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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andreychenko, A., Mikeev, L., Spieler, D., Wolf, V.: Approximate maximum likelihood estimation for stochastic chemical kinetics. EURASIP Journal on Bioinformatics and Systems Biology 2012(1), 9 (2012)
Borgström, J., Gordon, A.D., Greenberg, M., Margetson, J., Van Gael, J.: Measure transformer semantics for Bayesian machine learning. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 77–96. Springer, Heidelberg (2011)
Boys, R., Wilkinson, D., Kirkwood, T.: Bayesian inference for a discretely observed stochastic kinetic model. Statistics and Computing 18, 125–135 (2008)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81(25), 2340–2361 (1977)
Goodman, N.D., Mansinghka, V.K., Roy, D.M., Bonawitz, K., Tenenbaum, J.B.: Church: a language for generative models. In: UAI, pp. 220–229 (2008)
Gordon, A., Aizatulin, M., Borgström, J., Claret, G., Graepel, T., Nori, A., Rajamani, S., Russo, C.: A model-learner pattern for Bayesian reasoning. In: Proceedings of the ACM SIGPLAN Conference on Principles of Programming Languages, POPL (2013)
Koller, D., Friedman, N.: Probabilistic Graphical Models. MIT Press, Cambridge (2010)
Liepe, J., Barnes, C., Cule, E., Erguler, K., Kirk, P., Toni, T., Stumpf, M.P.: ABC-SysBio—approximate Bayesian computation in Python with GPU support. Bioinformatics 26(14), 1797–1799 (2010)
Minka, T., Winn, J., Guiver, J., Knowles, D.: Infer.NET 2.5, Microsoft Research Cambridge (2012), http://research.microsoft.com/infernet
Ocone, A., Millar, A.J., Sanguinetti, G.: Hybrid Regulatory Models: a statistically tractable approach to model regulatory network dynamics. Bioinformatics 29(7), 910–916 (2013)
Opper, M., Ruttor, A., Sanguinetti, G.: Approximate inference for Gaussian-jump processes. In: Advances in Neural Information Processing Systems 24 (2010)
Opper, M., Sanguinetti, G.: Variational inference for Markov jump processes. In: Platt, J., Koller, D., Singer, Y., Roweis, S. (eds.) Advances in Neural Information Processing Systems 20, pp. 1105–1112. MIT Press, Cambridge (2008)
Pfeffer, A.: The Design and Implementation of IBAL: A General-Purpose Probabilistic Language. In: Getoor, L., Taskar, B. (eds.) Introduction to Statistical Relational Learning. The MIT Press (2007)
Ptashne, M., Gann, A.: Genes and signals. Cold Harbor Spring Laboratory Press, New York (2002)
Rao, V., Teh, Y.W.: Fast MCMC sampling for Markov jump processes and continuous time Bayesian networks. In: UAI (2011)
Sanguinetti, G., Ruttor, A., Opper, M., Archambeau, C.: Switching regulatory models of cellular stress response. Bioinformatics 25(10), 1280–1286 (2009)
Sisson, S.A., Fan, Y., Tanaka, M.M.: Sequential Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences 104(6), 1760–1765 (2007)
Suter, D.M., Molina, N., Gatfield, D., Schneider, K., Schibler, U., Naef, F.: Mammalian genes are transcribed with widely different bursting kinetics. Science 332(6028), 472–474 (2011)
Toni, T., Welch, D., Strelkowa, N., Ipsen, A., Stumpf, M.P.: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface 6(31), 187–202 (2009)
Zechner, C., Pelet, S., Peter, M., Koeppl, H.: Recursive Bayesian estimation of stochastic rate constants from heterogeneous cell populations. In: IEEE CDC-ECE, pp. 5837–5843 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Georgoulas, A., Hillston, J., Sanguinetti, G. (2013). ABC–Fun: A Probabilistic Programming Language for Biology. In: Gupta, A., Henzinger, T.A. (eds) Computational Methods in Systems Biology. CMSB 2013. Lecture Notes in Computer Science(), vol 8130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40708-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-40708-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40707-9
Online ISBN: 978-3-642-40708-6
eBook Packages: Computer ScienceComputer Science (R0)