Bayesian neural networks speed up numerical integration.
problem Scalability of Bayesian quadrature methods.
method Bayesian Stein networks using neural networks and Laplace approximation.
result Orders of magnitude speed-up on benchmark functions and real-world problems.
Bayesian Neural Networks help quantify uncertainty in deep learning predictions.
problem Uncertainty quantification in deep learning predictions.
method Bayesian statistics applied to neural networks.
result Design, implementation, training, and evaluation of Bayesian Neural Networks.
Hybrid approach combines VI and HMC for efficient Bayesian inference in neural networks.
problem Computational demands and inaccuracies in Bayesian inference for neural networks.
method Combines VI and HMC, reducing parameter space and accelerating inference.
result Significantly reduces inference time for large neural networks, improving uncertainty quantification.
NEON uses neural networks to optimize functions in infinite-dimensional spaces.
problem Optimizing composite functions in function spaces.
method NEON (Neural Epistemic Operator Networks) for sequential decision-making.
result NEON achieves state-of-the-art performance with fewer parameters.
VB-DeepONet uses Bayesian inference to improve DeepONet's predictions and uncertainty quantification.
problem Overfitting and lack of uncertainty quantification in DeepONet.
method Variational Bayes approach to approximate posterior distribution, reducing computational cost.
result VB-DeepONet alleviates DeepONet's limitations and provides uncertainty quantification.
LUNO linearizes neural operators to quantify their predictive uncertainty.
problem Quantifying the predictive error of neural operators for high-stakes simulations.
method Model linearization to push weight-space uncertainty forward to predictions.
result LUNO provides a practical and theoretically sound way to apply Bayesian methods to neural operators.
A system for Operational Risk management based on the computational paradigm of Bayesian Networks is presented. The algorithm allows the construction of a Bayesian Network targeted for each bank using only internal loss data, and takes into account in a simple and realistic way the correlations among different processe…
DiBS learns Bayesian network structure and parameters efficiently.
problem Bayesian structure learning with uncertainty reasoning.
method Differentiable framework for continuous latent graph representation, agnostic to local conditional distributions.
result Significantly outperforms related approaches in posterior inference.
This paper aims to propose a novel deep learning-integrated framework for deriving reliable simulation input models through incorporating multi-source information. The framework sources and extracts multisource data generated from construction operations, which provides rich information for input modeling. The framewor…
DeepONets combine neural networks with physics constraints for PDEs and parameter estimation.
problem Estimating parameters in PDEs with uncertainty quantification.
method Physics-informed neural networks (PINNs) integrated with Deep Operator Networks (DeepONets) for Bayesian inference.
result Robust and accurate solutions with comprehensive uncertainty quantification.
Bayesian method optimizes rescheduling for multipurpose batch processes with incomplete look-ahead information.
problem Optimizing rescheduling for multipurpose batch processes under incomplete look-ahead information.
method Proposes a Bayesian dynamic scheduling method that learns from disturbances and updates schedules online.
result Achieves statistically better long-term costs and system nervousness compared to existing periodic rescheduling strategies.
Bayesian layer improves image segmentation and out-of-distribution detection.
problem Outlier detection in image segmentation.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates improve out-of-distribution detection.
Improved neural network convergence with causal Bayesian modeling in retail performance.
problem Improving neural network convergence in retail performance models.
method Causal Bayesian neural network implementation, removal of weakest SEM path, Flipout layers, Vadam optimizer.
result Neural network convergence improved with removal of the weakest SEM path.
New method solves high-dimensional Bayesian inverse problems efficiently.
problem Efficiently solving high-dimensional Bayesian inverse problems with limited data.
method Physics-informed Neural Operators with RealNVP architecture for invertibility and differentiability.
result Accurate approximations of the full posterior without additional forward solves or sampling.
Development systems for deep learning (DL), such as Theano, Torch, TensorFlow, or MXNet, are easy-to-use tools for creating complex neural network models. Since gradient computations are automatically baked in, and execution is mapped to high performance hardware, these models can be trained end-to-end on large amounts…
Enhanced DeepONet framework with uncertainty quantification for complex operators.
problem Learning complex operators with uncertainty quantification.
method Generalised variational inference (GVI) using Rényi's α-divergence.
result Superior predictive accuracy and uncertainty quantification.
Hybrid Bayesian MOT uses neural networks to improve model aspects, achieving state-of-the-art performance.
problem Improving multiobject tracking performance across various scenarios.
method Hybrid approach combining neural network enhancements with Bayesian estimation and belief propagation.
result State-of-the-art performance in autonomous driving dataset evaluation.
New algorithms for fast online decision making using neural networks and martingale posteriors.
problem Online sequential decision making under uncertainty.
method Martingale posterior neural networks for fast online learning and decision making.
result Achieves competitive performance-speed trade-offs in non-stationary contextual bandits and Bayesian optimization.
Injective and surjective neural operators for function spaces.
problem Tackles injective and surjective neural operators in function spaces.
method Combines prior work in ReLU and operator learning, uses Fredholm theory and Leray-Schauder degree theory.
result Injective and surjective neural operators are universal approximators and maintain their properties in finite-rank implementations.
Bayesian Deep Learning tackles inverse problems with neural networks and approximate computations.
problem Solving inverse problems with indirect measurements and uncertainties.
method Bayesian Deep Learning, using neural networks and approximate computations.
result Effective solutions for inverse problems using Bayesian Deep Learning.
Bayesian Recurrent Neural Networks improve fault detection and identification in manufacturing.
problem Detect and identify faults in chemical processes to ensure optimal operations.
method Bayesian Recurrent Neural Networks (BRNNs) with variational dropout.
result BRNNs provide uncertainty estimates for fault detection and identification.
Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' rule, imposing posterior regularization is arguably more direct and in s…
Bayesian model learns physics laws from data with uncertainty quantification.
problem Lack of uncertainty in discovering governing physical laws from data.
method Bayesian approach with leaf and root modules, Gaussian process for operators, automatic differentiation.
result Quantifies reliability of learned physics laws and propagates uncertainty.
Efficiently discovers Bayesian network structure with reduced memory usage.
problem Bayesian network structure discovery is NP-hard and memory-intensive.
method Progressively leveled scoring approach with hierarchical computation.
result Achieved processing of a 28-variable Bayesian network using only memory.
ICON learns differential equation operators from examples, revealing probabilistic inference.
problem Learning operators for differential equations from limited examples.
method Probabilistic operator learning using ICON architectures trained on diverse datasets.
result ICON implicitly performs Bayesian inference on solution operators.
Brain uses synaptic failure to sample from posterior distributions.
problem Bayesian inference in the brain's probabilistic computations.
method Adapting synaptic failure to sample posterior predictive distributions.
result Synaptic failure enables sampling of complete posterior predictive distributions.
We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks on semi-supervised learning benchmark experiments, and outperforms the neural net…
Two methods reduce BN and DNN complexity, balancing size and accuracy.
problem Balancing model size and prediction accuracy in Bayesian networks and deep neural networks.
method Quantization-aware training and tree-augmented naive Bayes structure learning extension.
result Pareto optimal models found for small-scale scenarios.
A significant theoretical advantage of search-and-score methods for learning Bayesian Networks is that they can accept informative prior beliefs for each possible network, thus complementing the data. In this paper, a method is presented for assigning priors based on beliefs on the presence or absence of certain paths …
Locally learned synaptic failure enables complete Bayesian inference.
problem Bayesian inference in neural networks.
method Biologically constrained neural network with synaptic failure and lateral inhibition.
result Synaptic failure allows sampling from both epistemic and aleatoric distributions.
Neural operators correct PDE residuals to improve BIP solutions.
problem Reducing error in infinite-dimensional Bayesian inverse problems with neural operators.
method Error correction using PDE residuals to improve neural operator approximation.
result Trained neural operators with error correction achieve a quadratic reduction in approximation error.
GNPs learn operators on non-Euclidean geometries using neural networks.
problem Learning operators on complex geometries like manifolds.
method Geometric Neural Operators (GNPs) that incorporate geometric properties.
result GNPs can estimate metrics, solve PDEs, and learn LB operators on manifolds.
CoNBONet improves reliability analysis of complex systems with fast, energy-efficient predictions.
problem Time-dependent reliability analysis of nonlinear systems under stochastic excitations is computationally demanding.
method CoNBONet combines deep operator networks with neuroscience-inspired neuron models for fast, energy-efficient inference.
result CoNBONet provides reliable coverage of failure probabilities with theoretical guarantees.
EDAs with matrix transpose improve Bayesian structure learning performance.
problem Improving Bayesian structure learning performance.
method Introducing a matrix transpose mutation operator for EDAs in Bayesian structure learning.
result EDAs with transpose mutation give markedly better performance than conventional EDAs.
DIGing-SGLD improves SGLD for scalable Bayesian learning in dynamic networks.
problem Scalable Bayesian learning in multi-agent systems with time-varying networks.
method Integrates Langevin sampling with gradient-tracking for decentralized learning over time-varying networks.
result Achieves geometric convergence to the target distribution with finite-time guarantees.
This paper improves Bayesian inference for predictive models with limited data.
problem Effective uncertainty quantification for training predictive models with limited data.
method Entropy-regularized gradient estimators to approximate the Bayesian posterior.
result The method generates diverse samples from the posterior distribution efficiently.
NSIBF detects anomalies in CPS using neural system identification and Bayesian filtering.
problem Detecting anomalies in CPS with complex dynamics and sensor noise.
method Neural System Identification and Bayesian Filtering (NSIBF).
result NSIBF outperforms state-of-the-art methods in anomaly detection for CPS.
Kernel-based Bayesian filter for nonlinear systems using infinite-dimensional operators.
problem Modeling and predicting nonlinear dynamical systems.
method Functional Bayesian perspective, reproducing kernel Hilbert space, Gaussian kernel.
result Effective approximation and accurate results for nonlinear systems.
Bayesian Gaussian Processes layer detects out-of-distribution data in medical imaging.
problem Detecting out-of-distribution data in medical imaging tasks.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates enable superior out-of-distribution detection compared to previous methods.
A new machine learning method for Bayesian inverse problems in function spaces.
problem Bayesian inverse problems in function spaces with incompatibility of white noise sources.
method One-step generative transport with amortized neural operator and prior-aligned Gaussian random field.
result Generative operator trained on prior samples and noisy observations generates posterior samples efficiently.
RP-WNO extends WNO with uncertainty quantification, useful for scientists and engineers.
problem Uncertainty in predictions of deep learning models.
method Randomized Prior Wavelet Neural Operator (RP-WNO) with uncertainty quantification module.
result RP-WNO effectively estimates uncertainty in predictions.
Bayesian Neural Networks improve high-dimensional level set estimation.
problem Scalability issue in existing LSE methods for high-dimensional inputs.
method Bayesian Neural Networks with information-based acquisition functions.
result Proposed method achieves better results than state-of-the-art approaches.
Bayesian SSI improves modal parameter uncertainty in operational systems.
problem Uncertainty in modal parameters due to stochastic operational systems and lack of forcing information.
method Proposes a Bayesian stochastic subspace identification (SSI) algorithm with a hierarchical probabilistic model and two inference schemes (Markov Chain Monte Carlo and variational Bayes).
result Posterior distributions over modal properties are obtained, showing lower variance for mean values coinciding with natural frequencies.
LIC compiles probabilistic models to generate efficient MCMC proposals.
problem Creating accurate Metropolis-Hastings proposals for Bayesian inference.
method Integrates probabilistic graphical models and neural networks in an open-source framework to optimize proposal distributions.
result LIC produces more efficient and robust MCMC proposals compared to existing methods.
Bayesian framework predicts post-disruption travel times in metro networks.
problem Uncertainty in post-disruption travel times in metro networks.
method Bayesian spatiotemporal modeling framework capturing train interactions and non-Gaussian distributional characteristics.
result The proposed models consistently outperform baseline specifications in point prediction and uncertainty quantification.
Stein variational neural network ensembles improve diversity and uncertainty estimation.
problem Lack of proper Bayesian justification and diversity guarantees in deep neural network ensembles.
method Particle-based inference methods, specifically Stein variational gradient descent (SVGD), operating in weight space, function space, and hybrid settings.
result SVGD methods improve diversity and uncertainty estimation, approaching the true Bayesian posterior more closely.
PFP-BNNs offer a fast, deterministic approach to Bayesian neural networks.
problem Limited uncertainty handling in traditional neural networks restricts their use in safety-critical settings.
method Probabilistic Forward Pass (PFP) approximates Stochastic Variational Inference (SVI) for efficient BNNs.
result PFP-BNNs achieve up to 4200x speedup over SVI-BNNs while maintaining similar accuracy and uncertainty.
Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attemp…