We present bfact, a Python package for performing accurate low-rank Boolean matrix factorisation (BMF). bfact uses a hybrid combinatorial optimisation approach based on a priori candidate factors generated from clustering algorithms. It selects the best disjoint factors before performing either a second combinatorial or heuristic algorithm to recover the BMF. We show that bfact does particularly well at estimating the true rank of matrices in simulated settings. In real benchmarks, using a collation of single-cell RNA-sequencing datasets from the Human Lung Cell Atlas, we show that bfact achieves strong signal recovery, with a much lower rank.

Estimating heterogeneous treatment effects (HTEs) of continuous-valued interventions on survival, that is, time-to-event (TTE) outcomes, is crucial in various fields, notably in clinical decision-making and in driving the advancement of next-generation clinical trials. However, while HTE estimation for continuous-valued (i.e., dosage-dependent) interventions and for TTE outcomes have been separately explored, their combined application remains largely overlooked in the machine learning literature. We propose DoseSurv, a varying-coefficient network designed to estimate HTEs for different dosage-dependent and non-dosage treatment options from TTE data. DoseSurv uses radial basis functions to model continuity in dose-response relationships and learns balanced representations to address covariate shifts arising in HTE estimation from observational TTE data. We present experiments across various treatment scenarios on both simulated and real-world data, demonstrating DoseSurv's superior performance over existing baseline models.

The identification of tumor-specific molecular dependencies is essential for the development of effective cancer therapies. Genetic and chemical perturbations are powerful tools for discovering these dependencies. Even though chemical perturbations can be applied to primary cancer samples at large scale, the interpretation of experiment outcomes is often complicated by the fact that one chemical compound can affect multiple proteins. To overcome this challenge, Batzilla et al. (PLoS Comput Biol 18(8): e1010438, 2022) proposed DepInfeR, a regularized multi-response regression model designed to identify and estimate specific molecular dependencies of individual cancers from their ex-vivo drug sensitivity profiles. Inspired by their work, we propose a Bayesian extension to DepInfeR. Our proposed approach offers several advantages over DepInfeR, including e.g. the ability to handle missing values in both protein-drug affinity and drug sensitivity profiles without the need for data pre-processing steps such as imputation. Moreover, our approach uses Gaussian Processes to capture more complex molecular dependency structures, and provides probabilistic statements about whether a protein in the protein-drug affinity profiles is informative to the drug sensitivity profiles. Simulation studies demonstrate that our proposed approach achieves better prediction accuracy, and is able to discover unreported dependency structures.

MOTIVATION: Cell type identification plays an important role in the analysis and interpretation of single-cell data and can be carried out via supervised or unsupervised clustering approaches. Supervised methods are best suited where we can list all cell types and their respective marker genes a priori, while unsupervised clustering algorithms look for groups of cells with similar expression properties. This property permits the identification of both known and unknown cell populations, making unsupervised methods suitable for discovery. Success is dependent on the relative strength of the expression signature of each group as well as the number of cells. Rare cell types therefore present a particular challenge that is magnified when they are defined by differentially expressing a small number of genes. RESULTS: Typical unsupervised approaches fail to identify such rare subpopulations, and these cells tend to be absorbed into more prevalent cell types. In order to balance these competing demands, we have developed a novel statistical framework for unsupervised clustering, named Rarity, that enables the discovery process for rare cell types to be more robust, consistent, and interpretable. We achieve this by devising a novel clustering method based on a Bayesian latent variable model in which we assign cells to inferred latent binary on/off expression profiles. This lets us achieve increased sensitivity to rare cell populations while also allowing us to control and interpret potential false positive discoveries. We systematically study the challenges associated with rare cell type identification and demonstrate the utility of Rarity on various IMC datasets. AVAILABILITY AND IMPLEMENTATION: Implementation of Rarity together with examples is available from the Github repository (https://github.com/kasparmartens/rarity).

BACKGROUND: Genomic insights in settings where tumour sample sizes are limited to just hundreds or even tens of cells hold great clinical potential, but also present significant technical challenges. We previously developed the DigiPico sequencing platform to accurately identify somatic mutations from such samples. RESULTS: Here, we complete this genomic characterisation with copy number. We present a novel protocol, PicoCNV, to call allele-specific somatic copy number alterations from picogram quantities of tumour DNA. We find that PicoCNV provides exactly accurate copy number in 84% of the genome for even the smallest samples, and demonstrate its clinical potential in maintenance therapy. CONCLUSIONS: PicoCNV complements our existing platform, allowing for accurate and comprehensive genomic characterisations of cancers in settings where only microscopic samples are available.

Survival models — particularly those able to account for patient comorbidities via competing risks analysis — offer valuable prognostic information to clinicians making critical decisions and represent a growing area of application for machine learning approaches. However, current methods typically involve restrictive parameterisations, discretisation of time or the modelling of only one event cause. In this paper, we highlight how general cumulative distribution functions can be naturally expressed via neural network-based ordinary differential equations and how this observation can be utilised in survival analysis. In particular, we present DeSurv, a neural derivative-based approach capable of avoiding aforementioned restrictions and flexibly modelling competing-risk survival data in continuous time. We apply DeSurv to both single-risk and competing-risk synthetic and real-world datasets and obtain results which compare favourably with current state-of-the-art models.

U-Net architectures are ubiquitous in state-of-the-art deep learning, however their regularisation properties and relationship to wavelets are understudied. In this paper, we formulate a multi-resolution framework which identifies U-Nets as finite-dimensional truncations of models on an infinite-dimensional function space. We provide theoretical results which prove that average pooling corresponds to projection within the space of square-integrable functions and show that U-Nets with average pooling implicitly learn a Haar wavelet basis representation of the data. We then leverage our framework to identify state-of-the-art hierarchical VAEs (HVAEs), which have a U-Net architecture, as a type of two-step forward Euler discretisation of multi-resolution diffusion processes which flow from a point mass, introducing sampling instabilities. We also demonstrate that HVAEs learn a representation of time which allows for improved parameter efficiency through weight-sharing. We use this observation to achieve state-of-the-art HVAE performance with half the number of parameters of existing models, exploiting the properties of our continuous-time formulation.

The Variational Autoencoder (VAE) performs effective nonlinear dimensionality reduction in a variety of problem settings. However, the black-box neural network decoder function typically employed limits the ability of the decoder function to be constrained and interpreted, making the use of VAEs problematic in settings where prior knowledge should be embedded within the decoder. We present DeVAE, a novel VAE-based model with a derivative-based forward mapping, allowing for greater control over decoder behaviour via specification of the decoder function in derivative space. Additionally, we show how DeVAE can be paired with a sparse clustering prior to create BasisDeVAE and perform interpretable simultaneous dimensionality reduction and feature-level clustering. We demonstrate the performance and scalability of the DeVAE and BasisDeVAE models on synthetic and real-world data and present how the derivative-based approach allows for expressive yet interpretable forward models which respect prior knowledge.

Work in deep clustering focuses on finding a single partition of data. However, high-dimensional data, such as images, typically feature multiple interesting characteristics one could cluster over. For example, images of objects against a background could be clustered over the shape of the object and separately by the colour of the background. In this paper, we introduce Multi-Facet Clustering Variational Autoencoders (MFCVAE), a novel class of variational autoencoders with a hierarchy of latent variables, each with a Mixture-of-Gaussians prior, that learns multiple clusterings simultaneously, and is trained fully unsupervised and end-to-end. MFCVAE uses a progressively-trained ladder architecture which leads to highly stable performance. We provide novel theoretical results for optimising the ELBO analytically with respect to the categorical variational posterior distribution, correcting earlier influential theoretical work. On image benchmarks, we demonstrate that our approach separates out and clusters over different aspects of the data in a disentangled manner. We also show other advantages of our model: the compositionality of its latent space and that it provides controlled generation of samples.

Variational Autoencoders (VAEs) have become a popular approach for dimensionality reduction. However, despite their ability to identify latent low-dimensional structures embedded within high-dimensional data, these latent representations are typically hard to interpret on their own. Due to the black-box nature of VAEs, their utility for healthcare and genomics applications has been limited. In this paper, we focus on characterising the sources of variation in Conditional VAEs. Our goal is to provide a feature-level variance decomposition, i.e. to decompose variation in the data by separating out the marginal additive effects of latent variables z and fixed inputs c from their non-linear interactions. We propose to achieve this through what we call Neural Decomposition – an adaptation of the well-known concept of functional ANOVA variance decomposition from classical statistics to deep learning models. We show how identifiability can be achieved by training models subject to constraints on the marginal properties of the decoder networks. We demonstrate the utility of our Neural Decomposition on a series of synthetic examples as well as high-dimensional genomics data.

Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box approach to dimensionality reduction does not provide sufficient insights. Common data analysis workflows additionally use clustering techniques to identify groups of similar features. This usually leads to a two-stage process, however, it would be desirable to construct a joint modelling framework for simultaneous dimensionality reduction and clustering of features. In this paper, we propose to achieve this through the BasisVAE: a combination of the VAE and a probabilistic clustering prior, which lets us learn a one-hot basis function representation as part of the decoder network. Furthermore, for scenarios where not all features are aligned, we develop an extension to handle translation-invariant basis functions. We show how a collapsed variational inference scheme leads to scalable and efficient inference for BasisVAE, demonstrated on various toy examples as well as on single-cell gene expression data.

Bayesian inference for Factorial Hidden Markov Models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often restricted to exploration around localised regions that depend on initialisation. We introduce a general purpose ensemble Markov Chain Monte Carlo (MCMC) technique to improve on existing poorly mixing samplers. This is achieved by combining parallel tempering and an auxiliary variable scheme to exchange information between the chains in an efficient way. The latter exploits a genetic algorithm within an augmented Gibbs sampler. We compare our technique with various existing samplers in a simulation study as well as in a cancer genomics application, demonstrating the improvements obtained by our augmented ensemble approach.

The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this through a structured kernel decomposition in a hybrid Gaussian Process model which we call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We demonstrate the utility of our model on simulated examples and applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes. In each setting we show how the c-GPLVM can extract low-dimensional structures from high-dimensional data sets whilst allowing a breakdown of feature-level variability that is not present in other commonly used dimensionality reduction approaches.

Motivation: Pseudotime estimation from single-cell gene expression data allows the recovery of temporal information from otherwise static profiles of individual cells. Conventional pseudotime inference methods emphasize an unsupervised transcriptome-wide approach and use retrospective analysis to evaluate the behaviour of individual genes. However, the resulting trajectories can only be understood in terms of abstract geometric structures and not in terms of interpretable models of gene behaviour. Results: Here we introduce an orthogonal Bayesian approach termed 'Ouija' that learns pseudotimes from a small set of marker genes that might ordinarily be used to retrospectively confirm the accuracy of unsupervised pseudotime algorithms. Crucially, we model these genes in terms of switch-like or transient behaviour along the trajectory, allowing us to understand why the pseudotimes have been inferred and learn informative parameters about the behaviour of each gene. Since each gene is associated with a switch or peak time the genes are effectively ordered along with the cells, allowing each part of the trajectory to be understood in terms of the behaviour of certain genes. We demonstrate that this small panel of marker genes can recover pseudotimes that are consistent with those obtained using the entire transcriptome. Furthermore, we show that our method can detect differences in the regulation timings between two genes and identify 'metastable' states-discrete cell types along the continuous trajectories-that recapitulate known cell types. Availability and implementation: An open source implementation is available as an R package at http://www.github.com/kieranrcampbell/ouija and as a Python/TensorFlow package at http://www.github.com/kieranrcampbell/ouijaflow. Supplementary information: Supplementary data are available at Bioinformatics online.

Multivariate analysis of high-dimensional datasets with multiple categorical variables (e.g. surveys, questionnaires) is a challenging task but can reveal patterns of responses that are masked from univariate analyses. In this paper we propose a novel variational inference algorithm to cluster high-dimensional categorical observations into latent classes. Variational inference is an approximate Bayesian inference algorithm, which combines fast optimization methods with the ability to propagate the uncertainty to the clustering (soft clustering). The model is robust to misspecification of the number of latent classes and can infer a reasonable number from the data. We assess the performance on synthetic and real world data and show that our algorithm has similar performance to the best other tested method if the correct number of classes is known and outperforms the other methods if it the number of classes needs to be inferred. An R-package implementing our algorithm is available at the Comprehensive R Archive Network.

Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules Boolean algebra. Here, we present its first probabilistic treatment. We facilitate scalable sampling-based posterior inference by exploitation of the combinatorial structure of the factor conditionals. Maximum a posteriori estimates consistently outperform existing non-probabilistic approaches. We show that our performance gains can partially be explained by convergence to solutions that occupy relatively large regions of the parameter space, as well as by implicit model averaging. Moreover, the Bayesian treatment facilitates model selection with much greater accuracy than the previously suggested minimum description length based approach. We investigate three real-world data sets. First, temporal interaction networks and behavioural data of university students demonstrate the inference of instructive latent patterns. Next, we decompose a tensor with more than 10 Billion data points, indicating relations of gene expression in cancer patients. Not only does this demonstrate scalability, it also provides an entirely novel perspective on relational properties of continuous data and, in the present example, on the molecular heterogeneity of cancer. Our implementation is available on GitHub: https://github.com/TammoR/LogicalFactorisationMachines

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic generative model for Boolean matrix factorisation and derive a Metropolised Gibbs sampler that facilitates efficient parallel posterior inference. On real world and simulated data, our method outperforms all currently existing approaches for Boolean matrix factorisation and completion. This is the first method to provide full posterior inference for Boolean Matrix factorisation which is relevant in applications, e.g. for controlling false positive rates in collaborative filtering and, crucially, improves the interpretability of the inferred patterns. The proposed algorithm scales to large datasets as we demonstrate by analysing single cell gene expression data in 1.3 million mouse brain cells across 11 thousand genes on commodity hardware.

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that all possible differences between samples are of interest -- discovered differences can be due to different types of measurement noise, data collection artefacts or other irrelevant sources of variability. We propose distances between distributions which encode invariance to additive symmetric noise, aimed at testing whether the assumed true underlying processes differ. Moreover, we construct invariant features of distributions, leading to learning algorithms robust to the impairment of the input distributions with symmetric additive noise.

Motivation: Pseudotime analyses of single-cell RNA-seq data have become increasingly common. Typically, a latent trajectory corresponding to a biological process of interest-such as differentiation or cell cycle-is discovered. However, relatively little attention has been paid to modelling the differential expression of genes along such trajectories. Results: We present switchde , a statistical framework and accompanying R package for identifying switch-like differential expression of genes along pseudotemporal trajectories. Our method includes fast model fitting that provides interpretable parameter estimates corresponding to how quickly a gene is up or down regulated as well as where in the trajectory such regulation occurs. It also reports a P -value in favour of rejecting a constant-expression model for switch-like differential expression and optionally models the zero-inflation prevalent in single-cell data. Availability and Implementation: The R package switchde is available through the Bioconductor project at https://bioconductor.org/packages/switchde . Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: Advances in single cell genomics provide a way of routinely generating transcriptomics data at the single cell level. A frequent requirement of single cell expression analysis is the identification of novel patterns of heterogeneity across single cells that might explain complex cellular states or tissue composition. To date, classical statistical analysis tools have being routinely applied, but there is considerable scope for the development of novel statistical approaches that are better adapted to the challenges of inferring cellular hierarchies. RESULTS: We have developed a novel agglomerative clustering method that we call pcaReduce to generate a cell state hierarchy where each cluster branch is associated with a principal component of variation that can be used to differentiate two cell states. Using two real single cell datasets, we compared our approach to other commonly used statistical techniques, such as K-means and hierarchical clustering. We found that pcaReduce was able to give more consistent clustering structures when compared to broad and detailed cell type labels. CONCLUSIONS: Our novel integration of principal components analysis and hierarchical clustering establishes a connection between the representation of the expression data and the number of cell types that can be discovered. In doing so we found that pcaReduce performs better than either technique in isolation in terms of characterising putative cell states. Our methodology is complimentary to other single cell clustering techniques and adds to a growing palette of single cell bioinformatics tools for profiling heterogeneous cell populations.

Single cell gene expression profiling can be used to quantify transcriptional dynamics in temporal processes, such as cell differentiation, using computational methods to label each cell with a 'pseudotime' where true time series experimentation is too difficult to perform. However, owing to the high variability in gene expression between individual cells, there is an inherent uncertainty in the precise temporal ordering of the cells. Pre-existing methods for pseudotime estimation have predominantly given point estimates precluding a rigorous analysis of the implications of uncertainty. We use probabilistic modelling techniques to quantify pseudotime uncertainty and propagate this into downstream differential expression analysis. We demonstrate that reliance on a point estimate of pseudotime can lead to inflated false discovery rates and that probabilistic approaches provide greater robustness and measures of the temporal resolution that can be obtained from pseudotime inference.

Abstract Motivation: The identification of nucleosomes along the chromatin is key to understanding their role in the regulation of gene expression and other DNA-related processes. However, current experimental methods (MNase-ChIP, MNase-Seq) sample nucleosome positions from a cell population and contain biases, making thus the precise identification of individual nucleosomes not straightforward. Recent works have only focused on the first point, where noise reduction approaches have been developed to identify nucleosome positions. Results: In this article, we propose a new approach, termed NucleoFinder, that addresses both the positional heterogeneity across cells and experimental biases by seeking nucleosomes consistently positioned in a cell population and showing a significant enrichment relative to a control sample. Despite the absence of validated dataset, we show that our approach (i) detects fewer false positives than two other nucleosome calling methods and (ii) identifies two important features of the nucleosome organization (the nucleosome spacing downstream of active promoters and the enrichment/depletion of GC/AT dinucleotides at the centre of in vitro nucleosomes) with equal or greater ability than the other two methods. Availability: The R code of NucleoFinder, an example datafile and instructions are available for download from https://sites.google.com/site/beckerjeremie/ Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

SUMMARY: Recent major cancer genome sequencing studies have used whole-genome sequencing to detect various types of genomic variation. However, a number of these studies have continued to rely on SNP array information to provide additional results for copy number and loss-of-heterozygosity estimation and assessing tumour purity. OncoSNP-SEQ is a statistical model-based approach for inferring copy number profiles directly from high-coverage whole genome sequencing data that is able to account for unknown tumour purity and ploidy. AVAILABILITY: MATLAB code is available at the following URL: https://sites.google.com/site/oncosnpseq/.

UNLABELLED: Current genotyping algorithms typically call genotypes by clustering allele-specific intensity data on a single nucleotide polymorphism (SNP) by SNP basis. This approach assumes the availability of a large number of control samples that have been sampled on the same array and platform. We have developed a SNP genotyping algorithm for the Illumina Infinium SNP genotyping assay that is entirely within-sample and does not require the need for a population of control samples nor parameters derived from such a population. Our algorithm exhibits high concordance with current methods and >99% call accuracy on HapMap samples. The ability to call genotypes using only within-sample information makes the method computationally light and practical for studies involving small sample sizes and provides a valuable independent quality control metric for other population-based approaches. AVAILABILITY: http://www.stats.ox.ac.uk/~giannoul/GenoSNP/.