative properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation.

Section: Methodsmentioning

confidence: 99%

Learning and Designing Stochastic Processes from Logical Constraints

Bortolussi

Lecture Notes in Computer Science

2013

“…A major computational hurdle in applying Bayes' rule is the estimation of the proportionality constant Z in equation (1). This term, the marginal likelihood or evidence, represents the probability of the data under all possible settings of the parameters; its value is obtained by performing (usually analytically intractable) integrals over the parameter space, which become prohibitive in even moderate dimensions.…”

Section: Bayesian Inferencementioning

confidence: 99%

“…In the case of CTMCs, this problem is further compounded by the fact that (in general) even the likelihood cannot be computed analytically: the probability of the state of a CTMC taking a particular value at a certain time can only be obtained by solving the chemical master equation, which is impossible in most cases. In general, Bayesian inference in CTMCs remains a challenging problem: current methods either resort to approximations to the chemical master equations [12,1] or sampling approximations [15,3]. In all of these approaches, inference relies on a low level mathematical description of the system as a Markov transition system, and often specific characteristics of the system (e.g.…”

Section: Bayesian Inferencementioning

confidence: 99%

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ABC–Fun: A Probabilistic Programming Language for Biology

Georgoulas

Hillston

Computational Methods in Systems Biology

2013

Abstract. Formal methods have long been employed to capture the dynamics of biological systems in terms of Continuous Time Markov Chains. The formal approach enables the use of elegant analysis tools such as model checking, but usually relies on a complete specification of the model of interest and cannot easily accommodate uncertain data. In contrast, data-driven modelling, based on machine learning techniques, can fit models to available data but their reliance on low level mathematical descriptions of systems makes it difficult to readily transfer methods from one problem to the next. Probabilistic programming languages potentially offer a framework in which the strengths of these two approaches can be combined, yet their expressivity is limited at the moment. We propose a high-level framework for specifying and performing inference on descriptions of models using a probabilistic programming language. We extend the expressivity of an existing probabilistic programming language, Infer.NET Fun, in order to enable inference and simulation of CTMCs. We demonstrate our method on simple test cases, including a more complex model of gene expression. Our results suggest that this is a promising approach with room for future development on the interface between formal methods and machine learning.

“…While most e↵orts are focussing on the problem of identifying parameter values that may match particular specifications in terms of observations or global properties (parameter synthesis, [1,12,4,8,10]), more recent e↵orts aim at characterising and exploiting the dependence of system properties on the parametrisation, and embedding the concept of uncertainty in formal modelling languages [7,9,15]. Despite the considerable interest such approaches are generating, user-friendly implementations of machine learning methodologies for formal analysis are currently lacking.…”

Section: Introductionmentioning

confidence: 99%

U-Check: Model Checking and Parameter Synthesis Under Uncertainty

Bortolussi

Milios

Quantitative Evaluation of Systems

2015

Abstract. Novel applications of formal modelling such as systems biology have highlighted the need to extend formal analysis techniques to domains with pervasive parametric uncertainty. Consequently, machine learning methods for parameter synthesis and uncertainty quantification are playing an increasingly significant role in quantitative formal modelling. In this paper, we introduce a toolbox for parameter synthesis and model checking in uncertain systems based on Gaussian Process emulation and optimisation. The toolbox implements in a user friendly way the techniques described in a series of recent papers at QEST and other primary venues, and it interfaces easily with widely used modelling languages such as PRISM and Bio-PEPA. We describe in detail the architecture and use of the software, demonstrating its application on a case study.