MOTIVATION: Combinatorial drug therapy holds great promise for tackling complex diseases, but the vast number of possible drug combinations makes exhaustive experimental testing infeasible. Computational models have been developed to guide experimental screens by assigning synergy scores to drug pair-cell line combinations, where they take input structural and chemical information on drugs and molecular features of cell lines. The premise of these models is that they leverage this biological and chemical information to predict synergy measurements. RESULTS: In this study, we demonstrate that replacing drug and cell line representations with simple one-hot encodings results in comparable or even slightly improved performance across diverse published drug combination models. This unexpected finding suggests that current models use these representations primarily as identifiers and exploit covariation in the synergy labels. Our synthetic data experiments show that models can learn from the true features; however, when drugs and cell lines recur across drug-drug-cell triplets, this repeating structure impairs feature-based learning. While the current synergy prediction models can aid in prioritizing drug pairs within a panel of tested drugs and cell lines, our results highlight the need for better strategies to learn from intended features and to generalize to unseen drugs and cell lines. AVAILABILITY AND IMPLEMENTATION: The scripts to run the experiments are available at: https://github.com/tastanlab/ohe.

Many cancer monotherapies demonstrate limited clinical efficacy, making combination therapies a relevant treatment strategy. The extensive number of potential drug combinations and context-specific response profiles complicates the prediction of drug combination responses. Existing computational models are typically trained to predict a single aggregated synergy score, which summarises drug responses across different dosage combinations, such as Bliss or Loewe scores. This oversimplification of the drug-response surface leads to high prediction uncertainty and limited actionability, as these models fail to distinguish between potency and efficacy. We introduce DeepSynBa, an actionable model that predicts the complete dose-response matrix of drug pairs instead of relying on an aggregated synergy score. This is achieved by predicting parameters describing the response surface as an intermediate layer in the model. Evaluated on the NCI-ALMANAC and the O'Neil datasets, DeepSynBa outperforms the state-of-the-art methods in the dose-response matrix prediction task across most evaluation scenarios, including testing on novel drug combinations, cell lines, and drugs, across nine different tissue types. We also show that DeepSynBa yields reliable synergy score predictions. More importantly, DeepSynBa can predict drug combination responses across different dosages for untested combinations. The intermediate dose-response parameter layer enables the separation of efficacy from potency, informing the selection of dosage ranges that optimise efficacy while limiting off-target toxicity in experimental screens. The predictive capability and the downstream actionability make DeepSynBa a powerful tool for advancing drug combination research beyond the limitations of the current approaches. The code and the dataset for DeepSynBa are available at https://github.com/hikuru/DeepSynBa.

Thermal proteome profiling (TPP) is a proteome wide technology that enables unbiased detection of protein drug interactions as well as changes in post-translational state of proteins between different biological conditions. Statistical analysis of temperature range TPP (TPP-TR) datasets relies on comparing protein melting curves, describing the amount of non-denatured proteins as a function of temperature, between different conditions (e.g. presence or absence of a drug). However, state-of-the-art models are restricted to sigmoidal melting behaviours while unconventional melting curves, representing up to 50% of TPP-TR datasets, have recently been shown to carry important biological information. We present a novel statistical framework, based on hierarchical Gaussian process models and named GPMelt, to make TPP-TR datasets analysis unbiased with respect to the melting profiles of proteins. GPMelt scales to multiple conditions, and extension of the model to deeper hierarchies (i.e. with additional sub-levels) allows to deal with complex TPP-TR protocols. Collectively, our statistical framework extends the analysis of TPP-TR datasets for both protein and peptide level melting curves, offering access to thousands of previously excluded melting curves and thus substantially increasing the coverage and the ability of TPP to uncover new biology.

MOTIVATION: There exists a range of different quantification frameworks to estimate the synergistic effect of drug combinations. The diversity and disagreement in estimates make it challenging to determine which combinations from a large drug screening should be proceeded with. Furthermore, the lack of accurate uncertainty quantification for those estimates precludes the choice of optimal drug combinations based on the most favourable synergistic effect. RESULTS: In this work, we propose SynBa, a flexible Bayesian approach to estimate the uncertainty of the synergistic efficacy and potency of drug combinations, so that actionable decisions can be derived from the model outputs. The actionability is enabled by incorporating the Hill equation into SynBa, so that the parameters representing the potency and the efficacy can be preserved. Existing knowledge may be conveniently inserted due to the flexibility of the prior, as shown by the empirical Beta prior defined for the normalized maximal inhibition. Through experiments on large combination screenings and comparison against benchmark methods, we show that SynBa provides improved accuracy of dose-response predictions and better-calibrated uncertainty estimation for the parameters and the predictions. AVAILABILITY AND IMPLEMENTATION: The code for SynBa is available at https://github.com/HaotingZhang1/SynBa. The datasets are publicly available (DOI of DREAM: 10.7303/syn4231880; DOI of the NCI-ALMANAC subset: 10.5281/zenodo.4135059).

MOTIVATION: The MS2-MCP (MS2 coat protein) live imaging system allows for visualization of transcription dynamics through the introduction of hairpin stem-loop sequences into a gene. A fluorescent signal at the site of nascent transcription in the nucleus quantifies mRNA production. Computational modelling can be used to infer the promoter states along with the kinetic parameters governing transcription, such as promoter switching frequency and polymerase loading rate. However, modelling of the fluorescent trace presents a challenge due its persistence; the observed fluorescence at a given time point depends on both current and previous promoter states. A compound state Hidden Markov Model (cpHMM) was recently introduced to allow inference of promoter activity from MS2-MCP data. However, the computational time for inference scales exponentially with gene length and the cpHMM is therefore not currently practical for application to many eukaryotic genes. RESULTS: We present a scalable implementation of the cpHMM for fast inference of promoter activity and transcriptional kinetic parameters. This new method can model genes of arbitrary length through the use of a time-adaptive truncated compound state space. The truncated state space provides a good approximation to the full state space by retaining the most likely set of states at each time during the forward pass of the algorithm. Testing on MS2-MCP fluorescent data collected from early Drosophila melanogaster embryos indicates that the method provides accurate inference of kinetic parameters within a computationally feasible timeframe. The inferred promoter traces generated by the model can also be used to infer single-cell transcriptional parameters. AVAILABILITY AND IMPLEMENTATION: Python implementation is available at https://github.com/ManchesterBioinference/burstInfer, along with code to reproduce the examples presented here. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The negative binomial distribution has been shown to be a good model for counts data from both bulk and single-cell RNA-sequencing (RNA-seq). Gaussian process (GP) regression provides a useful non-parametric approach for modelling temporal or spatial changes in gene expression. However, currently available GP regression methods that implement negative binomial likelihood models do not scale to the increasingly large datasets being produced by single-cell and spatial transcriptomics. RESULTS: The GPcounts package implements GP regression methods for modelling counts data using a negative binomial likelihood function. Computational efficiency is achieved through the use of variational Bayesian inference. The GP function models changes in the mean of the negative binomial likelihood through a logarithmic link function and the dispersion parameter is fitted by maximum likelihood. We validate the method on simulated time course data, showing better performance to identify changes in over-dispersed counts data than methods based on Gaussian or Poisson likelihoods. To demonstrate temporal inference, we apply GPcounts to single-cell RNA-seq datasets after pseudotime and branching inference. To demonstrate spatial inference, we apply GPcounts to data from the mouse olfactory bulb to identify spatially variable genes and compare to two published GP methods. We also provide the option of modelling additional dropout using a zero-inflated negative binomial. Our results show that GPcounts can be used to model temporal and spatial counts data in cases where simpler Gaussian and Poisson likelihoods are unrealistic. AVAILABILITY AND IMPLEMENTATION: GPcounts is implemented using the GPflow library in Python and is available at https://github.com/ManchesterBioinference/GPcounts along with the data, code and notebooks required to reproduce the results presented here. The version used for this paper is archived at https://doi.org/10.5281/zenodo.5027066. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: HiChIP is a powerful tool to interrogate 3D chromatin organization. Current tools to analyse chromatin looping mechanisms using HiChIP data require the identification of loop anchors to work properly. However, current approaches to discover these anchors from HiChIP data are not satisfactory, having either a very high false discovery rate or strong dependence on sequencing depth. Moreover, these tools do not allow quantitative comparison of peaks across different samples, failing to fully exploit the information available from HiChIP datasets. RESULTS: We develop a new tool based on a representation of HiChIP data centred on the re-ligation sites to identify peaks from HiChIP datasets, which can subsequently be used in other tools for loop discovery. This increases the reliability of these tools and improves recall rate as sequencing depth is reduced. We also provide a method to count reads mapping to peaks across samples, which can be used for differential peak analysis using HiChIP data. AVAILABILITY AND IMPLEMENTATION: HiChIP-Peaks is freely available at https://github.com/ChenfuShi/HiChIP_peaks. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Oscillatory genes, with periodic expression at the mRNA and/or protein level, have been shown to play a pivotal role in many biological contexts. However, with the exception of the circadian clock and cell cycle, only a few such genes are known. Detecting oscillatory genes from snapshot single-cell experiments is a challenging task due to the lack of time information. Oscope is a recently proposed method to identify co-oscillatory gene pairs using single-cell RNA-seq data. Although promising, the current implementation of Oscope does not provide a principled statistical criterion for selecting oscillatory genes. RESULTS: We improve the optimisation scheme underlying Oscope and provide a well-calibrated non-parametric hypothesis test to select oscillatory genes at a given FDR threshold. We evaluate performance on synthetic data and three real datasets and show that our approach is more sensitive than the original Oscope formulation, discovering larger sets of known oscillators while avoiding the need for less interpretable thresholds. We also describe how our proposed pseudo-time estimation method is more accurate in recovering the true cell order for each gene cluster while requiring substantially less computation time than the extended nearest insertion approach. CONCLUSIONS: OscoNet is a robust and versatile approach to detect oscillatory gene networks from snapshot single-cell data addressing many of the limitations of the original Oscope method.

Motivation: The Gaussian Process Latent Variable Model (GPLVM) is a popular approach for dimensionality reduction of single-cell data and has been used for pseudotime estimation with capture time information. However, current implementations are computationally intensive and will not scale up to modern droplet-based single-cell datasets which routinely profile many tens of thousands of cells. Results: We provide an efficient implementation which allows scaling up this approach to modern single-cell datasets. We also generalize the application of pseudotime inference to cases where there are other sources of variation such as branching dynamics. We apply our method on microarray, nCounter, RNA-seq, qPCR and droplet-based datasets from different organisms. The model converges an order of magnitude faster compared to existing methods whilst achieving similar levels of estimation accuracy. Further, we demonstrate the flexibility of our approach by extending the model to higher-dimensional latent spaces that can be used to simultaneously infer pseudotime and other structure such as branching. Thus, the model has the capability of producing meaningful biological insights about cell ordering as well as cell fate regulation. Availability and implementation: Software available at github.com/ManchesterBioinference/GrandPrix. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Regulation of gene expression in prokaryotes involves complex co-regulatory mechanisms involving large numbers of transcriptional regulatory proteins and their target genes. Uncovering these genome-scale interactions constitutes a major bottleneck in systems biology. Sparse latent factor models, assuming activity of transcription factors (TFs) as unobserved, provide a biologically interpretable modelling framework, integrating gene expression and genome-wide binding data, but at the same time pose a hard computational inference problem. Existing probabilistic inference methods for such models rely on subjective filtering and suffer from scalability issues, thus are not well-suited for realistic genome-scale applications. RESULTS: We present a fast Bayesian sparse factor model, which takes input gene expression and binding sites data, either from ChIP-seq experiments or motif predictions, and outputs active TF-gene links as well as latent TF activities. Our method employs an efficient variational Bayes scheme for model inference enabling its application to large datasets which was not feasible with existing MCMC-based inference methods for such models. We validate our method on synthetic data against a similar model in the literature, employing MCMC for inference, and obtain comparable results with a small fraction of the computational time. We also apply our method to large-scale data from Mycobacterium tuberculosis involving ChIP-seq data on 113 TFs and matched gene expression data for 3863 putative target genes. We evaluate our predictions using an independent transcriptomics experiment involving over-expression of TFs. AVAILABILITY AND IMPLEMENTATION: An easy-to-use Jupyter notebook demo of our method with data is available at https://github.com/zhenwendai/SITAR. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Time course data are often used to study the changes to a biological process after perturbation. Statistical methods have been developed to determine whether such a perturbation induces changes over time, e.g. comparing a perturbed and unperturbed time course dataset to uncover differences. However, existing methods do not provide a principled statistical approach to identify the specific time when the two time course datasets first begin to diverge after a perturbation; we call this the perturbation time. Estimation of the perturbation time for different variables in a biological process allows us to identify the sequence of events following a perturbation and therefore provides valuable insights into likely causal relationships. RESULTS: We propose a Bayesian method to infer the perturbation time given time course data from a wild-type and perturbed system. We use a non-parametric approach based on Gaussian Process regression. We derive a probabilistic model of noise-corrupted and replicated time course data coming from the same profile before the perturbation time and diverging after the perturbation time. The likelihood function can be worked out exactly for this model and the posterior distribution of the perturbation time is obtained by a simple histogram approach, without recourse to complex approximate inference algorithms. We validate the method on simulated data and apply it to study the transcriptional change occurring in Arabidopsis following inoculation with Pseudomonas syringae pv. tomato DC3000 versus the disarmed strain DC3000hrpA AVAILABILITY AND IMPLEMENTATION: : An R package, DEtime, implementing the method is available at https://github.com/ManchesterBioinference/DEtime along with the data and code required to reproduce all the results. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Assigning RNA-seq reads to their transcript of origin is a fundamental task in transcript expression estimation. Where ambiguities in assignments exist due to transcripts sharing sequence, e.g. alternative isoforms or alleles, the problem can be solved through probabilistic inference. Bayesian methods have been shown to provide accurate transcript abundance estimates compared with competing methods. However, exact Bayesian inference is intractable and approximate methods such as Markov chain Monte Carlo and Variational Bayes (VB) are typically used. While providing a high degree of accuracy and modelling flexibility, standard implementations can be prohibitively slow for large datasets and complex transcriptome annotations. RESULTS: We propose a novel approximate inference scheme based on VB and apply it to an existing model of transcript expression inference from RNA-seq data. Recent advances in VB algorithmics are used to improve the convergence of the algorithm beyond the standard Variational Bayes Expectation Maximization algorithm. We apply our algorithm to simulated and biological datasets, demonstrating a significant increase in speed with only very small loss in accuracy of expression level estimation. We carry out a comparative study against seven popular alternative methods and demonstrate that our new algorithm provides excellent accuracy and inter-replicate consistency while remaining competitive in computation time. AVAILABILITY AND IMPLEMENTATION: The methods were implemented in R and C++, and are available as part of the BitSeq project at github.com/BitSeq. The method is also available through the BitSeq Bioconductor package. The source code to reproduce all simulation results can be accessed via github.com/BitSeq/BitSeqVB_benchmarking.

In this publication, we combine two Bayesian nonparametric models: the Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP model is to introduce a variation on the GP prior which enables us to model structured time-series data, i.e., data containing groups where we wish to model inter- and intra-group variability. Our innovation in the DP model is an implementation of a new fast collapsed variational inference procedure which enables us to optimize our variational approximation significantly faster than standard VB approaches. In a biological time series application we show how our model better captures salient features of the data, leading to better consistency with existing biological classifications, while the associated inference algorithm provides a significant speed-up over EM-based variational inference.

Gene transcription mediated by RNA polymerase II (pol-II) is a key step in gene expression. The dynamics of pol-II moving along the transcribed region influence the rate and timing of gene expression. In this work, we present a probabilistic model of transcription dynamics which is fitted to pol-II occupancy time course data measured using ChIP-Seq. The model can be used to estimate transcription speed and to infer the temporal pol-II activity profile at the gene promoter. Model parameters are estimated using either maximum likelihood estimation or via Bayesian inference using Markov chain Monte Carlo sampling. The Bayesian approach provides confidence intervals for parameter estimates and allows the use of priors that capture domain knowledge, e.g. the expected range of transcription speeds, based on previous experiments. The model describes the movement of pol-II down the gene body and can be used to identify the time of induction for transcriptionally engaged genes. By clustering the inferred promoter activity time profiles, we are able to determine which genes respond quickly to stimuli and group genes that share activity profiles and may therefore be co-regulated. We apply our methodology to biological data obtained using ChIP-seq to measure pol-II occupancy genome-wide when MCF-7 human breast cancer cells are treated with estradiol (E2). The transcription speeds we obtain agree with those obtained previously for smaller numbers of genes with the advantage that our approach can be applied genome-wide. We validate the biological significance of the pol-II promoter activity clusters by investigating cluster-specific transcription factor binding patterns and determining canonical pathway enrichment. We find that rapidly induced genes are enriched for both estrogen receptor alpha (ERα) and FOXA1 binding in their proximal promoter regions.

BACKGROUND: Time course data from microarrays and high-throughput sequencing experiments require simple, computationally efficient and powerful statistical models to extract meaningful biological signal, and for tasks such as data fusion and clustering. Existing methodologies fail to capture either the temporal or replicated nature of the experiments, and often impose constraints on the data collection process, such as regularly spaced samples, or similar sampling schema across replications. RESULTS: We propose hierarchical Gaussian processes as a general model of gene expression time-series, with application to a variety of problems. In particular, we illustrate the method's capacity for missing data imputation, data fusion and clustering.The method can impute data which is missing both systematically and at random: in a hold-out test on real data, performance is significantly better than commonly used imputation methods. The method's ability to model inter- and intra-cluster variance leads to more biologically meaningful clusters. The approach removes the necessity for evenly spaced samples, an advantage illustrated on a developmental Drosophila dataset with irregular replications. CONCLUSION: The hierarchical Gaussian process model provides an excellent statistical basis for several gene-expression time-series tasks. It has only a few additional parameters over a regular GP, has negligible additional complexity, is easily implemented and can be integrated into several existing algorithms. Our experiments were implemented in python, and are available from the authors' website: http://staffwww.dcs.shef.ac.uk/people/J.Hensman/.

BACKGROUND: Microarrays have been a popular tool for gene expression profiling at genome-scale for over a decade due to the low cost, short turn-around time, excellent quantitative accuracy and ease of data generation. The Bioconductor package puma incorporates a suite of analysis methods for determining uncertainties from Affymetrix GeneChip data and propagating these uncertainties to downstream analysis. As isoform level expression profiling receives more and more interest within genomics in recent years, exon microarray technology offers an important tool to quantify expression level of the majority of exons and enables the possibility of measuring isoform level expression. However, puma does not include methods for the analysis of exon array data. Moreover, the current expression summarisation method for Affymetrix 3' GeneChip data suffers from instability for low expression genes. For the downstream analysis, the method for differential expression detection is computationally intensive and the original expression clustering method does not consider the variance across the replicated technical and biological measurements. It is therefore necessary to develop improved uncertainty propagation methods for gene and transcript expression analysis. RESULTS: We extend the previously developed Bioconductor package puma with a new method especially designed for GeneChip Exon arrays and a set of improved downstream approaches. The improvements include: (i) a new gamma model for exon arrays which calculates isoform and gene expression measurements and a level of uncertainty associated with the estimates, using the multi-mappings between probes, isoforms and genes, (ii) a variant of the existing approach for the probe-level analysis of Affymetrix 3' GeneChip data to produce more stable gene expression estimates, (iii) an improved method for detecting differential expression which is computationally more efficient than the existing approach in the package and (iv) an improved method for robust model-based clustering of gene expression, which takes technical and biological replicate information into consideration. CONCLUSIONS: With the extensions and improvements, the puma package is now applicable to the analysis of both Affymetrix 3' GeneChips and Exon arrays for gene and isoform expression estimation. It propagates the uncertainty of expression measurements into more efficient and comprehensive downstream analysis at both gene and isoform level. Downstream methods are also applicable to other expression quantification platforms, such as RNA-Seq, when uncertainty information is available from expression measurements. puma is available through Bioconductor and can be found at http://www.bioconductor.org.

We present a general method for deriving collapsed variational inference algorithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. We exploit the information geometry of the bound to derive much faster optimization methods based on conjugate gradients for these models. Our approach is very general and is easily applied to any model where the mean field update equations have been derived. Empirically we show significant speed-ups for probabilistic models optimized using our bound.

MOTIVATION: High-throughput sequencing enables expression analysis at the level of individual transcripts. The analysis of transcriptome expression levels and differential expression (DE) estimation requires a probabilistic approach to properly account for ambiguity caused by shared exons and finite read sampling as well as the intrinsic biological variance of transcript expression. RESULTS: We present Bayesian inference of transcripts from sequencing data (BitSeq), a Bayesian approach for estimation of transcript expression level from RNA-seq experiments. Inferred relative expression is represented by Markov chain Monte Carlo samples from the posterior probability distribution of a generative model of the read data. We propose a novel method for DE analysis across replicates which propagates uncertainty from the sample-level model while modelling biological variance using an expression-level-dependent prior. We demonstrate the advantages of our method using simulated data as well as an RNA-seq dataset with technical and biological replication for both studied conditions. AVAILABILITY: The implementation of the transcriptome expression estimation and differential expression analysis, BitSeq, has been written in C++ and Python. The software is available online from http://code.google.com/p/bitseq/, version 0.4 was used for generating results presented in this article.

UNLABELLED: tigre is an R/Bioconductor package for inference of transcription factor activity and ranking candidate target genes from gene expression time series. The underlying methodology is based on Gaussian process inference on a differential equation model that allows the use of short, unevenly sampled, time series. The method has been designed with efficient parallel implementation in mind, and the package supports parallel operation even without additional software. AVAILABILITY: The tigre package is included in Bioconductor since release 2.6 for R 2.11. The package and a user's guide are available at http://www.bioconductor.org.

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.

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.

Sampling functions in Gaussian process (GP) models is challenging because of the highly correlated posterior distribution. We describe an efficient Markov chain Monte Carlo algorithm for sampling from the posterior process of the GP model. This algorithm uses control variables which are auxiliary function values that provide a low dimensional representation of the function. At each iteration, the algorithm proposes new values for the control variables and generates the function from the conditional GP prior. The control variable input locations are found by continuously minimizing an objective function. We demonstrate the algorithm on regression and classification problems and we use it to estimate the parameters of a differential equation model of gene regulation.

MOTIVATION: Genetic modifications or pharmaceutical interventions can influence multiple sites in metabolic pathways, and often these are 'distant' from the primary effect. In this regard, the ability to identify target and off-target effects of a specific compound or gene therapy is both a major challenge and critical in drug discovery. RESULTS: We applied Markov Chain Monte Carlo (MCMC) for parameter estimation and perturbation identification in the kinetic modeling of metabolic pathways. Variability in the steady-state measurements in cells taken from a population can be caused by differences in initial conditions within the population, by variation of parameters among individuals and by possible measurement noise. MCMC-based parameter estimation is proposed as a method to help in inferring parameter distributions, taking into account uncertainties in the initial conditions and in the measurement data. The inferred parameter distributions are then used to predict changes in the network via a simple classification method. The proposed technique is applied to analyze changes in the pathways of pyruvate metabolism of mutants of Lactococcus lactis, based on previously published experimental data. AVAILABILITY: MATLAB code used in the simulations is available from ftp://[email protected]/pub/Bioinformatics_BJ.zip

The present work aims to model the correspondence between facial motion and speech. The face and sound are modelled separately, with phonemes being the link between both. We propose a sequential model and evaluate its suitability for the generation of the facial animation from a sequence of phonemes, which we obtain from speech. We evaluate the results both by computing the error between generated sequences and real video, as well as with a rigorous double-blind test with human subjects. Experiments show that our model compares favourably to other existing methods and that the sequences generated are comparable to real video sequences.

BACKGROUND: Clustering is an important analysis performed on microarray gene expression data since it groups genes which have similar expression patterns and enables the exploration of unknown gene functions. Microarray experiments are associated with many sources of experimental and biological variation and the resulting gene expression data are therefore very noisy. Many heuristic and model-based clustering approaches have been developed to cluster this noisy data. However, few of them include consideration of probe-level measurement error which provides rich information about technical variability. RESULTS: We augment a standard model-based clustering method to incorporate probe-level measurement error. Using probe-level measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we include the probe-level measurement error directly into the standard Gaussian mixture model. Our augmented model is shown to provide improved clustering performance on simulated datasets and a real mouse time-course dataset. CONCLUSION: The performance of model-based clustering of gene expression data is improved by including probe-level measurement error and more biologically meaningful clustering results are obtained.

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: Finding differentially expressed genes is a fundamental objective of a microarray experiment. Numerous methods have been proposed to perform this task. Existing methods are based on point estimates of gene expression level obtained from each microarray experiment. This approach discards potentially useful information about measurement error that can be obtained from an appropriate probe-level analysis. Probabilistic probe-level models can be used to measure gene expression and also provide a level of uncertainty in this measurement. This probe-level measurement error provides useful information which can help in the identification of differentially expressed genes. RESULTS: We propose a Bayesian method to include probe-level measurement error into the detection of differentially expressed genes from replicated experiments. A variational approximation is used for efficient parameter estimation. We compare this approximation with MAP and MCMC parameter estimation in terms of computational efficiency and accuracy. The method is used to calculate the probability of positive log-ratio (PPLR) of expression levels between conditions. Using the measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we test PPLR on a spike-in dataset and a mouse time-course dataset. Results show that the inclusion of probe-level measurement error improves accuracy in detecting differential gene expression. AVAILABILITY: The MAP approximation and variational inference described in this paper have been implemented in an R package pplr. The MCMC method is implemented in Matlab. Both software are 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. 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: Affymetrix GeneChip arrays are currently the most widely used microarray technology. Many summarization methods have been developed to provide gene expression levels from Affymetrix probe-level data. Most of the currently popular methods do not provide a measure of uncertainty for the expression level of each gene. The use of probabilistic models can overcome this limitation. A full hierarchical Bayesian approach requires the use of computationally intensive MCMC methods that are impractical for large datasets. An alternative computationally efficient probabilistic model, mgMOS, uses Gamma distributions to model specific and non-specific binding with a latent variable to capture variations in probe affinity. Although promising, the main limitations of this model are that it does not use information from multiple chips and does not account for specific binding to the mismatch (MM) probes. RESULTS: We extend mgMOS to model the binding affinity of probe-pairs across multiple chips and to capture the effect of specific binding to MM probes. The new model, multi-mgMOS, provides improved accuracy, as demonstrated on some bench-mark datasets and a real time-course dataset, and is much more computationally efficient than a competing hierarchical Bayesian approach that requires MCMC sampling. We demonstrate how the probabilistic model can be used to estimate credibility intervals for expression levels and their log-ratios between conditions. AVAILABILITY: Both mgMOS and the new model multi-mgMOS have been implemented in an R package, which is available at http://www.bioinf.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.

We derive the limiting form of the eigenvalue spectrum for sample co- variance matrices produced from non-isotropic data. For the analysis of standard PCA we study the case where the data has increased variance along a small number of symmetry-breaking directions. The spectrum depends on the strength of the symmetry-breaking signals and on a pa- rameter (cid:11) which is the ratio of sample size to data dimension. Results are derived in the limit of large data dimension while keeping (cid:11) fixed. As (cid:11) increases there are transitions in which delta functions emerge from the upper end of the bulk spectrum, corresponding to the symmetry-breaking directions in the data, and we calculate the bias in the corresponding eigenvalues. For kernel PCA the covariance matrix in feature space may contain symmetry-breaking structure even when the data components are independently distributed with equal variance. We show examples of phase-transition behaviour analogous to the PCA results in this case.

MOTIVATION: Typical analysis of microarray data has focused on spot by spot comparisons within a single organism. Less analysis has been done on the comparison of the entire distribution of spot intensities between experiments and between organisms. RESULTS: Here we show that mRNA transcription data from a wide range of organisms and measured with a range of experimental platforms show close agreement with Benford's law (Benford, PROC: Am. Phil. Soc., 78, 551-572, 1938) and Zipf's law (Zipf, The Psycho-biology of Language: an Introduction to Dynamic Philology, 1936 and Human Behaviour and the Principle of Least Effort, 1949). The distribution of the bulk of microarray spot intensities is well approximated by a log-normal with the tail of the distribution being closer to power law. The variance, sigma(2), of log spot intensity shows a positive correlation with genome size (in terms of number of genes) and is therefore relatively fixed within some range for a given organism. The measured value of sigma(2) can be significantly smaller than the expected value if the mRNA is extracted from a sample of mixed cell types. Our research demonstrates that useful biological findings may result from analyzing microarray data at the level of entire intensity distributions.

Previous analytical studies of on-line independent component analysis (ICA) learning rules have focused on asymptotic stability and efficiency. In practice, the transient stages of learning are often more significant in determining the success of an algorithm. This is demonstrated here with an analysis of a Hebbian ICA algorithm, which can find a small number of nongaussian components given data composed of a linear mixture of independent source signals. An idealized data model is considered in which the sources comprise a number of nongaussian and gaussian sources, and a solution to the dynamics is obtained in the limit where the number of gaussian sources is infinite. Previous stability results are confirmed by expanding around optimal fixed points, where a closed-form solution to the learning dynamics is obtained. However, stochastic effects are shown to stabilize otherwise unstable suboptimal fixed points. Conditions required to destabilize one such fixed point are obtained for the case of a single nongaussian component, indicating that the initial learning rate eta required to escape successfully is very low (eta = O(N(-2)) where N is the data dimension), resulting in very slow learning typically requiring O(N(3)) iterations. Simulations confirm that this picture holds for a finite system.

We study the dynamics of a Hebbian ICA algorithm extracting a sin- gle non-Gaussian component from a high-dimensional Gaussian back- ground. For both on-line and batch learning we find that a surprisingly large number of examples are required to avoid trapping in a sub-optimal state close to the initial conditions. To extract a skewed signal at least 
 examples are required for  -dimensional data and 
  exam- ples are required to extract a symmetrical signal with non-zero kurtosis.

A Riemannian distance is defined which is appropriate for clustering multivariate data. This distance requires that data is first fitted with a differentiable density model allowing the definition of an appropriate Riemannian metric. A tractable approximation is developed for the case of a Gaussian mixture model and the distance is tested on artificial data, demonstrating an ability to deal with differing length scales and linearly inseparable data clusters. Further work is required to investigate performance on larger data sets.