Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods

Network Reconstruction with Realistic Models

We extend a recently proposed gradient-matching method for inferring interactions in complex systems described by differential equations in various respects: improved gradient inference, evaluation of the influence of the prior on kinetic parameters, comparative evaluation of two model selection paradigms: marginal likelihood versus DIC (divergence information criterion), comparative evaluation of different numerical procedures for computing the marginal likelihood, extension of the methodology from protein phosphorylation to transcriptional regulation, based on a realistic simulation of the underlying molecular processes with Markov jump processes

Network Reconstruction with Realistic Models

We extend a recently proposed gradient-matching method for inferring interactions in complex systems described by differential equations in various respects: improved gradient inference, evaluation of the influence of the prior on kinetic parameters, comparative evaluation of two model selection paradigms: marginal likelihood versus DIC (divergence information criterion), comparative evaluation of different numerical procedures for computing the marginal likelihood, extension of the methodology from protein phosphorylation to transcriptional regulation, based on a realistic simulation of the underlying molecular processes with Markov jump processes

Changes and classification in myocardial contractile function in the left ventricle following acute myocardial infarction

In this research, we hypothesized that novel biomechanical parameters are discriminative in patients following acute ST-segment elevation myocardial infarction (STEMI). To identify these biomechanical biomarkers and bring computational biomechanics ‘closer to the clinic’, we applied state-of-the-art multiphysics cardiac modelling combined with advanced machine learning and multivariate statistical inference to a clinical database of myocardial infarction. We obtained data from 11 STEMI patients (ClinicalTrials.gov NCT01717573) and 27 healthy volunteers, and developed personalized mathematical models for the left ventricle (LV) using an immersed boundary method. Subject-specific constitutive parameters were achieved by matching to clinical measurements. We have shown, for the first time, that compared with healthy controls, patients with STEMI exhibited increased LV wall active tension when normalized by systolic blood pressure, which suggests an increased demand on the contractile reserve of remote functional myocardium. The statistical analysis reveals that the required patient-specific contractility, normalized active tension and the systolic myofilament kinematics have the strongest explanatory power for identifying the myocardial function changes post-MI. We further observed a strong correlation between two biomarkers and the changes in LV ejection fraction at six months from baseline (the required contractility (r = − 0.79, p < 0.01) and the systolic myofilament kinematics (r = 0.70, p = 0.02)). The clinical and prognostic significance of these biomechanical parameters merits further scrutinization

Network reconstruction with realistic models

Abstract: We extend a recently proposed gradient-matching method for inferring interactions in complex systems described by differential equations in various respects: improved gradient inference, evaluation of the influence of the prior on kinetic parameters, comparative evaluation of two model selection paradigms: marginal likelihood versus DIC (divergence information criterion), comparative evaluation of different numerical procedures for computing the marginal likelihood, extension of the methodology from protein phosphorylation to transcriptional regulation, based on a realistic simulation of the underlying molecular processes with Markov jump processes

Approximate Bayesian inference in semi-mechanistic models

Inference of interaction networks represented by systems of differential equations is a challenging problem in many scientific disciplines. In the present article, we follow a semi-mechanistic modelling approach based on gradient matching. We investigate the extent to which key factors, including the kinetic model, statistical formulation and numerical methods, impact upon performance at network reconstruction. We emphasize general lessons for computational statisticians when faced with the challenge of model selection, and we assess the accuracy of various alternative paradigms, including recent widely applicable information criteria and different numerical procedures for approximating Bayes factors. We conduct the comparative evaluation with a novel inferential pipeline that systematically disambiguates confounding factors via an ANOVA scheme

Inference of Circadian Regulatory Networks

Abstract. We assess the accuracy of various state-of-the-art methods for reconstructing gene and protein regulatory networks in the context of circadian regulation. Gene expression and protein concentration time series are simulated from a recently published regulatory network of the circadian clock in A. thaliana, which is mathematically described by a Markov jump process based on Michaelis-Menten kinetics. Our study provides relative network reconstruction accuracy scores for a critical comparative performance evaluation, quantifies the influence of systematically missing values related to unknown protein concentrations and mRNA transcription rates, and investigates the dependence of the performance on the network topology and the degree of recurrency. An application to recent gene expression time series from qPCR experiments suggests new hypotheses about the structure of the central circadian gene regulatory network in A. thaliana

Machine learning in systems biology at different scales : from molecular biology to ecology

Machine learning has been a source for continuous methodological advances in the field of computational learning from data. Systems biology has profited in various ways from machine learning techniques but in particular from network inference, i.e. the learning of interactions given observed quantities of the involved components or data that stem from interventional experiments. Originally this domain of system biology was confined to the inference of gene regulation networks but recently expanded to other levels of organization of biological and ecological systems. Especially the application to species interaction networks in a varying environment is of mounting importance in order to improve our understanding of the dynamics of species extinctions, invasions, and population behaviour in general. The aim of this thesis is to demonstrate an extensive study of various state-of-art machine learning techniques applied to a genetic regulation system in plants and to expand and modify some of these methods to infer species interaction networks in an ecological setting. The first study attempts to improve the knowledge about circadian regulation in the plant Arabidopsis thaliana from the view point of machine learning and gives suggestions on what methods are best suited for inference, how the data should be processed and modelled mathematically, and what quality of network learning can be expected by doing so. To achieve this, I generate a rich and realistic synthetic data set that is used for various studies under consideration of different effects and method setups. The best method and setup is applied to real transcriptional data, which leads to a new hypothesis about the circadian clock network structure. The ecological study is focused on the development of two novel inference methods that exploit a common principle from transcriptional time-series, which states that expression profiles over time can be temporally heterogeneous. A corresponding concept in a spatial domain of 2 dimensions is that species interaction dynamics can be spatially heterogeneous, i.e. can change in space dependent on the environment and other factors. I will demonstrate the expansion from the 1-dimensional time domain to the 2-dimensional spatial domain, introduce two distinct space segmentation schemes, and consider species dispersion effects with spatial autocorrelation. The two novel methods display a significant improvement in species interaction inference compared to competing methods and display a high confidence in learning the spatial structure of different species neighbourhoods or environments

Statistical inference of regulatory networks for circadian regulation

The work described in the present article is part of the TiMet project on linking the circadian clock to metabolism in plants. TiMet is a collaborative project (Grant Agreement 245143) funded by the European Commission FP7, in response to call FP7-KBBE-2009-3. Parts of the work were done while M.G. was supported by the German Research Foundation (DFG), research grant GR3853/1-1. A.A. is supported by the BBSRC and the TiMet project.We assess the accuracy of various state-of-the-art statistics and machine learning methods for reconstructing gene and protein regulatory networks in the context of circadian regulation. Our study draws on the increasing availability of gene expression and protein concentration time series for key circadian clock components in Arabidopsis thaliana. In addition, gene expression and protein concentration time series are simulated from a recently published regulatory network of the circadian clock in A. thaliana, in which protein and gene interactions are described by a Markov jump process based on Michaelis-Menten kinetics. We closely follow recent experimental protocols, including the entrainment of seedlings to different light-dark cycles and the knock-out of various key regulatory genes. Our study provides relative network reconstruction accuracy scores for a critical comparative performance evaluation, and sheds light on a series of highly relevant questions: it quantifies the influence of systematically missing values related to unknown protein concentrations and mRNA transcription rates, it investigates the dependence of the performance on the network topology and the degree of recurrency, it provides deeper insight into when and why non-linear methods fail to outperform linear ones, it offers improved guidelines on parameter settings in different inference procedures, and it suggests new hypotheses about the structure of the central circadian gene regulatory network in A. thaliana.Publisher PDFPeer reviewe