# Matching Models Across Abstraction Levels with Gaussian Processes

- 715 Downloads

## Abstract

Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it is generally unclear whether model predictions are quantitatively in agreement, and whether such agreement holds for different parametrisations. Here we present a generally applicable statistical machine learning methodology to automatically reconcile the predictions of different models across abstraction levels. Our approach is based on defining a correction map, a random function which modifies the output of a model in order to match the statistics of the output of a different model of the same system. We use two biological examples to give a proof-of-principle demonstration of the methodology, and discuss its advantages and potential further applications.

## Keywords

Computational abstraction Emulation Gaussian Processes Heteroschedasticity## References

- 1.Aitken, S., Alexander, R.D., Beggs, J.D.: A rule-based kinetic model of rna polymerase ii c-terminal domain phosphorylation. J Roy. Soc. Interface
**10**(86), 20130438 (2013)CrossRefGoogle Scholar - 2.Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM
**43**(1), 116–146 (1996)MathSciNetCrossRefzbMATHGoogle Scholar - 3.Barber, D.: Bayesian Reasoning and Machine Learning. Cambridge University Press, Cambridge (2012)zbMATHGoogle Scholar
- 4.Bortolussi, L., Milios, D., Sanguinetti, G.: Smoothed model checking for uncertain continuous-time markov chains. Inf. Comput.
**247**, 235–253 (2016)MathSciNetCrossRefzbMATHGoogle Scholar - 5.Bortolussi, L., Sanguinetti, G.: Learning and designing stochastic processes from logical constraints. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 89–105. Springer, Heidelberg (2013)CrossRefGoogle Scholar
- 6.Caravagna, G.: Formal modeling and simulation of biological systems with delays. Ph.D. thesis, University of Pisa (2011)Google Scholar
- 7.Cressie, N., Wikle, C.K.: Statistics for Spatio-Temporal Data. Wiley, New York (2015)zbMATHGoogle Scholar
- 8.Hoyle, D.C., Rattray, M., Jupp, R., Brass, A.: Making sense of microarray data distributions. Bioinformatics
**18**(4), 576–584 (2002)CrossRefGoogle Scholar - 9.Kennedy, M.C., O’Hagan, A.: Bayesian calibration of computer models. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.)
**63**(3), 425–464 (2001)MathSciNetCrossRefzbMATHGoogle Scholar - 10.Lawrence, N.D., Sanguinetti, G., Rattray, M.: Modelling transcriptional regulation using gaussian processes. In: Advances in Neural Information Processing Systems, pp. 785–792 (2006)Google Scholar
- 11.Noble, D.: Modeling the heart-from genes to cells to the whole organ. Science
**295**(5560), 1678–1682 (2002)CrossRefGoogle Scholar - 12.Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)zbMATHGoogle Scholar