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With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of spatially referenced data collected over time, motivated by environmental studies utilizing remotely sensed satellite data. In particular, we specify a semiparametric autoregressive model without the usual Gaussian assumption and devise a computationally scalable procedure that enables the regression analysis of large datasets. We estimate the model parameters by quasi maximum likelihood and show that the computational complexity can be reduced from cubic to linear of the sample size. Asymptotic properties under suitable regularity conditions are further established that inform the computational procedure to be efficient and scalable. A simulation study is conducted to evaluate the finite-sample properties of the parameter estimation and statistical inference. We illustrate our methodology by a dataset with over 2.96 million observations of annual land surface temperature and the comparison with an existing state-of-the-art approach highlights the advantages of our method.

Seismic networks provide data that are used as basis both for public safety decisions and for scientific research. Their configuration affects the data completeness, which in turn, critically affects several seismological scientific targets (e.g., earthquake prediction, seismic hazard...). In this context, a key aspect is how to map earthquakes density in seismogenic areas from censored data or even in areas that are not covered by the network. We propose to predict the spatial distribution of earthquakes from the knowledge of presence locations and geological relationships, taking into account any interactions between records. Namely, in a more general setting, we aim to estimate the intensity function of a point process, conditional to its censored realization, as in geostatistics for continuous processes. We define a predictor as the best linear unbiased combination of the observed point pattern. We show that the weight function associated to the predictor is the solution of a Fredholm equation of second kind. Both the kernel and the source term of the Fredholm equation are related to the first-and second-order characteristics of the point process through the intensity and the pair correlation function. Results are presented and illustrated on simulated non-stationary point processes and real data for mapping Greek Hellenic seismicity in a region with unreliable and incomplete records.

Precision medicine is a clinical approach for disease prevention, detection and treatment, which considers each individual's genetic background, environment and lifestyle. The development of this tailored avenue has been driven by the increased availability of omics methods, large cohorts of temporal samples, and their integration with clinical data. Despite the immense progression, existing computational methods for data analysis fail to provide appropriate solutions for this complex, high-dimensional and longitudinal data. In this work we have developed a new method termed TCAM, a dimensionality reduction technique for multi-way data, that overcomes major limitations when doing trajectory analysis of longitudinal omics data. Using real-world data, we show that TCAM outperforms traditional methods, as well as state-of-the-art tensor-based approaches for longitudinal microbiome data analysis. Moreover, we demonstrate the versatility of TCAM by applying it to several different omics datasets, and the applicability of it as a drop-in replacement within straightforward ML tasks.

A widely-used model for determining the long-term health impacts of public health interventions, often called a "multistate lifetable", requires estimates of incidence, case fatality, and sometimes also remission rates, for multiple diseases by age and gender. Generally, direct data on both incidence and case fatality are not available in every disease and setting. For example, we may know population mortality and prevalence rather than case fatality and incidence. This paper presents Bayesian continuous-time multistate models for estimating transition rates between disease states based on incomplete data. This builds on previous methods by using a formal statistical model with transparent data-generating assumptions, while providing accessible software as an R package. Rates for people of different ages and areas can be related flexibly through splines or hierarchical models. Previous methods are also extended to allow age-specific trends through calendar time. The model is used to estimate case fatality for multiple diseases in the city regions of England, based on incidence, prevalence and mortality data from the Global Burden of Disease study. The estimates can be used to inform health impact models relating to those diseases and areas. Different assumptions about rates are compared, and we check the influence of different data sources.

Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are typically controlled by free parameters that are estimated from data by maximum-likelihood estimation. However, when faced with real-world datasets many of the models run into a critical issue: they are formulated in terms of fully-observed data, whereas in practice the datasets are plagued with missing data. The theory of statistical model estimation from incomplete data is conceptually similar to the estimation of latent-variable models, where powerful tools such as variational inference (VI) exist. However, in contrast to standard latent-variable models, parameter estimation with incomplete data often requires estimating exponentially-many conditional distributions of the missing variables, hence making standard VI methods intractable. We address this gap by introducing variational Gibbs inference (VGI), a new general-purpose method to estimate the parameters of statistical models from incomplete data. We validate VGI on a set of synthetic and real-world estimation tasks, estimating important machine learning models, VAEs and normalising flows, from incomplete data. The proposed method, whilst general-purpose, achieves competitive or better performance than existing model-specific estimation methods.

Arsenic (As) and other toxic elements contamination of groundwater in Bangladesh poses a major threat to millions of people on a daily basis. Understanding complex relationships between arsenic and other elements can provide useful insights for mitigating arsenic poisoning in drinking water and requires multivariate modeling of the elements. However, environmental monitoring of such contaminants often involves a substantial proportion of left-censored observations falling below a minimum detection limit (MDL). This problem motivates us to propose a multivariate spatial Bayesian model for left-censored data for investigating the abundance of arsenic in Bangladesh groundwater and for creating spatial maps of the contaminants. Inference about the model parameters is drawn using an adaptive Markov Chain Monte Carlo (MCMC) sampling. The computation time for the proposed model is of the same order as a multivariate Gaussian process model that does not impute the censored values. The proposed method is applied to the arsenic contamination dataset made available by the Bangladesh Water Development Board (BWDB). Spatial maps of arsenic, barium (Ba), and calcium (Ca) concentrations in groundwater are prepared using the posterior predictive means calculated on a fine lattice over Bangladesh. Our results indicate that Chittagong and Dhaka divisions suffer from excessive concentrations of arsenic and only the divisions of Rajshahi and Rangpur have safe drinking water based on recommendations by the World Health Organization (WHO).

Comprehensive visual understanding requires detection frameworks that can effectively learn and utilize object interactions while analyzing objects individually. This is the main objective in Human-Object Interaction (HOI) detection task. In particular, relative spatial reasoning and structural connections between objects are essential cues for analyzing interactions, which is addressed by the proposed Visual-Spatial-Graph Network (VSGNet) architecture. VSGNet extracts visual features from the human-object pairs, refines the features with spatial configurations of the pair, and utilizes the structural connections between the pair via graph convolutions. The performance of VSGNet is thoroughly evaluated using the Verbs in COCO (V-COCO) and HICO-DET datasets. Experimental results indicate that VSGNet outperforms state-of-the-art solutions by 8% or 4 mAP in V-COCO and 16% or 3 mAP in HICO-DET.

We present an approach to learn an object-centric forward model, and show that this allows us to plan for sequences of actions to achieve distant desired goals. We propose to model a scene as a collection of objects, each with an explicit spatial location and implicit visual feature, and learn to model the effects of actions using random interaction data. Our model allows capturing the robot-object and object-object interactions, and leads to more sample-efficient and accurate predictions. We show that this learned model can be leveraged to search for action sequences that lead to desired goal configurations, and that in conjunction with a learned correction module, this allows for robust closed loop execution. We present experiments both in simulation and the real world, and show that our approach improves over alternate implicit or pixel-space forward models. Please see our project page (//judyye.github.io/ocmpc/) for result videos.

In recent years, Generative Adversarial Networks (GAN) have emerged as a powerful method for learning the mapping from noisy latent spaces to realistic data samples in high-dimensional space. So far, the development and application of GANs have been predominantly focused on spatial data such as images. In this project, we aim at modeling of spatio-temporal sensor data instead, i.e. dynamic data over time. The main goal is to encode temporal data into a global and low-dimensional latent vector that captures the dynamics of the spatio-temporal signal. To this end, we incorporate auto-regressive RNNs, Wasserstein GAN loss, spectral norm weight constraints and a semi-supervised learning scheme into InfoGAN, a method for retrieval of meaningful latents in adversarial learning. To demonstrate the modeling capability of our method, we encode full-body skeletal human motion from a large dataset representing 60 classes of daily activities, recorded in a multi-Kinect setup. Initial results indicate competitive classification performance of the learned latent representations, compared to direct CNN/RNN inference. In future work, we plan to apply this method on a related problem in the medical domain, i.e. on recovery of meaningful latents in gait analysis of patients with vertigo and balance disorders.