Seth Flaxman

Emily Muller, Emily Gemmell, Ishmam Choudhury et al.

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/.

Makkunda Sharma, Fan Yang, Duy-Nhat Vo et al.

Satellite imagery has emerged as an important tool to analyse demographic, health, and development indicators. While various deep learning models have been built for these tasks, each is specific to a particular problem, with few standard benchmarks available. We propose a new dataset pairing satellite imagery and high-quality survey data on child poverty to benchmark satellite feature representations. Our dataset consists of 33,608 images, each 10 km $\times$ 10 km, from 19 countries in Eastern and Southern Africa in the time period 1997-2022. As defined by UNICEF, multidimensional child poverty covers six dimensions and it can be calculated from the face-to-face Demographic and Health Surveys (DHS) Program . As part of the benchmark, we test spatial as well as temporal generalization, by testing on unseen locations, and on data after the training years. Using our dataset we benchmark multiple models, from low-level satellite imagery models such as MOSAIKS , to deep learning foundation models, which include both generic vision models such as Self-Distillation with no Labels (DINOv2) models and specific satellite imagery models such as SatMAE. We provide open source code for building the satellite dataset, obtaining ground truth data from DHS and running various models assessed in our work.

Elizaveta Semenova, Prakhar Verma, Max Cairney-Leeming et al. · oxford

Recent advances have shown that GP priors, or their finite realisations, can be encoded using deep generative models such as variational autoencoders (VAEs). These learned generators can serve as drop-in replacements for the original priors during MCMC inference. While this approach enables efficient inference, it loses information about the hyperparameters of the original models, and consequently makes inference over hyperparameters impossible and the learned priors indistinct. To overcome this limitation, we condition the VAE on stochastic process hyperparameters. This allows the joint encoding of hyperparameters with GP realizations and their subsequent estimation during inference. Further, we demonstrate that our proposed method, PriorCVAE, is agnostic to the nature of the models which it approximates, and can be used, for instance, to encode solutions of ODEs. It provides a practical tool for approximate inference and shows potential in real-life spatial and spatiotemporal applications.

Xenia Miscouridou, Samir Bhatt, George Mohler et al.

Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events. Here we develop a new class of spatiotemporal Hawkes processes that can capture both triggering and clustering behavior and we provide an efficient method for performing inference. We use a log-Gaussian Cox process (LGCP) as prior for the background rate of the Hawkes process which gives arbitrary flexibility to capture a wide range of underlying background effects (for infectious diseases these are called endemic effects). The Hawkes process and LGCP are computationally expensive due to the former having a likelihood with quadratic complexity in the number of observations and the latter involving inversion of the precision matrix which is cubic in observations. Here we propose a novel approach to perform MCMC sampling for our Hawkes process with LGCP background, using pre-trained Gaussian Process generators which provide direct and cheap access to samples during inference. We show the efficacy and flexibility of our approach in experiments on simulated data and use our methods to uncover the trends in a dataset of reported crimes in the US.

Giovanni Charles, Timothy M. Wolock, Peter Winskill et al.

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.

Alexander Terenin, David R. Burt, Artem Artemev et al.

Gaussian processes are frequently 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 of the system. In this work, we study the numerical stability of scalable sparse approximations based on inducing points. To do so, we first review numerical stability, and illustrate typical situations in which Gaussian process models can be unstable. Building on stability theory originally developed in the interpolation literature, 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 provide illustrative examples showing the relationship between stability of calculations and predictive performance of inducing point methods on spatial tasks.

Giovanni Charles, Cosmo Santoni, Seth Flaxman et al.

The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site neural surrogate of the simulator and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.

Daniel Jenson, Jhonathan Navott, Mengyan Zhang et al. · oxford

Neural Processes (NPs) are a rapidly evolving class of models designed to directly model the posterior predictive distribution of stochastic processes. Originally developed as a scalable alternative to Gaussian Processes (GPs), which are limited by $O(n^3)$ runtime complexity, the most accurate modern NPs can often rival GPs but still suffer from an $O(n^2)$ bottleneck due to their attention mechanism. We introduce the Transformer Neural Process - Kernel Regression (TNP-KR), a scalable NP featuring: (1) a Kernel Regression Block (KRBlock), a simple, extensible, and parameter efficient transformer block with complexity $O(n_c^2 + n_c n_t)$, where $n_c$ and $n_t$ are the number of context and test points, respectively; (2) a kernel-based attention bias; and (3) two novel attention mechanisms: scan attention (SA), a memory-efficient scan-based attention that when paired with a kernel-based bias can make TNP-KR translation invariant, and deep kernel attention (DKA), a Performer-style attention that implicitly incoporates a distance bias and further reduces complexity to $O(n_c)$. These enhancements enable both TNP-KR variants to perform inference with 100K context points on over 1M test points in under a minute on a single 24GB GPU. On benchmarks spanning meta regression, Bayesian optimization, image completion, and epidemiology, TNP-KR with DKA outperforms its Performer counterpart on nearly every benchmark, while TNP-KR with SA achieves state-of-the-art results.

Daniel Jenson, Jhonathan Navott, Piotr Grynfelder et al. · oxford

Neural Processes (NPs) are a rapidly evolving class of models designed to directly model the posterior predictive distribution of stochastic processes. While early architectures were developed primarily as a scalable alternative to Gaussian Processes (GPs), modern NPs tackle far more complex and data hungry applications spanning geology, epidemiology, climate, and robotics. These applications have placed increasing pressure on the scalability of these models, with many architectures compromising accuracy for scalability. In this paper, we demonstrate that this tradeoff is often unnecessary, particularly when modeling fully or partially translation invariant processes. We propose a versatile new architecture, the Biased Scan Attention Transformer Neural Process (BSA-TNP), which introduces Kernel Regression Blocks (KRBlocks), group-invariant attention biases, and memory-efficient Biased Scan Attention (BSA). BSA-TNP is able to: (1) match or exceed the accuracy of the best models while often training in a fraction of the time, (2) exhibit translation invariance, enabling learning at multiple resolutions simultaneously, (3) transparently model processes that evolve in both space and time, (4) support high dimensional fixed effects, and (5) scale gracefully -- running inference with over 1M test points with 100K context points in under a minute on a single 24GB GPU.

Siyi Sun, David Antony Selby, Yunchuan Huang et al.

Missing data imputation in tabular datasets remains a pivotal challenge in data science and machine learning, particularly within socioeconomic research. However, real-world socioeconomic datasets are typically subject to strict data protection protocols, which often prohibit public sharing, even for synthetic derivatives. This severely limits the reproducibility and accessibility of benchmark studies in such settings. Further, there are very few publicly available synthetic datasets. Thus, there is limited availability of benchmarks for systematic evaluation of imputation methods on socioeconomic datasets, whether real or synthetic. In this study, we utilize the World Bank's publicly available synthetic dataset, Synthetic Data for an Imaginary Country, which closely mimics a real World Bank household survey while being fully public, enabling broad access for methodological research. With this as a starting point, we derived the IMAGIC-500 dataset: we select a subset of 500k individuals across approximately 100k households with 19 socioeconomic features, designed to reflect the hierarchical structure of real-world household surveys. This paper introduces a comprehensive missing data imputation benchmark on IMAGIC-500 under various missing mechanisms (MCAR, MAR, MNAR) and missingness ratios (10\%, 20\%, 30\%, 40\%, 50\%). Our evaluation considers the imputation accuracy for continuous and categorical variables, computational efficiency, and impact on downstream predictive tasks, such as estimating educational attainment at the individual level. The results highlight the strengths and weaknesses of statistical, traditional machine learning, and deep learning imputation techniques, including recent diffusion-based methods. The IMAGIC-500 dataset and benchmark aim to facilitate the development of robust imputation algorithms and foster reproducible social science research.

Jhonathan Navott, Daniel Jenson, Seth Flaxman et al. · oxford

Gaussian Processes (GPs) provide a flexible and statistically principled foundation for modelling spatiotemporal phenomena, but their $O(N^3)$ scaling makes them intractable for large datasets. Approximate methods such as variational inference (VI), inducing points (sparse GPs), low-rank factorizations (RFFs), local factorizations and approximations (INLA), improve scalability but trade off accuracy or flexibility. We introduce DeepRV, a neural-network surrogate that closely matches full GP accuracy including hyperparameter estimates, while reducing computational complexity to $O(N^2)$, increasing scalability and inference speed. DeepRV serves as a drop-in replacement for GP prior realisations in e.g. MCMC-based probabilistic programming pipelines, preserving full model flexibility. Across simulated benchmarks, non-separable spatiotemporal GPs, and a real-world application to education deprivation in London (n = 4,994 locations), DeepRV achieves the highest fidelity to exact GPs while substantially accelerating inference. Code is provided in the accompanying ZIP archive, with all experiments run on a single consumer-grade GPU to ensure accessibility for practitioners.

Mengyan Zhang, Shahine Bouabid, Cheng Soon Ong et al.

We develop the framework of Indirect Query Bayesian Optimization (IQBO), a new class of Bayesian optimization problems where the integrated feedback is given via a conditional expectation of the unknown function $f$ to be optimized. The underlying conditional distribution can be unknown and learned from data. The goal is to find the global optimum of $f$ by adaptively querying and observing in the space transformed by the conditional distribution. This is motivated by real-world applications where one cannot access direct feedback due to privacy, hardware or computational constraints. We propose the Conditional Max-Value Entropy Search (CMES) acquisition function to address this novel setting, and propose a hierarchical search algorithm with multi-resolution feedback to improve computational efficiency. We show regret bounds for our proposed methods and demonstrate the effectiveness of our approaches on simulated optimization tasks.

Fan Yang, Sahoko Ishida, Mengyan Zhang et al.

Remote sensing imagery offers rich spectral data across extensive areas for Earth observation. Many attempts have been made to leverage these data with transfer learning to develop scalable alternatives for estimating socio-economic conditions, reducing reliance on expensive survey-collected data. However, much of this research has primarily focused on daytime satellite imagery due to the limitation that most pre-trained models are trained on 3-band RGB images. Consequently, modeling techniques for spectral bands beyond the visible spectrum have not been thoroughly investigated. Additionally, quantifying uncertainty in remote sensing regression has been less explored, yet it is essential for more informed targeting and iterative collection of ground truth survey data. In this paper, we introduce a novel framework that leverages generic foundational vision models to process remote sensing imagery using combinations of three spectral bands to exploit multi-spectral data. We also employ methods such as heteroscedastic regression and Bayesian modeling to generate uncertainty estimates for the predictions. Experimental results demonstrate that our method outperforms existing models that use RGB or multi-spectral models with unstructured band usage. Moreover, our framework helps identify uncertain predictions, guiding future ground truth data acquisition.

Sumantrak Mukherjee, Mengyan Zhang, Seth Flaxman et al.

We study the problem of globally optimising a target variable of an unknown causal graph on which a sequence of soft or hard interventions can be performed. The problem of optimising the target variable associated with a causal graph is formalised as Causal Bayesian Optimisation (CBO). We study the CBO problem under the cumulative regret objective with unknown causal graphs for two settings, namely structural causal models with hard interventions and function networks with soft interventions. We propose Graph Agnostic Causal Bayesian Optimisation (GACBO), an algorithm that actively discovers the causal structure that contributes to achieving optimal rewards. GACBO seeks to balance exploiting the actions that give the best rewards against exploring the causal structures and functions. To the best of our knowledge, our work is the first to study causal Bayesian optimization with cumulative regret objectives in scenarios where the graph is unknown or partially known. We show our proposed algorithm outperforms baselines in simulated experiments and real-world applications.

Elizaveta Semenova, Swapnil Mishra, Samir Bhatt et al.

Model-based disease mapping remains a fundamental policy-informing tool in the fields of public health and disease surveillance. Hierarchical Bayesian models have emerged as the state-of-the-art approach for disease mapping since they are able to both capture structure in the data and robustly characterise uncertainty. When working with areal data, e.g.~aggregates at the administrative unit level such as district or province, current models rely on the adjacency structure of areal units to account for spatial correlations and perform shrinkage. The goal of disease surveillance systems is to track disease outcomes over time. This task is especially challenging in crisis situations which often lead to redrawn administrative boundaries, meaning that data collected before and after the crisis are no longer directly comparable. Moreover, the adjacency-based approach ignores the continuous nature of spatial processes and cannot solve the change-of-support problem, i.e.~when estimates are required to be produced at different administrative levels or levels of aggregation. We present a novel, practical, and easy to implement solution to solve these problems relying on a methodology combining deep generative modelling and fully Bayesian inference: we build on the recently proposed PriorVAE method able to encode spatial priors over small areas with variational autoencoders by encoding aggregates over administrative units. We map malaria prevalence in Kenya, a country in which administrative boundaries changed in 2010.

Sílvia Casacuberta, Esra Suel, Seth Flaxman

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.

Elizaveta Semenova, Yidan Xu, Adam Howes et al.

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context they are used to encode correlation structures over space 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, termed PriorVAE: for a particular spatial 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 spatial 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 spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two stage approach on Bayesian, small-area estimation tasks.

Iwona Hawryluk, Henrique Hoeltgebaum, Swapnil Mishra et al.

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 against 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.

Iwona Hawryluk, Swapnil Mishra, Seth Flaxman et al.

Model selection is a fundamental part of the applied Bayesian statistical methodology. Metrics such as the Akaike Information Criterion are commonly used in practice to select models but do not incorporate the uncertainty of the models' parameters and can give misleading choices. One approach that uses the full posterior distribution is to compute the ratio of two models' normalising constants, known as the Bayes factor. Often in realistic problems, this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a variation of the TI method, referred to as referenced TI, which computes a single model's normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with explicit pedagogical 1 and 2D examples. Benchmarking is presented with comparable methods and we find favourable convergence performance. The approach is shown to be useful in practice when applied to a real problem - to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.

Miguel Boland, Edward A. K. Cohen, Seth Flaxman et al.

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.

Michaela A. C. Vollmer, Ben Glampson, Thomas A. Mellan et al.

There were 25.6 million attendances at Emergency Departments (EDs) in England in 2019 corresponding to an increase of 12 million attendances over the past ten years. The steadily rising demand at EDs creates a constant challenge to provide adequate quality of care while maintaining standards and productivity. Managing hospital demand effectively requires an adequate knowledge of the future rate of admission. Using 8 years of electronic admissions data from two major acute care hospitals in London, we develop a novel ensemble methodology that combines the outcomes of the best performing time series and machine learning approaches in order to make highly accurate forecasts of demand, 1, 3 and 7 days in the future. Both hospitals face an average daily demand of 208 and 106 attendances respectively and experience considerable volatility around this mean. However, our approach is able to predict attendances at these emergency departments one day in advance up to a mean absolute error of +/- 14 and +/- 10 patients corresponding to a mean absolute percentage error of 6.8% and 8.6% respectively. Our analysis compares machine learning algorithms to more traditional linear models. We find that linear models often outperform machine learning methods and that the quality of our predictions for any of the forecasting horizons of 1, 3 or 7 days are comparable as measured in MAE. In addition to comparing and combining state-of-the-art forecasting methods to predict hospital demand, we consider two different hyperparameter tuning methods, enabling a faster deployment of our models without compromising performance. We believe our framework can readily be used to forecast a wide range of policy relevant indicators.

Harrison Zhu, Xing Liu, Ruya Kang et al.

Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand. As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting very high-dimensional or non-smooth target functions. This paper proposes to tackle this issue with a new Bayesian numerical integration algorithm based on Bayesian Additive Regression Trees (BART) priors, which we call BART-Int. BART priors are easy to tune and well-suited for discontinuous functions. We demonstrate that they also lend themselves naturally to a sequential design setting and that explicit convergence rates can be obtained in a variety of settings. The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.

Stamatina Lamprinakou, Mauricio Barahona, Seth Flaxman et al.

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson processes is introduced. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. The new approach enables full posterior inference of the intensity in a non-parametric regression setting. The performance of the novel scheme is demonstrated through simulation studies on synthetic and real datasets up to five dimensions, and the new scheme is compared with alternative approaches.

Swapnil Mishra, Seth Flaxman, Tresnia Berah et al.

Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($π$VAE). The $π$VAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use $π$VAE to learn low dimensional embeddings of function classes. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process). For popular tasks, such as spatial interpolation, $π$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate that the low dimensional independently distributed latent space representation learnt provides an elegant and scalable means of performing Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.

Edoardo Lisi, Mohammad Malekzadeh, Hamed Haddadi et al.

Conditional Generative Adversarial Networks~(CGAN) are a recent and popular method for generating samples from a probability distribution conditioned on latent information. The latent information often comes in the form of a discrete label from a small set. We propose a novel method for training CGANs which allows us to condition on a sequence of continuous latent distributions $f^{(1)}, \ldots, f^{(K)}$. This training allows CGANs to generate samples from a sequence of distributions. We apply our method to paintings from a sequence of artistic movements, where each movement is considered to be its own distribution. Exploiting the temporal aspect of the data, a vector autoregressive (VAR) model is fitted to the means of the latent distributions that we learn, and used for one-step-ahead forecasting, to predict the latent distribution of a future art movement $f^{(K+1)}$. Realisations from this distribution can be used by the CGAN to generate "future" paintings. In experiments, this novel methodology generates accurate predictions of the evolution of art. The training set consists of a large dataset of past paintings. While there is no agreement on exactly what current art period we find ourselves in, we test on plausible candidate sets of present art, and show that the mean distance to our predictions is small.

Jonathan Ish-Horowicz, Dana Udwin, Seth Flaxman et al.

While the success of deep neural networks (DNNs) is well-established across a variety of domains, our ability to explain and interpret these methods is limited. Unlike previously proposed local methods which try to explain particular classification decisions, we focus on global interpretability and ask a universally applicable question: given a trained model, which features are the most important? In the context of neural networks, a feature is rarely important on its own, so our strategy is specifically designed to leverage partial covariance structures and incorporate variable dependence into feature ranking. Our methodological contributions in this paper are two-fold. First, we propose an effect size analogue for DNNs that is appropriate for applications with highly collinear predictors (ubiquitous in computer vision). Second, we extend the recently proposed "RelATive cEntrality" (RATE) measure (Crawford et al., 2019) to the Bayesian deep learning setting. RATE applies an information theoretic criterion to the posterior distribution of effect sizes to assess feature significance. We apply our framework to three broad application areas: computer vision, natural language processing, and social science.

Anthony Hu, Seth Flaxman

We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.

Ho Chung Leon Law, Dino Sejdinovic, Ewan Cameron et al.

While a typical supervised learning framework assumes that the inputs and the outputs are measured at the same levels of granularity, many applications, including global mapping of disease, only have access to outputs at a much coarser level than that of the inputs. Aggregation of outputs makes generalization to new inputs much more difficult. We consider an approach to this problem based on variational learning with a model of output aggregation and Gaussian processes, where aggregation leads to intractability of the standard evidence lower bounds. We propose new bounds and tractable approximations, leading to improved prediction accuracy and scalability to large datasets, while explicitly taking uncertainty into account. We develop a framework which extends to several types of likelihoods, including the Poisson model for aggregated count data. We apply our framework to a challenging and important problem, the fine-scale spatial modelling of malaria incidence, with over 1 million observations.

Seth Flaxman, Michael Chirico, Pau Pereira et al.

We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian processes with autoregressive smoothing kernels in a regularized supervised learning framework. While the smoothing kernels capture the two main approaches in current use in the field of crime forecasting, kernel density estimation (KDE) and self-exciting point process (SEPP) models, the RKHS component of the model can be understood as an approximation to the popular log-Gaussian Cox Process model. For inference, we discretize the spatiotemporal point pattern and learn a log-intensity function using the Poisson likelihood and highly efficient gradient-based optimization methods. Model hyperparameters including quality of RKHS approximation, spatial and temporal kernel lengthscales, number of autoregressive lags, bandwidths for smoothing kernels, as well as cell shape, size, and rotation, were learned using crossvalidation. Resulting predictions significantly exceeded baseline KDE estimates and SEPP models for sparse events.

Jean-Francois Ton, Seth Flaxman, Dino Sejdinovic et al.

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order interactions. However, until recently, there has been a strong reliance on a limited class of stationary kernels such as the Matern or squared exponential, limiting the expressiveness of these modelling approaches. Recent machine learning research has focused on spectral representations to model arbitrary stationary kernels and introduced more general representations that include classes of nonstationary kernels. In this paper, we exploit the connections between Fourier feature representations, Gaussian processes and neural networks to generalise previous approaches and develop a simple and efficient framework to learn arbitrarily complex nonstationary kernel functions directly from the data, while taking care to avoid overfitting using state-of-the-art methods from deep learning. We highlight the very broad array of kernel classes that could be created within this framework. We apply this to a time series dataset and a remote sensing problem involving land surface temperature in Eastern Africa. We show that without increasing the computational or storage complexity, nonstationary kernels can be used to improve generalisation performance and provide more interpretable results.

Ho Chung Leon Law, Danica J. Sutherland, Dino Sejdinovic et al.

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the groups. This effectively assumes that small and large groups are estimated equally well, and should have equal weight in the final regression. We account for this uncertainty with a Bayesian distribution regression formalism, improving the robustness and performance of the model when group sizes vary. We frame our models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. We demonstrate our approach on illustrative toy datasets, as well as on a challenging problem of predicting age from images.

Seth Flaxman, Danica J. Sutherland, Yu-Xiang Wang et al.

We combine fine-grained spatially referenced census data with the vote outcomes from the 2016 US presidential election. Using this dataset, we perform ecological inference using distribution regression (Flaxman et al, KDD 2015) with a multinomial-logit regression so as to model the vote outcome Trump, Clinton, Other / Didn't vote as a function of demographic and socioeconomic features. Ecological inference allows us to estimate "exit poll" style results like what was Trump's support among white women, but for entirely novel categories. We also perform exploratory data analysis to understand which census variables are predictive of voting for Trump, voting for Clinton, or not voting for either. All of our methods are implemented in Python and R, and are available online for replication.

Seth Flaxman, Yee Whye Teh, Dino Sejdinovic

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space. In this paper we develop a new, computationally tractable Reproducing Kernel Hilbert Space (RKHS) formulation for the inhomogeneous Poisson process. We model the square root of the intensity as an RKHS function. Whereas RKHS models used in supervised learning rely on the so-called representer theorem, the form of the inhomogeneous Poisson process likelihood means that the representer theorem does not apply. However, we prove that the representer theorem does hold in an appropriately transformed RKHS, guaranteeing that the optimization of the penalized likelihood can be cast as a tractable finite-dimensional problem. The resulting approach is simple to implement, and readily scales to high dimensions and large-scale datasets.

Bryce Goodman, Seth Flaxman

We summarize the potential impact that the European Union's new General Data Protection Regulation will have on the routine use of machine learning algorithms. Slated to take effect as law across the EU in 2018, it will restrict automated individual decision-making (that is, algorithms that make decisions based on user-level predictors) which "significantly affect" users. The law will also effectively create a "right to explanation," whereby a user can ask for an explanation of an algorithmic decision that was made about them. We argue that while this law will pose large challenges for industry, it highlights opportunities for computer scientists to take the lead in designing algorithms and evaluation frameworks which avoid discrimination and enable explanation.

Hyunjik Kim, Xiaoyu Lu, Seth Flaxman et al.

We tackle the problem of collaborative filtering (CF) with side information, through the lens of Gaussian Process (GP) regression. Driven by the idea of using the kernel to explicitly model user-item similarities, we formulate the GP in a way that allows the incorporation of low-rank matrix factorisation, arriving at our model, the Tucker Gaussian Process (TGP). Consequently, TGP generalises classical Bayesian matrix factorisation models, and goes beyond them to give a natural and elegant method for incorporating side information, giving enhanced predictive performance for CF problems. Moreover we show that it is a novel model for regression, especially well-suited to grid-structured data and problems where the dependence on covariates is close to being separable.

Seth Flaxman, Dino Sejdinovic, John P. Cunningham et al.

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of kernel mean embeddings of probability measures. For characteristic kernels, which include most commonly used ones, the kernel mean embedding uniquely determines its probability measure, so it can be used to design a powerful statistical testing framework, which includes nonparametric two-sample and independence tests. In practice, however, the performance of these tests can be very sensitive to the choice of kernel and its lengthscale parameters. To address this central issue, we propose a new probabilistic model for kernel mean embeddings, the Bayesian Kernel Embedding model, combining a Gaussian process prior over the Reproducing Kernel Hilbert Space containing the mean embedding with a conjugate likelihood function, thus yielding a closed form posterior over the mean embedding. The posterior mean of our model is closely related to recently proposed shrinkage estimators for kernel mean embeddings, while the posterior uncertainty is a new, interesting feature with various possible applications. Critically for the purposes of kernel learning, our model gives a simple, closed form marginal pseudolikelihood of the observed data given the kernel hyperparameters. This marginal pseudolikelihood can either be optimized to inform the hyperparameter choice or fully Bayesian inference can be used.

William Herlands, Andrew Wilson, Hannes Nickisch et al.

We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly define a change surface in combination with expressive spectral mixture kernels to capture the complex statistical structure. Finally, through the use of novel methods for additive non-separable kernels, we can scale the model to large datasets. We demonstrate the model on numerical and real world data, including a large spatio-temporal disease dataset where we identify previously unknown heterogeneous changes in space and time.