MOTIVATION: Networks underlie the generation and interpretation of many biological datasets: gene networks shed light on the regulatory structure of the genome, and cell networks can capture structure of the tumor micro-environment. However, most methods that learn such networks make the faulty "independence assumption"; to learn the gene network, they assume that no cell network exists. "Multi-axis" methods, which do not make this assumption, fail to scale beyond a few thousand cells or genes. This limits their applicability to only the smallest datasets. RESULTS: We develop a multi-axis method, which learns conditional dependency networks, capable of processing million-cell datasets within minutes. This was previously impossible, and unlocks the use of such methods on modern scRNA-seq datasets, as well as more complex datasets. We apply the method to a new scRNA-seq dataset for neuronal cell development, and compare the result to an existing state of the art method, hdWGCNA. We demonstrate that the new method yields gene networks that have a more focused biological interpretation and that the simultaneously learned cell network has advantages over a conventional kNN-based clustering. Further, our method yields novel biological insights by identifying long non-coding RNAs that potentially have a role in neuronal development. AVAILABILITY AND IMPLEMENTATION: Our methodology is available as a Python package GmGM on PyPI (https://pypi.org/project/GmGM/0.5.3/). The code for all experiments performed in this article is available on GitHub (https://github.com/BaileyAndrew/GmGM-Bioinformatics) and Zenodo (10.5281/zenodo.20384566).

The independence assumption between random variables is a useful tool to increase the tractability of a modelling framework. However, this assumption can be too simplistic; failing to take dependencies into account can cause models to fail dramatically. The field of multi-axis graphical modelling (also called multi-way modelling, Kronecker-separable modelling) has seen growth over the past decade, but these models require that the data have zero mean. In the multi-axis case, inference is typically done in the single sample scenario, making mean inference impossible. In this paper, we demonstrate how the zero-mean assumption can cause egregious modelling errors for Kronecker-sum-decomposable Gaussian graphical models, as well as propose a relaxation to the zero-mean assumption that allows the avoidance of such errors. Specifically, we propose the "Kronecker-sum-structured mean" assumption, which leads to models with nonconvex-but-unimodal log-likelihoods that can be solved efficiently with coordinate descent.

Multi-axis graphical modelling techniques allow us to perform network inference without making independence assumptions. This is done by replacing the independence assumption with a weaker assumption about the interaction between the axes; there are several choices for which assumption to use. In single-cell RNA sequencing data, genes may interact differently depending on whether they are expressed in the same cell, or in different cells. Unfortunately, current methods are not able to make this distinction. In this paper, we address this problem by introducing the strong product model for Gaussian graphical modelling.

Cases of laryngeal cancer are rising, with diagnosis often involving invasive biopsy procedures. An alternate approach is to identify high-risk patients by analysis of voice recordings which can alert clinical teams to those patients that need prioritisation. We propose a pipeline for evaluating speech classifier performance in the presence of noise. We perform experiments using the pipeline with several classifiers and denoising techniques. Random forest classifier performed best with an accuracy of 81.2% on clean data dropping to 63.8% when noise was added to recordings. The accuracy of all classifiers was reduced by added noise, signal denoising improved classifier accuracy but could not fully reverse the effects of noise. The effects of noise on classification is a complex issue which must be resolved for these detection systems to be implemented in clinical practice. We show that the proposed pipeline allows for the evaluation of classifier performance in the presence of noise.

Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters. However, for $n \approx p$ or $p > n$ such models are poorly determined. Kalaitzis et al. (2013) introduced the Bigraphical Lasso, an estimator for sparse precision matrices based on the Cartesian product of graphs. Unfortunately, the original Bigraphical Lasso algorithm is not applicable in case of large $p$ and $n$ due to memory requirements. We exploit eigenvalue decomposition of the Cartesian product graph to present a more efficient version of the algorithm which reduces memory requirements from $O(n^2p^2)$ to $O(n^2 +p^2)$. Many datasets in different application fields, such as biology, medicine and social science, come with count data, for which Gaussian based models are not applicable. Our multiway network inference approach can be used for discrete data. Our methodology accounts for the dependencies across both instances and features, reduces the computational complexity for high dimensional data and enables to deal with both discrete and continuous data. Numerical studies on both synthetic and real datasets are presented to showcase the performance of our method.

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.

SUMMARY: Elucidation of molecular targets of a compound [mode of action (MoA)] and its off-targets is a crucial step in drug development. We developed an online collaborative resource (MANTRA 2.0) that supports this process by exploiting similarities between drug-induced transcriptional profiles. Drugs are organized in a network of nodes (drugs) and edges (similarities) highlighting 'communities' of drugs sharing a similar MoA. A user can upload gene expression profiles before and after drug treatment in one or multiple cell types. An automated processing pipeline transforms the gene expression profiles into a unique drug 'node' embedded in the drug-network. Visual inspection of the neighbouring drugs and communities helps in revealing its MoA and to suggest new applications of known drugs (drug repurposing). MANTRA 2.0 allows storing and sharing user-generated network nodes, thus making MANTRA 2.0 a collaborative ever-growing resource. AVAILABILITY AND IMPLEMENTATION: The web tool is freely available for academic use at http://mantra.tigem.it.

BACKGROUND: Gene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient. RESULTS: The software package BATS (Bayesian Analysis of Time Series) presented here implements the methodology described above. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles when at least 5-6 time points are available. The package has a user-friendly interface. BATS successfully manages various technical difficulties which arise in time-course microarray experiments, such as a small number of observations, non-uniform sampling intervals and replicated or missing data. CONCLUSION: BATS is a free user-friendly software for the analysis of both simulated and real microarray time course experiments. The software, the user manual and a brief illustrative example are freely available online at the BATS website: http://www.na.iac.cnr.it/bats.