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Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…
Modern deep learning tools are remarkably effective in addressing intricate problems. However, their operation as black-box models introduces increased uncertainty in predictions. Additionally, they contend with various challenges,…
Efficiently quantifying predictive uncertainty in medical images remains a challenge. While Bayesian neural networks (BNN) offer predictive uncertainty, they require substantial computational resources to train. Although Bayesian…
The aim of this work is to enable inference of deep networks that retain high accuracy for the least possible model complexity, with the latter deduced from the data during inference. To this end, we revisit deep networks that comprise…
Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps…
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
This paper describes stochastic search approaches, including a new stochastic algorithm and an adaptive mutation operator, for learning Bayesian networks from incomplete data. This problem is characterized by a huge solution space with a…
Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…
Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…
In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…
Many real-world mission-critical applications require continual online learning from noisy data and real-time decision making with a defined confidence level. Probabilistic models and stochastic neural networks can explicitly handle…
Utilizing physics-informed neural networks (PINN) to solve partial differential equations (PDEs) becomes a hot issue and also shows its great powers, but still suffers from the dilemmas of limited predicted accuracy in the sampling domain…
Very deep convolutional networks with hundreds of layers have led to significant reductions in error on competitive benchmarks. Although the unmatched expressiveness of the many layers can be highly desirable at test time, training very…
We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…
Bayesian Neural Networks (BNNs) provide superior estimates of uncertainty by generating an ensemble of predictive distributions. However, inference via ensembling is resource-intensive, requiring additional entropy sources to generate…
interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest.…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…