arXiv subjects

Magnus Rattray

Publications and source records attributed to Magnus Rattray.

At least 19 recordsLinked to original sources

arXiv2026

Transformed Latent Variable Multi-Output Gaussian Processes

Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To maintain tractability, existing methods typically resort to restrictive assumptions, such as employing low-rank or sum-of-separable kernels, which can limit expressiveness. We propose the Transformed Latent Variable MOGP (T-LVMOGP), a novel framework that scales MOGPs to a massive number of outputs while preserving the capacity to capture meaningful inter-output dependencies. T-LVMOGP constructs a flexible multi-output deep kernel by mapping inputs and output-specific latent variables into an embedding space using a Lipschitz-regularised neural network. Combined with stochastic variational inference, our model effectively scales to high-dimensional output settings. Across diverse benchmarks, including climate modelling with over 10,000 outputs and zero-inflated spatial transcriptomics data, T-LVMOGP outperforms baselines in both predictive accuracy and computational efficiency.

cs.LG↗

arXiv2026

Multimodal Spatial Omics: From Data Acquisition to Computational Integration

Recent developments in spatial omics technologies have enabled the generation of high dimensional molecular data, such as transcriptomes, proteomes, and epigenomes, within their spatial tissue context, either through coprofiling on the same slice or through serial tissue sections. These datasets, which are often complemented by images, have given rise to multimodal frameworks that capture both the cellular and architectural complexity of tissues across multiple molecular layers. Integration in such multimodal data poses significant computational challenges due to differences in scale, resolution, and data modality. In this review, we present a comprehensive overview of computational methods developed to integrate multimodal spatial omics and imaging datasets. We highlight key algorithmic principles underlying these methods, ranging from probabilistic to the latest deep learning approaches.

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arXiv2024

Scalable Multi-Output Gaussian Processes with Stochastic Variational Inference

The Multi-Output Gaussian Process is is a popular tool for modelling data from multiple sources. A typical choice to build a covariance function for a MOGP is the Linear Model of Coregionalization (LMC) which parametrically models the covariance between outputs. The Latent Variable MOGP (LV-MOGP) generalises this idea by modelling the covariance between outputs using a kernel applied to latent variables, one per output, leading to a flexible MOGP model that allows efficient generalization to new outputs with few data points. Computational complexity in LV-MOGP grows linearly with the number of outputs, which makes it unsuitable for problems with a large number of outputs. In this paper, we propose a stochastic variational inference approach for the LV-MOGP that allows mini-batches for both inputs and outputs, making computational complexity per training iteration independent of the number of outputs.

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arXiv2017

Bayesian estimation of Differential Transcript Usage from RNA-seq data

Next generation sequencing allows the identification of genes consisting of differentially expressed transcripts, a term which usually refers to changes in the overall expression level. A specific type of differential expression is differential transcript usage (DTU) and targets changes in the relative within gene expression of a transcript. The contribution of this paper is to: (a) extend the use of cjBitSeq to the DTU context, a previously introduced Bayesian model which is originally designed for identifying changes in overall expression levels and (b) propose a Bayesian version of DRIMSeq, a frequentist model for inferring DTU. cjBitSeq is a read based model and performs fully Bayesian inference by MCMC sampling on the space of latent state of each transcript per gene. BayesDRIMSeq is a count based model and estimates the Bayes Factor of a DTU model against a null model using Laplace's approximation. The proposed models are benchmarked against the existing ones using a recent independent simulation study as well as a real RNA-seq dataset. Our results suggest that the Bayesian methods exhibit similar performance with DRIMSeq in terms of precision/recall but offer better calibration of False Discovery Rate.

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arXiv2017

Bayesian detection of piecewise linear trends in replicated time-series with application to growth data modelling

We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. We develop a Bayesian approach to infer the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence. A Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed for approximating the posterior distribution. Our method is benchmarked using simulated data and is applied to uncover differences in the dynamics of fungal growth from imaging time course data collected from different strains. The source code is available on CRAN.

stat.AP↗

arXiv2017

Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes

Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a {\it Hes1} promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5' LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.

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arXiv2017

BayesBinMix: an R Package for Model Based Clustering of Multivariate Binary Data

The BayesBinMix package offers a Bayesian framework for clustering binary data with or without missing values by fitting mixtures of multivariate Bernoulli distributions with an unknown number of components. It allows the joint estimation of the number of clusters and model parameters using Markov chain Monte Carlo sampling. Heated chains are run in parallel and accelerate the convergence to the target posterior distribution. Identifiability issues are addressed by implementing label switching algorithms. The package is demonstrated and benchmarked against the Expectation-Maximization algorithm using a simulation study as well as a real dataset.

stat.CO↗

arXiv2016

A Bayesian model selection approach for identifying differentially expressed transcripts from RNA-Seq data

Recent advances in molecular biology allow the quantification of the transcriptome and scoring transcripts as differentially or equally expressed between two biological conditions. Although these two tasks are closely linked, the available inference methods treat them separately: a primary model is used to estimate expression and its output is post-processed using a differential expression model. In this paper, both issues are simultaneously addressed by proposing the joint estimation of expression levels and differential expression: the unknown relative abundance of each transcript can either be equal or not between two conditions. A hierarchical Bayesian model builds upon the BitSeq framework and the posterior distribution of transcript expression and differential expression is inferred using Markov Chain Monte Carlo (MCMC). It is shown that the proposed model enjoys conjugacy for fixed dimension variables, thus the full conditional distributions are analytically derived. Two samplers are constructed, a reversible jump MCMC sampler and a collapsed Gibbs sampler, and the latter is found to perform best. A cluster representation of the aligned reads to the transcriptome is introduced, allowing parallel estimation of the marginal posterior distribution of subsets of transcripts under reasonable computing time. The proposed algorithm is benchmarked against alternative methods using synthetic datasets and applied to real RNA-sequencing data. Source code is available online (https://github.com/mqbssppe/cjBitSeq).

stat.ME↗

arXiv2016

Gaussian process models for periodicity detection

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in the arabidopsis genome.

math.ST↗

arXiv2016

Inferring the perturbation time from biological time course data

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. In this paper, 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 P. syringae pv. tomato DC3000 versus the disarmed strain DC3000hrpA. 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.

q-bio.QM↗

arXiv2015

Genome-wide modelling of transcription kinetics reveals patterns of RNA production delays

Genes with similar transcriptional activation kinetics can display very different temporal mRNA profiles due to differences in transcription time, degradation rate and RNA processing kinetics. Recent studies have shown that a splicing-associated RNA production delay can be significant. We introduce a joint model of transcriptional activation and mRNA accumulation which can be used for inference of transcription rate, RNA production delay and degradation rate given genome-wide data from high-throughput sequencing time course experiments. We combine a mechanistic differential equation model with a non-parametric statistical modelling approach allowing us to capture a broad range of activation kinetics, and use Bayesian parameter estimation to quantify the uncertainty in the estimates of the kinetic parameters. We apply the model to data from estrogen receptor (ER-α) activation in the MCF-7 breast cancer cell line. We use RNA polymerase II (pol-II) ChIP-Seq time course data to characterise transcriptional activation and mRNA-Seq time course data to quantify mature transcripts. We find that 11% of genes with a good signal in the data display a delay of more than 20 minutes between completing transcription and mature mRNA production. The genes displaying these long delays are significantly more likely to be short. We also find a statistical association between high delay and late intron retention in pre-mRNA data, indicating significant splicing-associated production delays in many genes.

q-bio.GN↗

arXiv2015

Fast and accurate approximate inference of transcript expression from RNA-seq data

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 to competing methods. However, exact Bayesian inference is intractable and approximate methods such as Markov chain Monte Carlo (MCMC) 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 Maximisation (VBEM) 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: The methods were implemented in R and C++, and are available as part of the BitSeq project at \url{https://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 \url{https://github.com/BitSeq/BitSeqVB_benchmarking}.

q-bio.QM↗

arXiv2015

Fast Approximate Inference of Transcript Expression Levels from RNA-seq Data

Motivation: The mapping of RNA-seq reads to their transcripts of origin is a fundamental task in transcript expression estimation and differential expression scoring. Where ambiguities in mapping exist due to transcripts sharing sequence, e.g. alternative isoforms or alleles, the problem becomes an instance of non-trivial probabilistic inference. Bayesian inference in such a problem is intractable and approximate methods must be used such as Markov chain Monte Carlo (MCMC) and Variational Bayes. Standard implementations of these methods can be prohibitively slow for large datasets and complex gene models. Results: We propose an approximate inference scheme based on Variational Bayes applied to an existing model of transcript expression inference from RNA-seq data. We apply recent advances in Variational Bayes algorithmics to improve the convergence of the algorithm beyond the standard variational expectation-maximisation approach. We apply our algorithm to simulated and biological datasets, demonstrating that the increase in speed requires only a small trade-off in accuracy of expression level estimation. Availability: The methods were implemented in R and C++, and are available as part of the BitSeq project at https://code.google.com/p/bitseq/. The methods will be made available through the BitSeq Bioconductor package at the next stable release.

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arXiv2014

Fast nonparametric clustering of structured time-series

In this publication, we combine two Bayesian non-parametric 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 variationala pproximation 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 twofold speed-up over EM-based variational inference.

cs.LG↗

arXiv2014

Inference of RNA Polymerase II Transcription Dynamics from Chromatin Immunoprecipitation Time Course Data

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 (ER$α$) and FOXA1 binding in their proximal promoter regions.

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arXiv2012

Fast Variational Inference in the Conjugate Exponential Family

We present a general method for deriving collapsed variational inference algo- rithms 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.

cs.LG↗

arXiv2012

Identifying differentially expressed transcripts from RNA-seq data with biological variation

Motivation: High-throughput sequencing enables expression analysis at the level of individual transcripts. The analysis of transcriptome expression levels and differential expression 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 BitSeq (Bayesian Inference of Transcripts from Sequencing data), a Bayesian approach for estimation of transcript expression level from RNA-seq experiments. Inferred relative expression is represented by Markov chain Monte Carlo (MCMC) samples from the posterior probability distribution of a generative model of the read data. We propose a novel method for differential expression 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++.

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arXiv2004

RNA-based Phylogenetic Methods: Application to Mammalian Mitochondrial RNA Sequences

The PHASE software package allows phylogenetic tree construction with a number of evolutionary models designed specifically for use with RNA sequences that have conserved secondary structure. Evolution in the paired regions of RNAs occurs via compensatory substitutions, hence changes on either side of a pair are correlated. Accounting for this correlation is important for phylogenetic inference because it affects the likelihood calculation. In the present study we use the complete set of tRNA and rRNA sequences from 69 complete mammalian mitochondrial genomes. The likelihood calculation uses two evolutionary models simultaneously for different parts of the sequence: a paired-site model for the paired sites and a single-site model for the unpaired sites. We use Bayesian phylogenetic methods and a Markov chain Monte Carlo algorithm is used to obtain the most probable trees and posterior probabilities of clades. The results are well resolved for almost all the important branches on the mammalian tree. They support the arrangement of mammalian orders within the four supra-ordinal clades that have been identified by studies of much larger data sets mainly comprising nuclear genes. Groups such as the hedgehogs and the murid rodents, which have been problematic in previous studies with mitochondrial proteins, appear in their expected position with the other members of their order. Our choice of genes and evolutionary model appears to be more reliable and less subject to biases caused by variation in base composition than previous studies with mitochondrial genomes.

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