Deep learning and MCMC with aggVAE for shifting administrative boundaries: mapping malaria prevalence in Kenya

Model-based disease mapping remains a fundamental policy-informing tool in public health and disease surveillance with hierarchical Bayesian models being the current state-of-the-art approach. When working with areal data, e.g. aggregates at the administrative unit level such as district or province, routinely used models rely on the adjacency structure of areal units to account for spatial correlations. The goal of disease surveillance systems is to track disease outcomes over time, but this provides challenging in situations of crises, such as political changes, leading to changes of administrative boundaries. Kenya is an example of such country. Moreover, adjacency-based approach ignores the continuous nature of spatial processes and cannot solve the change-of-support problem, i.e. when administrative boundaries change. We present a novel, practical, and easy to implement solution relying on a methodology combining deep generative modelling and fully Bayesian inference. We build on the recent work of PriorVAE able to encode spatial priors over small areas with variational autoencoders, to map malaria prevalence in Kenya. We solve the change-of-support problem arising from Kenya changing its district boundaries in 2010. We draw realisations of the Gaussian Process (GP) prior over a fine artificial spatial grid representing continuous space and then aggregate these realisations to the level of administrative boundaries. The aggregated values are then encoded using the PriorVAE technique. The trained priors (aggVAE) are then used at the inference stage instead of the GP priors within a Markov chain Monte Carlo (MCMC) scheme. We demonstrate that it is possible to use the flexible and appropriate model for areal data based on aggregation of continuous priors, and that inference is orders of magnitude faster when using aggVAE than combining the original GP priors and the aggregation step.

PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling

In applied fields where the speed of inference and model flexibility are crucial, the use of Bayesian inference for models with a stochastic process as their prior, e.g. Gaussian processes (GPs) is ubiquitous. Recent literature has demonstrated that the computational bottleneck caused by GP priors or their finite realizations can be encoded using deep generative models such as variational autoencoders (VAEs), and the learned generators can then be used instead of the original priors during Markov chain Monte Carlo (MCMC) inference in a drop-in manner. While this approach enables fast and highly efficient inference, it loses information about the stochastic process hyperparameters, and, as a consequence, makes inference over hyperparameters impossible and the learned priors indistinct. We propose to resolve this issue and disentangle the learned priors by conditioning the VAE on stochastic process hyperparameters. This way, the hyperparameters are encoded alongside GP realisations and can be explicitly estimated at the inference stage. We believe that the new method, termed PriorCVAE, will be a useful tool among approximate inference approaches and has the potential to have a large impact on spatial and spatiotemporal inference in crucial real-life applications. Code showcasing PriorCVAE can be found on GitHub: https://github.com/elizavetasemenova/PriorCVAE

City-Wide Perceptions of Neighbourhood Quality using Street View Images

The interactions of individuals with city neighbourhoods is determined, in part, by the perceived quality of urban environments. Perceived neighbourhood quality is a core component of urban vitality, influencing social cohesion, sense of community, safety, activity and mental health of residents. Large-scale assessment of perceptions of neighbourhood quality was pioneered by the Place Pulse projects. Researchers demonstrated the efficacy of crowd-sourcing perception ratings of image pairs across 56 cities and training a model to predict perceptions from street-view images. Variation across cities may limit Place Pulse's usefulness for assessing within-city perceptions. In this paper, we set forth a protocol for city-specific dataset collection for the perception: 'On which street would you prefer to walk?'. This paper describes our methodology, based in London, including collection of images and ratings, web development, model training and mapping. Assessment of within-city perceptions of neighbourhoods can identify inequities, inform planning priorities, and identify temporal dynamics. Code available: https://emilymuller1991.github.io/urban-perceptions/.

Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees

As Gaussian processes mature, they are increasingly being deployed as part of larger machine learning and decision-making systems, for instance in geospatial modeling, Bayesian optimization, or in latent Gaussian models. Within a system, the Gaussian process model needs to perform in a stable and reliable manner to ensure it interacts correctly with other parts the system. In this work, we study the numerical stability of scalable sparse approximations based on inducing points. We derive sufficient and in certain cases necessary conditions on the inducing points for the computations performed to be numerically stable. For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions. This is done via a modification of the cover tree data structure, which is of independent interest. We additionally propose an alternative sparse approximation for regression with a Gaussian likelihood which trades off a small amount of performance to further improve stability. We evaluate the proposed techniques on a number of examples, showing that, in geospatial settings, sparse approximations with guaranteed numerical stability often perform comparably to those without.

Seq2Seq Surrogates of Epidemic Models to Facilitate Bayesian Inference

Epidemic models are powerful tools in understanding infectious disease. However, as they increase in size and complexity, they can quickly become computationally intractable. Recent progress in modelling methodology has shown that surrogate models can be used to emulate complex epidemic models with a high-dimensional parameter space. We show that deep sequence-to-sequence (seq2seq) models can serve as accurate surrogates for complex epidemic models with sequence based model parameters, effectively replicating seasonal and long-term transmission dynamics. Once trained, our surrogate can predict scenarios a several thousand times faster than the original model, making them ideal for policy exploration. We demonstrate that replacing a traditional epidemic model with a learned simulator facilitates robust Bayesian inference.

PCACE: A Statistical Approach to Ranking Neurons for CNN Interpretability

In this paper we introduce a new problem within the growing literature of interpretability for convolution neural networks (CNNs). While previous work has focused on the question of how to visually interpret CNNs, we ask what it is that we care to interpret, that is, which layers and neurons are worth our attention? Due to the vast size of modern deep learning network architectures, automated, quantitative methods are needed to rank the relative importance of neurons so as to provide an answer to this question. We present a new statistical method for ranking the hidden neurons in any convolutional layer of a network. We define importance as the maximal correlation between the activation maps and the class score. We provide different ways in which this method can be used for visualization purposes with MNIST and ImageNet, and show a real-world application of our method to air pollution prediction with street-level images.

Encoding spatiotemporal priors with VAEs for small-area estimation

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatiotemporal statistical modelling. In this context they are used to encode correlation structures over space and time and can generalise well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge: for a particular spatiotemporal setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatiotemporal inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatiotemporal priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two stage approach on Bayesian, small-area estimation tasks.

Gaussian Process Nowcasting: Application to COVID-19 Mortality Reporting

Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields. An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty? Without this correction, raw data will often mislead by suggesting an improving situation. We present a flexible approach using a latent Gaussian process that is capable of describing the changing auto-correlation structure present in the reporting time-delay surface. This approach also yields robust estimates of uncertainty for the estimated nowcasted numbers of deaths. We test assumptions in model specification such as the choice of kernel or hyper priors, and evaluate model performance on a challenging real dataset from Brazil. Our experiments show that Gaussian process nowcasting performs favourably against both comparable methods, and a small sample of expert human predictions. Our approach has substantial practical utility in disease modelling -- by applying our approach to COVID-19 mortality data from Brazil, where reporting delays are large, we can make informative predictions on important epidemiological quantities such as the current effective reproduction number.

Simulating normalising constants with referenced thermodynamic integration: application to COVID-19 model selection

Model selection is a fundamental part of Bayesian statistical inference; a widely used tool in the field of epidemiology. Simple methods such as Akaike Information Criterion are commonly used but they do not incorporate the uncertainty of the model's parameters, which can give misleading choices when comparing models with similar fit to the data. One approach to model selection in a more rigorous way that uses the full posterior distributions of the models is to compute the ratio of the normalising constants (or model evidence), known as Bayes factors. These normalising constants integrate the posterior distribution over all parameters and balance over and under fitting. However, normalising constants often come in the form of intractable, high-dimensional integrals, therefore special probabilistic techniques need to be applied to correctly estimate the Bayes factors. One such method is thermodynamic integration (TI), which can be used to estimate the ratio of two models' evidence by integrating over a continuous path between the two un-normalised densities. In this paper we introduce a variation of the TI method, here referred to as referenced TI, which computes a single model's evidence in an efficient way by using a reference density such as a multivariate normal - where the normalising constant is known. We show that referenced TI, an asymptotically exact Monte Carlo method of calculating the normalising constant of a single model, in practice converges to the correct result much faster than other competing approaches such as the method of power posteriors. We illustrate the implementation of the algorithm on informative 1- and 2-dimensional examples, and apply it to a popular linear regression problem, and use it to select parameters for a model of the COVID-19 epidemic in South Korea.

Improving axial resolution in SIM using deep learning

Structured Illumination Microscopy is a widespread methodology to image live and fixed biological structures smaller than the diffraction limits of conventional optical microscopy. Using recent advances in image up-scaling through deep learning models, we demonstrate a method to reconstruct 3D SIM image stacks with twice the axial resolution attainable through conventional SIM reconstructions. We further evaluate our method for robustness to noise & generalisability to varying observed specimens, and discuss potential adaptions of the method to further improvements in resolution.