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Spatial prediction requires expensive computation to invert the spatial covariance matrix it depends on and also has considerable storage needs. This work concentrates on computationally efficient algorithms for prediction using very large…
Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization…
Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most popular method…
Geospatial observational datasets are often limited to point measurements, making temporal prediction and spatial interpolation essential for constructing continuous fields. This study evaluates two deep learning strategies for addressing…
Sensors are commonly deployed to perceive the environment. However, due to the high cost, sensors are usually sparsely deployed. Kriging is the tailored task to infer the unobserved nodes (without sensors) using the observed source nodes…
Interpolation in Spatio-temporal data has applications in various domains such as climate, transportation, and mining. Spatio-Temporal interpolation is highly challenging due to the complex spatial and temporal relationships. However,…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…
Deep learning has been extensively used in various fields, such as phase imaging, 3D imaging reconstruction, phase unwrapping, and laser speckle reduction, particularly for complex problems that lack analytic models. Its data-driven nature…
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…
Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of…
Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…
Domain invariant learning aims to learn models that extract invariant features over various training domains, resulting in better generalization to unseen target domains. Recently, Bayesian Neural Networks have achieved promising results in…
The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions…
Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…
Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…
We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search…
Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…