Abstract
Automating the process of model building from experimental data is a very desirable goal to palliate the lack of modellers for many applications. However, despite the spectacular progress of machine learning techniques in data analytics, classification, clustering and prediction making, learning dynamical models from data time-series is still challenging. In this paper we investigate the use of the Probably Approximately Correct (PAC) learning framework of Leslie Valiant as a method for the automated discovery of influence models of biochemical processes from Boolean and stochastic traces. We show that Thomas’ Boolean influence systems can be naturally represented by k-CNF formulae, and learned from time-series data with a number of Boolean activation samples per species quasi-linear in the precision of the learned model, and that positive Boolean influence systems can be represented by monotone DNF formulae and learned actively with both activation samples and oracle calls. We consider Boolean traces and Boolean abstractions of stochastic simulation traces, and study the space-time tradeoff there is between the diversity of initial states and the length of the time horizon, and its impact on the error bounds provided by the PAC learning algorithms. We evaluate the performance of this approach on a model of T-lymphocyte differentiation, with and without prior knowledge, and discuss its merits as well as its limitations with respect to realistic experiments.
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Notes
- 1.
For the sake of reproducibility, the code used in this article is available at http://lifeware.inria.fr/wiki/software/#CMSB17.
- 2.
More generally, the PAC learning protocol can discover partial vectors, but for the applications discussed in the current article it is enough to only consider total vectors.
- 3.
- 4.
More precisely, in a well-formed influence system, f is assumed to be partially differentiable; \(x_i\in P\) if and only if \(\sigma = +\) (resp. −) and \({\partial {f}}/ {\partial x_i}(\varvec{x})>0\) (resp. \(<0\)) for some value \(\varvec{x}\in \mathbb {R}_+^n\); and \(x_i\in I\) if and only if \(\sigma = +\) (resp. −) and \({\partial {f}}/ {\partial x_i}(\varvec{x})<0\) (resp. \(>0\)) for some value \(\varvec{x}\in \mathbb {R}_+^n\).
- 5.
Note that this function ignores the cases where \(v_i = 0\) and \({x_i}^-(v) =0\), or \(v_i=1\) and \({x_i}^+(v)=1\) which may create loops in non-terminal states in general influence systems.
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This work is partly supported by the ANR project Hyclock.
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Carcano, A., Fages, F., Soliman, S. (2017). Probably Approximately Correct Learning of Regulatory Networks from Time-Series Data. In: Feret, J., Koeppl, H. (eds) Computational Methods in Systems Biology. CMSB 2017. Lecture Notes in Computer Science(), vol 10545. Springer, Cham. https://doi.org/10.1007/978-3-319-67471-1_5
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