Genome aneuploidy, characterized by copy number variations (CNVs), profoundly alters gene expression in cancer through direct gene dosage effects and indirect compensatory regulatory mechanisms. However, existing differential gene expression (DGE) testing methods do not differentiate between these mechanisms, conflating all expression changes, limiting biological interpretability and obscuring key genes involved in tumor progression. To address this, we developed DeConveil, a computational framework that extends traditional DGE analysis by integrating CNV data. Using a generalized linear model with a negative binomial distribution, DeConveil models RNA-seq expression counts while accounting for copy number gene dosage effects. We proposed a more fine-grained gene decomposition into dosage-sensitive (DSGs), dosage-insensitive (DIGs), and dosage-compensated (DCGs), which explicitly de-couples changes due to CNVs and bona fide changes in transcriptional regulation. Analysis of TCGA datasets from aneuploid solid cancers resulted in notable reclassification of genes, refining and expanding upon the results from conventional methods. Functional enrichment analysis identified distinct biological roles for DSGs, DIGs, and DCGs in tumor progression, immune regulation, and cell adhesion. In a breast cancer case study, DeConveil's CN-aware analysis facilitated the identification of both known and novel prognostic biomarkers, including lncRNAs, linking gene expression signatures to survival outcomes. Utilizing these biomarkers for each gene group significantly improved patient risk stratification, yielding more accurate predictions compared to conventional methods. These results highlight DeConveil's ability to disentangle CNV-driven from regulatory transcriptional changes, enhancing gene classification and biomarker discovery. By improving transcriptomic analysis, DeConveil provides a powerful tool for cancer research, precision oncology, with potential applications in therapeutic target identification.

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, training deep learning models robust to adversarial attacks is still an open problem. In this article, we analyse the geometry of adversarial attacks in the over-parameterized limit for Bayesian neural networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lie on a lower dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in this limit, BNN posteriors are robust to gradient-based adversarial attacks. Crucially, by relying on the convergence of infinitely-wide BNNs to Gaussian processes (GPs), we prove that, under certain relatively mild assumptions, the expected gradient of the loss with respect to the BNN posterior distribution is vanishing, even when each NN sampled from the BNN posterior does not have vanishing gradients. The experimental results on the MNIST, Fashion MNIST, and a synthetic dataset with BNNs trained with Hamiltonian Monte Carlo and variational inference support this line of arguments, empirically showing that BNNs can display both high accuracy on clean data and robustness to both gradient-based and gradient-free adversarial attacks.

Machine learning models are famously vulnerable to adversarial attacks: small ad-hoc perturbations of the data that can catastrophically alter the model predictions. While a large literature has studied the case of test-time attacks on pre-trained models, the important case of attacks in an online learning setting has received little attention so far. In this work, we use a control-theoretical perspective to study the scenario where an attacker may perturb data labels to manipulate the learning dynamics of an online learner. We perform a theoretical analysis of the problem in a teacher-student setup, considering different attack strategies, and obtaining analytical results for the steady state of simple linear learners. These results enable us to prove that a discontinuous transition in the learner's accuracy occurs when the attack strength exceeds a critical threshold. We then study empirically attacks on learners with complex architectures using real data, confirming the insights of our theoretical analysis. Our findings show that greedy attacks can be extremely efficient, especially when data stream in small batches.

Pruning deep neural networks is a widely used strategy to alleviate the computational burden in machine learning. Overwhelming empirical evidence suggests that pruned models retain very high accuracy even with a tiny fraction of parameters. However, relatively little work has gone into characterising the small pruned networks obtained, beyond a measure of their accuracy. In this paper, we use the sparse double descent approach to identify univocally and characterise pruned models associated with classification tasks. We observe empirically that, for a given task, iterative magnitude pruning (IMP) tends to converge to networks of comparable sizes even when starting from full networks with sizes ranging over orders of magnitude. We analyse the best pruned models in a controlled experimental setup and show that their number of parameters reflects task difficulty and that they are much better than full networks at capturing the true conditional probability distribution of the labels. On real data, we similarly observe that pruned models are less prone to overconfident predictions. Our results suggest that pruned models obtained via IMP not only have advantageous computational properties but also provide a better representation of uncertainty in learning.

We consider the problem of the stability of saliency-based explanations of Neural Network predictions under adversarial attacks in a classification task. Saliency interpretations of deterministic Neural Networks are remarkably brittle even when the attacks fail, i.e. for attacks that do not change the classification label. We empirically show that interpretations provided by Bayesian Neural Networks are considerably more stable under adversarial perturbations of the inputs and even under direct attacks to the explanations. By leveraging recent results, we also provide a theoretical explanation of this result in terms of the geometry of the data manifold. Additionally, we discuss the stability of the interpretations of high level representations of the inputs in the internal layers of a Network. Our results demonstrate that Bayesian methods, in addition to being more robust to adversarial attacks, have the potential to provide more stable and interpretable assessments of Neural Network predictions.

Single-cell multi-omics assays offer unprecedented opportunities to explore epigenetic regulation at cellular level. However, high levels of technical noise and data sparsity frequently lead to a lack of statistical power in correlative analyses, identifying very few, if any, significant associations between different molecular layers. Here we propose SCRaPL, a novel computational tool that increases power by carefully modelling noise in the experimental systems. We show on real and simulated multi-omics single-cell data sets that SCRaPL achieves higher sensitivity and better robustness in identifying correlations, while maintaining a similar level of false positives as standard analyses based on Pearson and Spearman correlation.

We propose two training techniques for improving the robustness of Neural Networks to adversarial attacks, i.e. manipulations of the inputs that are maliciously crafted to fool networks into incorrect predictions. Both methods are independent of the chosen attack and leverage random projections of the original inputs, with the purpose of exploiting both dimensionality reduction and some characteristic geometrical properties of adversarial perturbations. The first technique is called RP-Ensemble and consists of an ensemble of networks trained on multiple projected versions of the original inputs. The second one, named RP-Regularizer, adds instead a regularization term to the training objective.

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in the limit BNN posteriors are robust to gradient-based adversarial attacks. Experimental results on the MNIST and Fashion MNIST datasets with BNNs trained with Hamiltonian Monte Carlo and Variational Inference support this line of argument, showing that BNNs can display both high accuracy and robustness to gradient based adversarial attacks.

BACKGROUND: The large-scale availability of whole-genome sequencing profiles from bulk DNA sequencing of cancer tissues is fueling the application of evolutionary theory to cancer. From a bulk biopsy, subclonal deconvolution methods are used to determine the composition of cancer subpopulations in the biopsy sample, a fundamental step to determine clonal expansions and their evolutionary trajectories. RESULTS: In a recent work we have developed a new model-based approach to carry out subclonal deconvolution from the site frequency spectrum of somatic mutations. This new method integrates, for the first time, an explicit model for neutral evolutionary forces that participate in clonal expansions; in that work we have also shown that our method improves largely over competing data-driven methods. In this Software paper we present mobster, an open source R package built around our new deconvolution approach, which provides several functions to plot data and fit models, assess their confidence and compute further evolutionary analyses that relate to subclonal deconvolution. CONCLUSIONS: We present the mobster package for tumour subclonal deconvolution from bulk sequencing, the first approach to integrate Machine Learning and Population Genetics which can explicitly model co-existing neutral and positive selection in cancer. We showcase the analysis of two datasets, one simulated and one from a breast cancer patient, and overview all package functionalities.

Large-scale neural recording methods now allow us to observe large populations of identified single neurons simultaneously, opening a window into neural population dynamics in living organisms. However, distilling such large-scale recordings to build theories of emergent collective dynamics remains a fundamental statistical challenge. The neural field models of Wilson, Cowan, and colleagues remain the mainstay of mathematical population modeling owing to their interpretable, mechanistic parameters and amenability to mathematical analysis. Inspired by recent advances in biochemical modeling, we develop a method based on moment closure to interpret neural field models as latent state-space point-process models, making them amenable to statistical inference. With this approach we can infer the intrinsic states of neurons, such as active and refractory, solely from spiking activity in large populations. After validating this approach with synthetic data, we apply it to high-density recordings of spiking activity in the developing mouse retina. This confirms the essential role of a long lasting refractory state in shaping spatiotemporal properties of neonatal retinal waves. This conceptual and methodological advance opens up new theoretical connections between mathematical theory and point-process state-space models in neural data analysis.

Motivation: High-throughput measurements of DNA methylation are increasingly becoming a mainstay of biomedical investigations. While the methylation status of individual cytosines can sometimes be informative, several recent papers have shown that the functional role of DNA methylation is better captured by a quantitative analysis of the spatial variation of methylation across a genomic region. Results: Here, we present BPRMeth, a Bioconductor package that quantifies methylation profiles by generalized linear model regression. The original implementation has been enhanced in two important ways: we introduced a fast, variational inference approach that enables the quantification of Bayesian posterior confidence measures on the model, and we adapted the method to use several observation models, making it suitable for a diverse range of platforms including single-cell analyses and methylation arrays. Availability and implementation: http://bioconductor.org/packages/BPRMeth. Supplementary information: Supplementary data are available at Bioinformatics online.

Modeling and interpreting spike train data is a task of central importance in computational neuroscience, with significant translational implications. Two popular classes of data-driven models for this task are autoregressive point-process generalized linear models (PPGLM) and latent state-space models (SSM) with point-process observations. In this letter, we derive a mathematical connection between these two classes of models. By introducing an auxiliary history process, we represent exactly a PPGLM in terms of a latent, infinite-dimensional dynamical system, which can then be mapped onto an SSM by basis function projections and moment closure. This representation provides a new perspective on widely used methods for modeling spike data and also suggests novel algorithmic approaches to fitting such models. We illustrate our results on a phasic bursting neuron model, showing that our proposed approach provides an accurate and efficient way to capture neural dynamics.

MOTIVATION: Isoform quantification is an important goal of RNA-seq experiments, yet it remains problematic for genes with low expression or several isoforms. These difficulties may in principle be ameliorated by exploiting correlated experimental designs, such as time series or dosage response experiments. Time series RNA-seq experiments, in particular, are becoming increasingly popular, yet there are no methods that explicitly leverage the experimental design to improve isoform quantification. RESULTS: Here, we present DICEseq, the first isoform quantification method tailored to correlated RNA-seq experiments. DICEseq explicitly models the correlations between different RNA-seq experiments to aid the quantification of isoforms across experiments. Numerical experiments on simulated datasets show that DICEseq yields more accurate results than state-of-the-art methods, an advantage that can become considerable at low coverage levels. On real datasets, our results show that DICEseq provides substantially more reproducible and robust quantifications, increasing the correlation of estimates from replicate datasets by up to 10% on genes with low or moderate expression levels (bottom third of all genes). Furthermore, DICEseq permits to quantify the trade-off between temporal sampling of RNA and depth of sequencing, frequently an important choice when planning experiments. Our results have strong implications for the design of RNA-seq experiments, and offer a novel tool for improved analysis of such datasets. AVAILABILITY AND IMPLEMENTATION: Python code is freely available at http://diceseq.sf.net CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: DNA methylation is an intensely studied epigenetic mark, yet its functional role is incompletely understood. Attempts to quantitatively associate average DNA methylation to gene expression yield poor correlations outside of the well-understood methylation-switch at CpG islands. RESULTS: Here, we use probabilistic machine learning to extract higher order features associated with the methylation profile across a defined region. These features quantitate precisely notions of shape of a methylation profile, capturing spatial correlations in DNA methylation across genomic regions. Using these higher order features across promoter-proximal regions, we are able to construct a powerful machine learning predictor of gene expression, significantly improving upon the predictive power of average DNA methylation levels. Furthermore, we can use higher order features to cluster promoter-proximal regions, showing that five major patterns of methylation occur at promoters across different cell lines, and we provide evidence that methylation beyond CpG islands may be related to regulation of gene expression. Our results support previous reports of a functional role of spatial correlations in methylation patterns, and provide a mean to quantitate such features for downstream analyses. AVAILABILITY AND IMPLEMENTATION: https://github.com/andreaskapou/BPRMeth CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Functional genomic and epigenomic research relies fundamentally on sequencing based methods like ChIP-seq for the detection of DNA-protein interactions. These techniques return large, high dimensional data sets with visually complex structures, such as multi-modal peaks extended over large genomic regions. Current tools for visualisation and data exploration represent and leverage these complex features only to a limited extent. RESULTS: We present DGW, an open source software package for simultaneous alignment and clustering of multiple epigenomic marks. DGW uses Dynamic Time Warping to adaptively rescale and align genomic distances which allows to group regions of interest with similar shapes, thereby capturing the structure of epigenomic marks. We demonstrate the effectiveness of the approach in a simulation study and on a real epigenomic data set from the ENCODE project. CONCLUSIONS: Our results show that DGW automatically recognises and aligns important genomic features such as transcription start sites and splicing sites from histone marks. DGW is available as an open source Python package.

Abstract Motivation: Reconstructing the topology of gene regulatory networks (GRNs) from time series of gene expression data remains an important open problem in computational systems biology. Existing GRN inference algorithms face one of two limitations: model-free methods are scalable but suffer from a lack of interpretability and cannot in general be used for out of sample predictions. On the other hand, model-based methods focus on identifying a dynamical model of the system. These are clearly interpretable and can be used for predictions; however, they rely on strong assumptions and are typically very demanding computationally. Results: Here, we propose a new hybrid approach for GRN inference, called Jump3, exploiting time series of expression data. Jump3 is based on a formal on/off model of gene expression but uses a non-parametric procedure based on decision trees (called ‘jump trees’) to reconstruct the GRN topology, allowing the inference of networks of hundreds of genes. We show the good performance of Jump3 on in silico and synthetic networks and applied the approach to identify regulatory interactions activated in the presence of interferon gamma. Availability and implementation: Our MATLAB implementation of Jump3 is available at http://homepages.inf.ed.ac.uk/vhuynht/software.html. Contact: [email protected] or [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: DNA methylation is an intensely studied epigenetic mark implicated in many biological processes of direct clinical relevance. Although sequencing-based technologies are increasingly allowing high-resolution measurements of DNA methylation, statistical modelling of such data is still challenging. In particular, statistical identification of differentially methylated regions across different conditions poses unresolved challenges in accounting for spatial correlations within the statistical testing procedure. RESULTS: We propose a non-parametric, kernel-based method, M(3)D, to detect higher order changes in methylation profiles, such as shape, across pre-defined regions. The test statistic explicitly accounts for differences in coverage levels between samples, thus handling in a principled way a major confounder in the analysis of methylation data. Empirical tests on real and simulated datasets show an increased power compared to established methods, as well as considerable robustness with respect to coverage and replication levels.

MOTIVATION: Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental cycles, from day/night to seasonal. Transcriptional regulatory networks are one of the mechanisms behind these biological oscillations. However, while identifying cyclically expressed genes from time series measurements is relatively easy, determining the structure of the interaction network underpinning the oscillation is a far more challenging problem. RESULTS: Here, we explicitly leverage the oscillatory nature of the transcriptional signals and present a method for reconstructing network interactions tailored to this special but important class of genetic circuits. Our method is based on projecting the signal onto a set of oscillatory basis functions using a Discrete Fourier Transform. We build a Bayesian Hierarchical model within a frequency domain linear model in order to enforce sparsity and incorporate prior knowledge about the network structure. Experiments on real and simulated data show that the method can lead to substantial improvements over competing approaches if the oscillatory assumption is met, and remains competitive also in cases it is not. AVAILABILITY: DSS, experiment scripts and data are available at http://homepages.inf.ed.ac.uk/gsanguin/DSS.zip. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We propose an approximate inference algorithm for continuous time Gaussian-Markov process models with both discrete and continuous time likelihoods. We show that the continuous time limit of the expectation propagation algorithm exists and results in a hybrid fixed point iteration consisting of (1) expectation propagation updates for the discrete time terms and (2) variational updates for the continuous time term. We introduce corrections methods that improve on the marginals of the approximation. This approach extends the classical Kalman-Bucy smoothing procedure to non-Gaussian observations, enabling continuous-time inference in a variety of models, including spiking neuronal models (state-space models with point process observations) and box likelihood models. Experimental results on real and simulated data demonstrate high distributional accuracy and significant computational savings compared to discrete-time approaches in a neural application.

MOTIVATION: Computational modelling of the dynamics of gene regulatory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and flexibility, but calibrating these models to data is often an extremely difficult statistical problem. RESULTS: Here, we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach, which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efficient variational approximation that allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two biological case studies, showing that the method allows a high degree of flexibility and is capable of testable novel biological predictions. AVAILABILITY AND IMPLEMENTATION: http://homepages.inf.ed.ac.uk/gsanguin/software.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We present a probabilistic framework for transferring learning across tasks and between labeled and unlabeled data. The approach is based on Gaussian process (GP) prediction and incorporates both the geometry of the data and the similarity between tasks within a GP covariance, allowing Bayesian prediction in a natural way. We discuss the transfer of learning in a multitask scenario in the two cases where the underlying geometry is assumed to be the same across tasks and where different tasks are assumed to have independent geometric structures. We demonstrate the method on a number of real datasets, indicating that the semisupervised multitask approach can result in very significant improvements in performance when very few labeled training examples are available.

We consider the problem of Bayesian inference for continuous time multi-stable stochastic systems which can change both their diffusion and drift parameters at discrete times. We propose exact inference and sampling methodologies for two specific cases where the discontinuous dynamics is given by a Poisson process and a two-state Markovian switch. We test the methodology on simulated data, and apply it to two real data sets in finance and systems biology. Our experimental results show that the approach leads to valid inferences and non-trivial insights.

MOTIVATION: Knowledge of the activation patterns of transcription factors (TFs) is fundamental to elucidate the dynamics of gene regulation in response to environmental conditions. Direct experimental measurement of TFs' activities is, however, challenging, resulting in a need to develop statistical tools to infer TF activities from mRNA expression levels of target genes. Current models, however, neglect important features of transcriptional regulation; in particular, the combinatorial nature of regulation, which is fundamental for signal integration, is not accounted for. RESULTS: We present a novel method to infer combinatorial regulation of gene expression by multiple transcription factors in large-scale transcriptional regulatory networks. The method implements a factorial hidden Markov model with a non-linear likelihood to represent the interactions between the hidden transcription factors. We explore our model's performance on artificial datasets and demonstrate the applicability of our method on genome-wide scale for three expression datasets. The results obtained using our model are biologically coherent and provide a tool to explore the concealed nature of combinatorial transcriptional regulation. AVAILABILITY: http://homepages.inf.ed.ac.uk/gsanguin/software.html.

MOTIVATION: A knowledge of the dynamics of transcription factors is fundamental to understand the transcriptional regulation mechanism. Nowadays, an experimental measure of transcription factor activities in vivo represents a challenge. Several methods have been developed to infer these activities from easily measurable quantities such as mRNA expression of target genes. A limitation of these methods is represented by the fact that they rely on very simple single-layer structures, typically consisting of one or more transcription factors regulating a number of target genes. RESULTS: We present a novel statistical inference methodology to reverse engineer the dynamics of transcription factors in hierarchical network motifs such as feed-forward loops. The approach we present is based on a continuous time representation of the system where the high-level master transcription factor is represented as a two state Markov jump process driving a system of differential equations. We solve the inference problem using an efficient variational approach and demonstrate our method on simulated data and two real datasets. The results on real data show that the predictions of our approach can capture biological behaviours in a more effective way than single-layer models of transcription, and can lead to novel biological insights. AVAILABILITY: http://homepages.inf.ed.ac.uk/gsanguin/software.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We present a variational Bayesian (VB) approach for the state and parameter inference of a state-space model with point-process observations, a physiologically plausible model for signal processing of spike data. We also give the derivation of a variational smoother, as well as an efficient online filtering algorithm, which can also be used to track changes in physiological parameters. The methods are assessed on simulated data, and results are compared to expectation-maximization, as well as Monte Carlo estimation techniques, in order to evaluate the accuracy of the proposed approach. The VB filter is further assessed on a data set of taste-response neural cells, showing that the proposed approach can effectively capture dynamical changes in neural responses in real time.

We present a novel approach to multitask learning in classification problems based on Gaussian process (GP) classification. The method extends previous work on multitask GP regression, constraining the overall covariance (across tasks and data points) to factorize as a Kronecker product. Fully Bayesian inference is possible but time consuming using sampling techniques. We propose approximations based on the popular variational Bayes and expectation propagation frameworks, showing that they both achieve excellent accuracy when compared to Gibbs sampling, in a fraction of time. We present results on a toy dataset and two real datasets, showing improved performance against the baseline results obtained by learning each task independently. We also compare with a recently proposed state-of-the-art approach based on support vector machines, obtaining comparable or better results.

We present a novel approach to inference in conditionally Gaussian continuous time stochastic processes, where the latent process is a Markovian jump process. We first consider the case of jump-diffusion processes, where the drift of a linear stochastic differential equation can jump at arbitrary time points. We derive partial differential equations for exact inference and present a very efficient mean field approximation. By introducing a novel lower bound on the free energy, we then generalise our approach to Gaussian processes with arbitrary covariance, such as the non-Markovian RBF covariance. We present results on both simulated and real data, showing that the approach is very accurate in capturing latent dynamics and can be useful in a number of real data modelling tasks.

SUMMARY: TFInfer is a novel open access, standalone tool for genome-wide inference of transcription factor activities from gene expression data. Based on an earlier MATLAB version, the software has now been extended in a number of ways. It has been significantly optimised in terms of performance, and it was given novel functionality, by allowing the user to model both time series and data from multiple independent conditions. With a full documentation and intuitive graphical user interface, together with an in-built data base of yeast and Escherichia coli transcription factors, the software does not require any mathematical or computational expertise to be used effectively. AVAILABILITY: http://homepages.inf.ed.ac.uk/gsanguin/TFInfer.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: mRNA transcriptional dynamics is governed by a complex network of transcription factor (TF) proteins. Experimental and theoretical analysis of this process is hindered by the fact that measurements of TF activity in vivo is very challenging. Current models that jointly infer TF activities and model parameters rely on either of the two main simplifying assumptions: either the dynamics is simplified (e.g. assuming quasi-steady state) or the interactions between TFs are ignored, resulting in models accounting for a single TF. RESULTS: We present a novel approach to reverse engineer the dynamics of multiple TFs jointly regulating the expression of a set of genes. The model relies on a continuous time, differential equation description of transcriptional dynamics where TFs are treated as latent on/off variables and are modelled using a switching stochastic process (telegraph process). The model can not only incorporate both activation and repression, but allows any non-trivial interaction between TFs, including AND and OR gates. By using a factorization assumption within a variational Bayesian treatment we formulate a framework that can reconstruct both the activity profiles of the TFs and the type of regulation from time series gene expression data. We demonstrate the identifiability of the model on a simple but non-trivial synthetic example, and then use it to formulate non-trivial predictions about transcriptional control during yeast metabolism. AVAILABILITY: http://homepages.inf.ed.ac.uk/gsanguin/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Stress response in cells is often mediated by quick activation of transcription factors (TFs). Given the difficulty in experimentally assaying TF activities, several statistical approaches have been proposed to infer them from microarray time courses. However, these approaches often rely on prior assumptions which rule out the rapid responses observed during stress response. RESULTS: We present a novel statistical model to infer how TFs mediate stress response in cells. The model is based on the assumption that sensory TFs quickly transit between active and inactive states. We therefore model mRNA production using a bistable dynamical systems whose behaviour is described by a system of differential equations driven by a latent stochastic process. We assume the stochastic process to be a two-state continuous time jump process, and devise both an exact solution for the inference problem as well as an efficient approximate algorithm. We evaluate the method on both simulated data and real data describing Escherichia coli's response to sudden oxygen starvation. This highlights both the accuracy of the proposed method and its potential for generating novel hypotheses and testable predictions. AVAILABILITY: MATLAB and C++ code used in the article can be downloaded from http://www.dcs.shef.ac.uk/~guido/.

BACKGROUND: Most analyses of microarray data are based on point estimates of expression levels and ignore the uncertainty of such estimates. By determining uncertainties from Affymetrix GeneChip data and propagating these uncertainties to downstream analyses it has been shown that we can improve results of differential expression detection, principal component analysis and clustering. Previously, implementations of these uncertainty propagation methods have only been available as separate packages, written in different languages. Previous implementations have also suffered from being very costly to compute, and in the case of differential expression detection, have been limited in the experimental designs to which they can be applied. RESULTS: puma is a Bioconductor package incorporating a suite of analysis methods for use on Affymetrix GeneChip data. puma extends the differential expression detection methods of previous work from the 2-class case to the multi-factorial case. puma can be used to automatically create design and contrast matrices for typical experimental designs, which can be used both within the package itself but also in other Bioconductor packages. The implementation of differential expression detection methods has been parallelised leading to significant decreases in processing time on a range of computer architectures. puma incorporates the first R implementation of an uncertainty propagation version of principal component analysis, and an implementation of a clustering method based on uncertainty propagation. All of these techniques are brought together in a single, easy-to-use package with clear, task-based documentation. CONCLUSION: For the first time, the puma package makes a suite of uncertainty propagation methods available to a general audience. These methods can be used to improve results from more traditional analyses of microarray data. puma also offers improvements in terms of scope and speed of execution over previously available methods. puma is recommended for anyone working with the Affymetrix GeneChip platform for gene expression analysis and can also be applied more generally.

BACKGROUND: Mixture model on graphs (MMG) is a probabilistic model that integrates network topology with (gene, protein) expression data to predict the regulation state of genes and proteins. It is remarkably robust to missing data, a feature particularly important for its use in quantitative proteomics. A new implementation in C and interfaced with R makes MMG extremely fast and easy to use and to extend. AVAILABILITY: The original implementation (Matlab) is still available from http://www.dcs.shef.ac.uk/~guido/; the new implementation is available from http://wrightlab.group.shef.ac.uk/people_noirel.htm, from CRAN, and has been submitted to BioConductor, http://www.bioconductor.org/.

MOTIVATION: A fundamental task in systems biology is the identification of groups of genes that are involved in the cellular response to particular signals. At its simplest level, this often reduces to identifying biological quantities (mRNA abundance, enzyme concentrations, etc.) which are differentially expressed in two different conditions. Popular approaches involve using t-test statistics, based on modelling the data as arising from a mixture distribution. A common assumption of these approaches is that the data are independent and identically distributed; however, biological quantities are usually related through a complex (weighted) network of interactions, and often the more pertinent question is which subnetworks are differentially expressed, rather than which genes. Furthermore, in many interesting cases (such as high-throughput proteomics and metabolomics), only very partial observations are available, resulting in the need for efficient imputation techniques. RESULTS: We introduce Mixture Model on Graphs (MMG), a novel probabilistic model to identify differentially expressed submodules of biological networks and pathways. The method can easily incorporate information about weights in the network, is robust against missing data and can be easily generalized to directed networks. We propose an efficient sampling strategy to infer posterior probabilities of differential expression, as well as posterior probabilities over the model parameters. We assess our method on artificial data demonstrating significant improvements over standard mixture model clustering. Analysis of our model results on quantitative high-throughput proteomic data leads to the identification of biologically significant subnetworks, as well as the prediction of the expression level of a number of enzymes, some of which are then verified experimentally. AVAILABILITY: MATLAB code is available from http://www.dcs.shef.ac.uk/~guido/software.html

We present a novel probabilistic latent variable model to perform linear dimensionality reduction on data sets which contain clusters. We prove that the maximum likelihood solution of the model is an unsupervised generalisation of linear discriminant analysis. This provides a completely new approach to one of the most established and widely used classification algorithms. The performance of the model is then demonstrated on a number of real and artificial data sets.

Markov jump processes play an important role in a large number of application domains. However, realistic systems are analytically intractable and they have traditionally been analysed using simulation based techniques, which do not provide a framework for statistical inference. We propose a mean field approximation to perform posterior inference and parameter estimation. The approximation allows a practical solution to the inference problem, {while still retaining a good degree of accuracy.} We illustrate our approach on two biologically motivated systems.

Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies.

Microarray technology is associated with many sources of experimental uncertainty. In this review we discuss a number of approaches for dealing with this uncertainty in the processing of data from microarray experiments. We focus here on the analysis of high-density oligonucleotide arrays, such as the popular Affymetrix GeneChip array, which contain multiple probes for each target. This set of probes can be used to determine an estimate for the target concentration and can also be used to determine the experimental uncertainty associated with this measurement. This measurement uncertainty can then be propagated through the downstream analysis using probabilistic methods. We give examples showing how these credibility intervals can be used to help identify differential expression, to combine information from replicated experiments and to improve the performance of principal component analysis.

MOTIVATION: Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. Recent experimental high-throughput techniques, such as Chromatin Immunoprecipitation (ChIP) provide important information about the architecture of the regulatory networks in the cell. However, it is very difficult to measure the concentration levels of transcription factor proteins and determine their regulatory effect on gene transcription. It is therefore an important computational challenge to infer these quantities using gene expression data and network architecture data. RESULTS: We develop a probabilistic state space model that allows genome-wide inference of both transcription factor protein concentrations and their effect on the transcription rates of each target gene from microarray data. We use variational inference techniques to learn the model parameters and perform posterior inference of protein concentrations and regulatory strengths. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates, as well as providing a tool to detect which binding events lead to significant regulation. We demonstrate our model on artificial data and on two yeast datasets in which the network structure has previously been obtained using ChIP data. Predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell. AVAILABILITY: MATLAB code is available from http://umber.sbs.man.ac.uk/resources/puma

MOTIVATION: Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. This task, however, is difficult for a number of reasons: transcription factors' expression levels are often low and noisy, and many transcription factors are post-transcriptionally regulated. It is therefore useful to infer the activity of the transcription factors from the expression levels of their target genes. RESULTS: We introduce a novel probabilistic model to infer transcription factor activities from microarray data when the structure of the regulatory network is known. The model is based on regression, retaining the computational efficiency to allow genome-wide investigation, but is rendered more flexible by sampling regression coefficients independently for each gene. This allows us to determine the strength with which a transcription factor regulates each of its target genes, therefore providing a quantitative description of the transcriptional regulatory network. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates of the activities. We demonstrate our model on two yeast datasets. In both cases the network structure was obtained using chromatin immunoprecipitation data. We show how predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell. AVAILABILITY: MATLAB code is available from http://umber.sbs.man.ac.uk/resources/puma.

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.