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We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…

Convolutional Neural Networks spread through computer vision like a wildfire, impacting almost all visual tasks imaginable. Despite this, few researchers dare to train their models from scratch. Most work builds on one of a handful of…

While offering a principled framework for uncertainty quantification in deep learning, the employment of Bayesian Neural Networks (BNNs) is still constrained by their increased computational requirements and the convergence difficulties…

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

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…

The accuracy of deep neural networks is significantly affected by how well mini-batches are constructed during the training step. In this paper, we propose a novel adaptive batch selection algorithm called Recency Bias that exploits the…

While modern machine learning has transformed numerous application domains, its growing computational demands increasingly constrain scalability and efficiency, particularly on embedded and resource-limited platforms. In practice, neural…

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…

Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of…

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…

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

Brain vessel segmentation of MR scans is a critical step in the diagnosis of cerebrovascular diseases. Due to the fine vessel structure, manual vessel segmentation is time consuming. Therefore, automatic deep learning (DL) based…

Background: Conventional prediction methods such as logistic regression and gradient boosting have been widely utilized for disease onset prediction for their reliability and interpretability. Deep learning methods promise enhanced…

Using a Bayesian network to analyze the causal relationship between nodes is a hot spot. The existing network learning algorithms are mainly constraint-based and score-based network generation methods. The constraint-based method is mainly…

Ensemble learning is a standard approach to building machine learning systems that capture complex phenomena in real-world data. An important aspect of these systems is the complete and valid quantification of model uncertainty. We…

Recent studies have shown that ensemble approaches could not only improve accuracy and but also estimate model uncertainty in deep learning. However, it requires a large number of parameters according to the increase of ensemble models for…

Multiple Classifier Systems (MCSs) allow evaluation of the uncertainty of classification outcomes that is of crucial importance for safety critical applications. The uncertainty of classification is determined by a trade-off between the…

The Deep Operator Networks~(DeepONet) is a fundamentally different class of neural networks that we train to approximate nonlinear operators, including the solution operator of parametric partial differential equations (PDE). DeepONets have…

Reliable channel estimation (CE) is fundamental for robust communication in dynamic wireless environments, where models must generalize across varying conditions such as signal-to-noise ratios (SNRs), the number of resource blocks (RBs),…