Physics-informed machine learning (PIML) has established itself as a new scientific paradigm which enables the seamless integration of observational data with partial differential equation (PDE) based physics models. A powerful tool for the analysis, reduction and solution of PDEs is the Lie symmetry method. Nevertheless, only recently has the integration of such symmetries into PIML frameworks begun to be explored. The present work adds to this growing literature by introducing an approach for incorporating a Lie symmetry into a physics-informed Gaussian process (GP) model. The symmetry is introduced as a constraint on the GP; either in a soft manner via virtual observations of an induced PDE called the invariant surface condition, or explicitly through the design of the kernel. Experimental results demonstrate that the use of symmetry constraints improves the performance of the GP for both forward and inverse problems, and that our approach offers competitive performance with neural networks in the low-data environment.

We introduce a framework for designing boundary constrained Gaussian process (BCGP) priors for exact enforcement of linear boundary conditions, and apply it to the machine learning of (initial) boundary value problems involving linear partial differential equations (PDEs).In contrast to existing work, we illustrate how to design boundary constrained mean and kernel functions for all classes of boundary conditions typically used in PDE modelling, namely Dirichlet, Neumann, Robin and mixed conditions. Importantly, this is done in a manner which allows for both forward and inverse problems to be naturally accommodated. We prove that the BCGP kernel has a universal representational capacity under Dirichlet conditions, and establish a formal equivalence between BCGPs and boundary-constrained neural networks (BCNNs) of infinite width.Finally, extensive numerical experiments are performed involving several linear PDEs, the results of which demonstrate the effectiveness and robustness of BCGP inference in the presence of sparse, noisy data.

The Bayesian inversion of electromagnetic data can obtain key information on the uncertainty of subsurface resistivity. However, due to its high computational cost, Bayesian inversion is largely limited to 1-D resistivity models. In this study, a fast Bayesian inversion method is implemented by introducing the spatial correlation as prior information. The contributions of this article mainly include: 1) explicitly introduce the expression of spatial correlation prior information and provide a method to determine the parameters in the expression through the variogram theory. The influence of parameters in the spatial correlation prior information on the inversion results is systematically analyzed with the 1-D synthetic model. 2) The information entropy theory of continuous functions is introduced to quantify the degrees of freedom (DOF) of the parameters of the spatial correlation prior model. The analysis shows that the DOF of model parameters are significantly smaller than the number of model parameters when spatial correlation prior information is introduced, which is the main reason for the rapid Bayesian inversion. 3) Introducing the Sengpiel fast imaging algorithm, combined with the variogram theory, realized the direct acquisition of spatial correlation prior information from the observation data, minimizing the dependence on other information. The inversion results of 1-D and 2-D synthetic models and field datasets show that considering the spatial correlation prior information, hundreds of thousands of Markov chain Monte Carlo sampling steps are needed to enable the inversion of up to thousands of model parameters. This result provides a possible idea for future Bayesian inversion of complex 3-D models.

We propose a novel transformer, capable of segmenting medical images of varying modalities. Challenges posed by the fine-grained nature of medical image analysis mean that the adaptation of the transformer for their analysis is still at nascent stages. The overwhelming success of the UNet lay in its ability to appreciate the fine-grained nature of the segmentation task, an ability which existing transformer based models do not currently posses. To address this shortcoming, we propose The Fully Convolutional Transformer (FCT), which builds on the proven ability of Convolutional Neural Networks to learn effective image representations, and combines them with the ability of Transformers to effectively capture long-term dependencies in its inputs. The FCT is the first fully convolutional Transformer model in medical imaging literature. It processes its input in two stages, where first, it learns to extract long range semantic dependencies from the input image, and then learns to capture hierarchical global attributes from the features. FCT is compact, accurate and robust. Our results show that it outperforms all existing transformer architectures by large margins across multiple medical image segmentation datasets of varying data modalities without the need for any pre-training. FCT outperforms its immediate competitor on the ACDC dataset by 1.3%, on the Synapse dataset by 4.4%, on the Spleen dataset by 1.2% and on ISIC 2017 dataset by 1.1% on the dice metric, with up to five times fewer parameters. On the ACDC Post-2017-MICCAI-Challenge online test set, our model sets a new state-of-the-art on unseen MRI test cases out-performing large ensemble models as well as nnUNet with considerably fewer parameters. Our code, environments and models will be available via GitHub†.

Surface antigens of pathogens are commonly targeted by vaccine-elicited antibodies but antigenic variability, notably in RNA viruses such as influenza, HIV and SARS-CoV-2, pose challenges for control by vaccination. For example, influenza A(H3N2) entered the human population in 1968 causing a pandemic and has since been monitored, along with other seasonal influenza viruses, for the emergence of antigenic drift variants through intensive global surveillance and laboratory characterisation. Statistical models of the relationship between genetic differences among viruses and their antigenic similarity provide useful information to inform vaccine development, though accurate identification of causative mutations is complicated by highly correlated genetic signals that arise due to the evolutionary process. Here, using a sparse hierarchical Bayesian analogue of an experimentally validated model for integrating genetic and antigenic data, we identify the genetic changes in influenza A(H3N2) virus that underpin antigenic drift. We show that incorporating protein structural data into variable selection helps resolve ambiguities arising due to correlated signals, with the proportion of variables representing haemagglutinin positions decisively included, or excluded, increased from 59.8% to 72.4%. The accuracy of variable selection judged by proximity to experimentally determined antigenic sites was improved simultaneously. Structure-guided variable selection thus improves confidence in the identification of genetic explanations of antigenic variation and we also show that prioritising the identification of causative mutations is not detrimental to the predictive capability of the analysis. Indeed, incorporating structural information into variable selection resulted in a model that could more accurately predict antigenic assay titres for phenotypically-uncharacterised virus from genetic sequence. Combined, these analyses have the potential to inform choices of reference viruses, the targeting of laboratory assays, and predictions of the evolutionary success of different genotypes, and can therefore be used to inform vaccine selection processes.

Combining biomechanical modelling of left ventricular (LV) function and dysfunction with cardiac magnetic resonance (CMR) imaging has the potential to improve the prognosis of patient-specific cardiovascular disease risks. Biomechanical studies of LV function in three dimensions usually rely on a computerized representation of the LV geometry based on finite element discretization, which is essential for numerically simulating in vivo cardiac dynamics. Detailed knowledge of the LV geometry is also relevant for various other clinical applications, such as assessing the LV cavity volume and wall thickness. Accurately and automatically reconstructing personalized LV geometries from conventional CMR images with minimal manual intervention is still a challenging task, which is a pre-requisite for any subsequent automated biomechanical analysis. We propose a deep learning-based automatic pipeline for predicting the three-dimensional LV geometry directly from routinely-available CMR cine images, without the need to manually annotate the ventricular wall. Our framework takes advantage of a low-dimensional representation of the high-dimensional LV geometry based on principal component analysis. We analyze how the inference of myocardial passive stiffness is affected by using our automatically generated LV geometries instead of manually generated ones. These insights will inform the development of statistical emulators of LV dynamics to avoid computationally expensive biomechanical simulations. Our proposed framework enables accurate LV geometry reconstruction, outperforming previous approaches by delivering a reconstruction error 50% lower than reported in the literature. We further demonstrate that for a nonlinear cardiac mechanics model, using our reconstructed LV geometries instead of manually extracted ones only moderately affects the inference of passive myocardial stiffness described by an anisotropic hyperelastic constitutive law. The developed methodological framework has the potential to make an important step towards personalized medicine by eliminating the need for time consuming and costly manual operations. In addition, our method automatically maps the CMR scan into a low-dimensional representation of the LV geometry, which constitutes an important stepping stone towards the development of an LV geometry-heterogeneous emulator.

Traditionally, ODE parameter inference relies on solving the system of ODEs and assessing fit of the estimated signal with the observations. However, nonlinear ODEs often do not permit closed form solutions. Using numerical methods to solve the equations results in prohibitive computational costs, particularly when one adopts a Bayesian approach in sampling parameters from a posterior distribution. With the introduction of gradient matching, we can abandon the need to numerically solve the system of equations. Inherent in these efficient procedures is an introduction of bias to the learning problem as we no longer sample based on the exact likelihood function. This paper presents a multiphase MCMC approach that attempts to close the gap between efficiency and accuracy. By sampling using a surrogate likelihood, we accelerate convergence to the stationary distribution before sampling using the exact likelihood. We demonstrate that this method combines the efficiency of gradient matching and the accuracy of the exact likelihood scheme.

Motivation: Mathematical modelling based on ordinary differential equations (ODEs) is widely used to describe the dynamics of biological systems, particularly in systems and pathway biology. Often the kinetic parameters of these ODE systems are unknown and have to be inferred from the data. Approximate parameter inference methods based on gradient matching (which do not require performing computationally expensive numerical integration of the ODEs) have been getting popular in recent years, but many implementations are difficult to run without expert knowledge. Here, we introduce ShinyKGode, an interactive web application to perform fast parameter inference on ODEs using gradient matching. Results: ShinyKGode can be used to infer ODE parameters on simulated and observed data using gradient matching. Users can easily load their own models in Systems Biology Markup Language format, and a set of pre-defined ODE benchmark models are provided in the application. Inferred parameters are visualized alongside diagnostic plots to assess convergence. Availability and implementation: The R package for ShinyKGode can be installed through the Comprehensive R Archive Network (CRAN). Installation instructions, as well as tutorial videos and source code are available at https://joewandy.github.io/shinyKGode. Supplementary information: Supplementary data are available at Bioinformatics online.

Parameter inference in mechanistic models of coupled differential equations is a topical and challenging problem. We propose a new method based on kernel ridge regression and gradient matching, and an objective function that simultaneously encourages goodness of fit and penalises inconsistencies with the differential equations. Fast minimisation is achieved by exploiting partial convexity inherent in this function, and setting up an iterative algorithm in the vein of the EM algorithm. An evaluation of the proposed method on various benchmark data suggests that it compares favourably with state-of-the-art alternatives.

Parameter inference in mechanistic models based on non-affine differential equations is computationally onerous, and various faster alternatives based on gradient matching have been proposed. A particularly promising approach is based on nonparametric Bayesian modelling with Gaussian processes, which exploits the fact that a Gaussian process is closed under differentiation. However, two alternative paradigms have been proposed. The first paradigm, proposed at NIPS 2008 and AISTATS 2013, is based on a product of experts approach and a marginalization over the derivatives of the state variables. The second paradigm, proposed at ICML 2014, is based on a probabilistic generative model and a marginalization over the state variables. The claim has been made that this leads to better inference results. In the present article, we offer a new interpretation of the second paradigm, which highlights the underlying assumptions, approximations and limitations. In particular, we show that the second paradigm suffers from an intrinsic identifiability problem, which the first paradigm is not affected by.

Vaccines created from closely related viruses are vital for offering protection against newly emerging strains. For Foot-and-Mouth disease virus (FMDV), where multiple serotypes co-circulate, testing large numbers of vaccines can be infeasible. Therefore the development of an in silico predictor of cross-protection between strains is important to help optimise vaccine choice. Here we describe a novel sparse Bayesian variable selection model using spike and slab priors which is able to predict antigenic variability and identify sites which are important for the neutralisation of the virus. We are able to identify multiple residues which are known to be key indicators of antigenic variability. Many of these were not identified previously using Frequentist mixed-effects models and still cannot be found when an L1 penalty is used. We further explore how the Markov chain Monte Carlo (MCMC) proposal method for the inclusion of variables can offer significant reductions in computational requirements, both for spike and slab priors in general, and our hierarchical Bayesian model in particular.

Ecological systems consist of complex sets of interactions among species and their environment, the understanding of which has implications for predicting environmental response to perturbations such as invading species and climate change. However, the revelation of these interactions is not straightforward, nor are the interactions necessarily stable across space. Machine learning can enable the recovery of such complex, spatially varying interactions from relatively easily obtained species abundance data. Here, we describe a novel Bayesian regression and Mondrian process model (BRAMP) for reconstructing species interaction networks from observed field data. BRAMP enables robust inference of species interactions considering autocorrelation in species abundances and allowing for variation in the interactions across space. We evaluate the model on spatially explicit simulated data, produced using a trophic niche model combined with stochastic population dynamics. We compare the model’s performance against L1-penalized sparse regression (LASSO) and non-linear Bayesian networks with the BDe scoring scheme. Finally, we apply BRAMP to real ecological data.

Parameter inference in mechanistic models based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the need to follow each parameter adaptation with a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differential equations, offer a computationally appealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently sampling from the joint distribution of the ODE parameters and GP hyperparameters. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a detailed comparison with the method in Calderhead et al. (2008) and the explicit ODE integration approach, both in terms of parameter inference accuracy and in terms of computational efficiency.

The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.

To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori independent. Under weak regularity conditions, the parameters can be integrated out in the likelihood, leading to a closed-form expression of the marginal likelihood. However, the assumption of prior independence is unrealistic in many real-world applications, where the segment-specific regulatory relationships among the interdependent quantities tend to undergo gradual evolutionary adaptations. We therefore propose a Bayesian coupling scheme to introduce systematic information sharing among the segment-specific interaction parameters. We investigate the effect this model improvement has on the network reconstruction accuracy in a reverse engineering context, where the objective is to learn the structure of a gene regulatory network from temporal gene expression profiles. The objective of the present paper is to expand and improve an earlier conference paper in six important aspects. Firstly, we offer a more comprehensive and self-contained exposition of the methodology. Secondly, we extend the model by introducing an extra layer to the model hierarchy, which allows for information-sharing among the network nodes, and we compare various coupling schemes for the noise variance hyperparameters. Thirdly, we introduce a novel collapsed Gibbs sampling step, which replaces a less efficient uncollapsed Gibbs sampling step of the original MCMC algorithm. Fourthly, we show how collapsing and blocking techniques can be used for developing a novel advanced MCMC algorithm with significantly improved convergence and mixing. Fifthly, we systematically investigate the influence of the (hyper-)hyperparameters of the proposed model. Sixthly, we empirically compare the proposed global information coupling scheme with an alternative paradigm based on sequential information sharing.

METHOD: Dynamic Bayesian networks (DBNs) have been applied widely to reconstruct the structure of regulatory processes from time series data, and they have established themselves as a standard modelling tool in computational systems biology. The conventional approach is based on the assumption of a homogeneous Markov chain, and many recent research efforts have focused on relaxing this restriction. An approach that enjoys particular popularity is based on a combination of a DBN with a multiple changepoint process, and the application of a Bayesian inference scheme via reversible jump Markov chain Monte Carlo (RJMCMC). In the present article, we expand this approach in two ways. First, we show that a dynamic programming scheme allows the changepoints to be sampled from the correct conditional distribution, which results in improved convergence over RJMCMC. Second, we introduce a novel Bayesian clustering and information sharing scheme among nodes, which provides a mechanism for automatic model complexity tuning. RESULTS: We evaluate the dynamic programming scheme on expression time series for Arabidopsis thaliana genes involved in circadian regulation. In a simulation study we demonstrate that the regularization scheme improves the network reconstruction accuracy over that obtained with recently proposed inhomogeneous DBNs. For gene expression profiles from a synthetically designed Saccharomyces cerevisiae strain under switching carbon metabolism we show that the combination of both: dynamic programming and regularization yields an inference procedure that outperforms two alternative established network reconstruction methods from the biology literature. AVAILABILITY AND IMPLEMENTATION: A MATLAB implementation of the algorithm and a supplementary paper with algorithmic details and further results for the Arabidopsis data can be downloaded from: http://www.statistik.tu-dortmund.de/bio2010.html.

Conventional dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption, which is too restrictive in many practical applications. Various approaches to relax the homogeneity assumption have therefore been proposed in the last few years. The present paper aims to improve the flexibility of two recent versions of non-homogeneous DBNs, which either (i) suffer from the need for data discretization, or (ii) assume a time-invariant network structure. Allowing the network structure to be fully flexible leads to the risk of overfitting and inflated inference uncertainty though, especially in the highly topical field of systems biology, where independent measurements tend to be sparse. In the present paper we investigate three conceptually different regularization schemes based on inter-segment information sharing. We assess the performance in a comparative evaluation study based on simulated data. We compare the predicted segmentation of gene expression time series obtained during embryogenesis in Drosophila melanogaster with other state-of-the-art techniques. We conclude our evaluation with an application to synthetic biology, where the objective is to predict a known regulatory network of five genes in Saccharomyces cerevisiae.

Dynamic Bayesian networks have been applied widely to reconstruct the structure of regulatory processes from time series data. The standard approach is based on the assumption of a homogeneous Markov chain, which is not valid in many real-world scenarios. Recent research efforts addressing this shortcoming have considered undirected graphs, directed graphs for discretized data, or over-flexible models that lack any information sharing between time series segments. In the present article, we propose a non-stationary dynamic Bayesian network for continuous data, in which parameters are allowed to vary between segments, and in which a common network structure provides essential information sharing across segments. Our model is based on a Bayesian change-point process, and we apply a variant of the allocation sampler of Nobile and Fearnside to infer the number and location of the change-points.

UNLABELLED: TOPALi v2 simplifies and automates the use of several methods for the evolutionary analysis of multiple sequence alignments. Jobs are submitted from a Java graphical user interface as TOPALi web services to either run remotely on high-performance computing clusters or locally (with multiple cores supported). Methods available include model selection and phylogenetic tree estimation using the Bayesian inference and maximum likelihood (ML) approaches, in addition to recombination detection methods. The optimal substitution model can be selected for protein or nucleic acid (standard, or protein-coding using a codon position model) data using accurate statistical criteria derived from ML co-estimation of the tree and the substitution model. Phylogenetic software available includes PhyML, RAxML and MrBayes. AVAILABILITY: Freely downloadable from http://www.topali.org for Windows, Mac OS X, Linux and Solaris.

METHOD: The objective of the present article is to propose and evaluate a probabilistic approach based on Bayesian networks for modelling non-homogeneous and non-linear gene regulatory processes. The method is based on a mixture model, using latent variables to assign individual measurements to different classes. The practical inference follows the Bayesian paradigm and samples the network structure, the number of classes and the assignment of latent variables from the posterior distribution with Markov Chain Monte Carlo (MCMC), using the recently proposed allocation sampler as an alternative to RJMCMC. RESULTS: We have evaluated the method using three criteria: network reconstruction, statistical significance and biological plausibility. In terms of network reconstruction, we found improved results both for a synthetic network of known structure and for a small real regulatory network derived from the literature. We have assessed the statistical significance of the improvement on gene expression time series for two different systems (viral challenge of macrophages, and circadian rhythms in plants), where the proposed new scheme tends to outperform the classical BGe score. Regarding biological plausibility, we found that the inference results obtained with the proposed method were in excellent agreement with biological findings, predicting dichotomies that one would expect to find in the studied systems. AVAILABILITY: Two supplementary papers on theoretical (T) and experi-mental (E) aspects and the datasets used in our study are available from http://www.bioss.ac.uk/associates/marco/supplement/

MOTIVATION: Short well-defined domains known as peptide recognition modules (PRMs) regulate many important protein-protein interactions involved in the formation of macromolecular complexes and biochemical pathways. Since high-throughput experiments like yeast two-hybrid and phage display are expensive and intrinsically noisy, it would be desirable to more specifically target or partially bypass them with complementary in silico approaches. In the present paper, we present a probabilistic discriminative approach to predicting PRM-mediated protein-protein interactions from sequence data. The model is motivated by the discriminative model of Segal and Sharan as an alternative to the generative approach of Reiss and Schwikowski. In our evaluation, we focus on predicting the interaction network. As proposed by Williams, we overcome the problem of susceptibility to over-fitting by adopting a Bayesian a posteriori approach based on a Laplacian prior in parameter space. RESULTS: The proposed method was tested on two datasets of protein-protein interactions involving 28 SH3 domain proteins in Saccharmomyces cerevisiae, where the datasets were obtained with different experimental techniques. The predictions were evaluated with out-of-sample receiver operator characteristic (ROC) curves. In both cases, Laplacian regularization turned out to be crucial for achieving a reasonable generalization performance. The Laplacian-regularized discriminative model outperformed the generative model of Reiss and Schwikowski in terms of the area under the ROC curve on both datasets. The performance was further improved with a hybrid approach, in which our model was initialized with the motifs obtained with the method of Reiss and Schwikowski. AVAILABILITY: Software and supplementary material is available from http://lehrach.com/wolfgang/dmf.

MOTIVATION: An important problem in systems biology is the inference of biochemical pathways and regulatory networks from postgenomic data. Various reverse engineering methods have been proposed in the literature, and it is important to understand their relative merits and shortcomings. In the present paper, we compare the accuracy of reconstructing gene regulatory networks with three different modelling and inference paradigms: (1) Relevance networks (RNs): pairwise association scores independent of the remaining network; (2) graphical Gaussian models (GGMs): undirected graphical models with constraint-based inference, and (3) Bayesian networks (BNs): directed graphical models with score-based inference. The evaluation is carried out on the Raf pathway, a cellular signalling network describing the interaction of 11 phosphorylated proteins and phospholipids in human immune system cells. We use both laboratory data from cytometry experiments as well as data simulated from the gold-standard network. We also compare passive observations with active interventions. RESULTS: On Gaussian observational data, BNs and GGMs were found to outperform RNs. The difference in performance was not significant for the non-linear simulated data and the cytoflow data, though. Also, we did not observe a significant difference between BNs and GGMs on observational data in general. However, for interventional data, BNs outperform GGMs and RNs, especially when taking the edge directions rather than just the skeletons of the graphs into account. This suggests that the higher computational costs of inference with BNs over GGMs and RNs are not justified when using only passive observations, but that active interventions in the form of gene knockouts and over-expressions are required to exploit the full potential of BNs. AVAILABILITY: Data, software and supplementary material are available from http://www.bioss.sari.ac.uk/staff/adriano/research.html

MOTIVATION: A promising sliding-window method for the detection of interspecific recombination in DNA sequence alignments is based on the monitoring of changes in the posterior distribution of tree topologies with a probabilistic divergence measure. However, as the number of taxa in the alignment increases or the sliding-window size decreases, the posterior distribution becomes increasingly diffuse. This diffusion blurs the probabilistic divergence signal and adversely affects the detection accuracy. The present study investigates how this shortcoming can be redeemed with a pruning method based on post-processing clustering, using the Robinson-Foulds distance as a metric in tree topology space. RESULTS: An application of the proposed scheme to three synthetic and two real-world DNA sequence alignments illustrates the amount of improvement that can be obtained with the pruning method. The study also includes a comparison with two established recombination detection methods: Recpars and the DSS (difference of sum of squares) method. AVAILABILITY: Software, data and further supplementary material are available at the following website: http://www.bioss.sari.ac.uk/~dirk/Supplements/

SUMMARY: TOPALi is a new Java graphical analysis application that allows the user to identify recombinant sequences within a DNA multiple alignment (either automatically or via manual investigation). TOPALi allows a choice of three statistical methods to predict the positions of breakpoints due to past recombination. The breakpoint predictions are then used to identify putative recombinant sequences and their relationships to other sequences. In addition to its sophisticated interface, TOPALi can import many sequence formats, estimate and display phylogenetic trees and allow interactive analysis and/or automatic HTML report generation. AVAILABILITY: TOPALi is freely available from http://www.bioss.ac.uk/software.html

MOTIVATION: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo. RESULTS: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequence-based information. AVAILABILITY: The programs and data used in the present study are available from http://www.bioss.sari.ac.uk/~dirk/Supplements

Abstract Motivation: We present a statistical method for detecting recombination, whose objective is to accurately locate the recombinant breakpoints in DNA sequence alignments of small numbers of taxa (4 or 5). Our approach explicitly models the sequence of phylogenetic tree topologies along a multiple sequence alignment. Inference under this model is done in a Bayesian way, using Markov chain Monte Carlo (MCMC). The algorithm returns the site-dependent posterior probability of each tree topology, which is used for detecting recombinant regions and locating their breakpoints. Results: The method was tested on a synthetic and three real DNA sequence alignments, where it was found to outperform the established detection methods PLATO, RECPARS, and TOPAL. Availability: The algorithm has been implemented in the C++ program package BARCE, which is freely available from http://www.bioss.sari.ac.uk/~dirk/my_software Contact: [email protected] Keywords: phylogenetic trees; DNA sequence alignments; recombination; hidden Markov models; Gibbs sampling; Markov chain Monte Carlo.

Abstract Motivation: As a result of recombination or rate variation, a DNA sequence alignment may have a mosaic structure, where different segments correspond to different evolutionary histories. While several methods have been developed to predict DNA mosaic structures, they do not properly address the question of whether the predicted segmentation itself is statistically significant, or whether it is significantly better than an alternative mosaic structure predicted with another method. The objective of the present article is to devise an approximate Bayesian hypothesis test to discriminate between alternative candidate mosaic structures. Results: We have applied the proposed discrimination scheme to various synthetic and real-world DNA sequence alignments. On the synthetic data, the algorithm identified the true mosaic structure in nine out of ten cases. On the real-world sequence alignments, it selected the same mosaic structures as predicted in the literature. Availability: Software written in MATLAB as well as the data sets used in our study are available from http://www.bioss.sari.ac.uk/~dirk/software/ABBESS/INFO.html. Contact: [email protected]; [email protected]

Training probability-density estimating neural networks with the expectation-maximization (EM) algorithm aims to maximize the likelihood of the training set and therefore leads to overfitting for sparse data. In this article, a regularization method for mixture models with generalized linear kernel centers is proposed, which adopts the Bayesian evidence approach and optimizes the hyperparameters of the prior by type II maximum likelihood. This includes a marginalization over the parameters, which is done by Laplace approximation and requires the derivation of the Hessian of the log-likelihood function. The incorporation of this approach into the standard training scheme leads to a modified form of the EM algorithm, which includes a regularization term and adapts the hyperparameters on-line after each EM cycle. The article presents applications of this scheme to classification problems, the prediction of stochastic time series, and latent space models.

This paper demonstrates a medical application of Bayesian neural networks, whose parameters and hyper-parameters are sampled from the posterior distribution by means of Monte Carlo Markov chain. The main objective is the determination of the relevance of various input variables. The paper focuses on typical difficulties one has to face when dealing with sparse data sets.

A Bayesian-based methodology is presented which automatically penalizes overcomplex models being fitted to unknown data. We show that, with a Gaussian mixture model, the approach is able to select an "optimal" number of components in the model and so partition data sets. The performance of the Bayesian method is compared to other methods of optimal model selection and found to give good results. The methods are tested on synthetic and real data sets.