Gaussian Process (GP) models are a class of flexible non-parametric models that have rich representational power. By using a Gaussian process with additive structure, complex responses can be modelled whilst retaining interpretability. Previous work showed that additive Gaussian process models require high-dimensional interaction terms. We propose the orthogonal additive kernel (OAK), which imposes an orthogonality constraint on the additive functions, enabling an identifiable, low-dimensional representation of the functional relationship. We connect the OAK kernel to functional ANOVA decomposition, and show improved convergence rates for sparse computation methods. With only a small number of additive low-dimensional terms, we demonstrate the OAK model achieves similar or better predictive performance compared to black-box models, while retaining interpretability.

In the univariate setting, using the kernel spectral representation is an appealing approach for generating stationary covariance functions. However, performing the same task for multiple-output Gaussian processes is substantially more challenging. We demonstrate that current approaches to modelling cross-covariances with a spectral mixture kernel possess a critical blind spot. Pairs of highly correlated (or highly anti-correlated) processes are not reproducible, aside from the special case when their spectral densities are of identical shape. We present a solution to this issue by replacing the conventional Gaussian components of a spectral mixture with block components of finite bandwidth (i.e. rectangular step functions). The proposed family of kernel represents the first multi-output generalisation of the spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.

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.

Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and highly flexible model. We focus on alternative mixtures of GP experts, which model the joint distribution of the inputs and targets explicitly. We highlight issues of this approach in multi-dimensional input spaces, namely, poor scalability and the need for an unnecessarily large number of experts, degrading the predictive performance and increasing uncertainty. We construct a novel model to address these issues through a nested partitioning scheme that automatically infers the number of components at both levels. Multiple response types are accommodated through a generalised GP framework, while multiple input types are included through a factorised exponential family structure. We show the effectiveness of our approach in estimating a parsimonious probabilistic description of both synthetic data of increasing dimension and an Alzheimer’s challenge dataset.

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.

We consider the problem of adaptively placing sensors along an interval to detect stochastically-generated events. We present a new formulation of the problem as a continuum-armed bandit problem with feedback in the form of partial observations of realisations of an inhomogeneous Poisson process. We design a solution method by combining Thompson sampling with nonparametric inference via increasingly granular Bayesian histograms and derive an $\tilde{O}(T^{2/3})$ bound on the Bayesian regret in $T$ rounds. This is coupled with the design of an efficent optimisation approach to select actions in polynomial time. In simulations we demonstrate our approach to have substantially lower and less variable regret than competitor algorithms.

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.

GPflow is a Gaussian process library that uses TensorFlow for its core computations and Python for its front end. The distinguishing features of GPflow are that it uses variational inference as the primary approximation method, provides concise code through the use of automatic differentiation, has been engineered with a particular emphasis on software testing and is able to exploit GPU hardware.

Passive infrared sensors have widespread use in many applications, including motion detectors for alarms, lighting systems and hand dryers. Combinations of multiple PIR sensors have also been used to count the number of humans passing through doorways. In this paper, we demonstrate the potential of the PIR sensor as a tool for occupancy estimation inside of a monitored environment. Our approach shows how flexible nonparametric machine learning algorithms extract useful information about the occupancy from a single PIR sensor. The approach allows us to understand and make use of the motion patterns generated by people within the monitored environment. The proposed counting system uses information about those patterns to provide an accurate estimate of room occupancy which can be updated every 30 seconds. The system was successfully tested on data from more than 50 real office meetings consisting of at most 14 room occupants.

Calibration of stochastic traffic microsimulation models is a challenging task. This paper proposes a fast iterative probabilistic precalibration framework and demonstrates how it can be successfully applied to a real-world traffic simulation model of a section of the M40 motorway and its surrounding area in the U.K. The efficiency of the method stems from the use of emulators of the stochastic microsimulator, which provides fast surrogates of the traffic model. The use of emulators minimizes the number of microsimulator runs required, and the emulators' probabilistic construction allows for the consideration of the extra uncertainty introduced by the approximation. It is shown that automatic precalibration of this real-world microsimulator, using turn-count observational data, is possible, considering all parameters at once, and that this precalibrated microsimulator improves on the fit to observations compared with the traditional expertly tuned microsimulation.