Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
Optimal neural network approximation for Wasserstein gradient direction via convex optimization.
problem Approximating Wasserstein gradient direction with limited data.
method Two-layer networks with squared-ReLU activations, SDP relaxation.
result Optimal approximation of Wasserstein gradient direction in two-layer networks.
New methods for Bayesian inference using mean shift particle systems.
problem Approximating expectations with unnormalized densities in Bayesian inference.
method Mean shift interacting particle systems that minimize maximum mean discrepancy (MMD).
result Mean shift interacting particle systems converge quickly and capture complex distributions.
Bayesian Gaussian process models handle uncertain data locations in PDE approximations.
problem Handling uncertainties in data locations for PDE approximations.
method Bayesian inference of uncertain inputs integrated into Gaussian process predictions.
result Substantial reduction in predictive uncertainties achieved through Bayesian inference.
Gradient-free framework for Bayesian experimental design in complex systems.
problem Optimal experimental design in systems where gradient information is unavailable.
method Combines EKI and ALDI for optimization and sampling, with approximations for scalable utility estimation.
result Demonstrates robust, accurate, and efficient experimental design in various complex systems.
Extends dimension reduction to data-driven settings without gradients.
problem Gradient-based dimension reduction limitations in data-driven settings.
method Score ratio matching framework, tailored parameterization, regularization, eigenvalue deflation.
result Outperforms standard score-matching for problems with low-dimensional structure.
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
Study uses outer metrics for PDE-constrained shape optimization over diffeomorphism group.
problem Optimizing shapes governed by PDEs over the diffeomorphism group.
method Outer metrics on diffeomorphism group, Riemannian steepest descent method.
result Riemannian approach outperforms other metrics in solving PDE-constrained shape optimization problems.
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
PDE-DKL combines NNs and GPs for high-dimensional PDE problems.
problem High-dimensional PDE problems with scarce data.
method PDE-constrained Deep Kernel Learning (PDE-DKL) framework.
result High accuracy with reduced data requirements.
We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical so…
A new MCMC method combines low and high-fidelity models to reduce computation.
problem Inefficient computation of expensive target densities in scientific applications.
method Pseudo-marginal MCMC approach using a telescoping series of low-fidelity models.
result Asymptotically exact multi-fidelity MCMC algorithms for reduced computational cost.
Estimates expected information gain using density approximations and dimension reduction.
problem Estimating expected information gain in nonlinear and non-Gaussian settings.
method Flexible transport-based schemes for EIG estimation, optimal sample allocation, and gradient-based upper bounds on mutual information.
result Optimal sample allocation and dimension reduction schemes improve EIG estimation accuracy and convergence rate.
New methods tackle complex inverse problems with scalable optimization-based MCMC.
problem Estimating high-dimensional model parameters and hyperparameters in nonlinear hierarchical statistical inverse problems.
method Optimization-based Markov chain Monte Carlo (MCMC) methods using RTO and pseudo-marginal MCMC.
result Efficient sampling tools for hierarchical Bayesian inversion with robust performance to model parameter dimensions.
Enhances robustness in experimental design through Generalised Bayesian inference.
problem Poor inference and estimates of information gain when statistical model is incorrectly specified.
method Generalised Bayesian (Gibbs) inference framework applied to experimental design.
result GBOED enhances robustness to outliers and incorrect assumptions about noise distribution.
UA-SABI uses surrogates to speed up Bayesian inference for expensive models.
problem Inference for computationally expensive models is slow and uncertain.
method Combines surrogate modeling with Amortized Bayesian Inference (ABI) to propagate uncertainties.
result Reliable, fast, and repeated Bayesian inference for expensive models is achieved.
Variational Inference shows promise for Bayesian GARCH model estimation.
problem Bayesian estimation of GARCH-family models using Monte Carlo sampling.
method Variational Inference as an alternative to Monte Carlo sampling.
result Variational Inference is a reliable and competitive method for Bayesian learning in GARCH-like models.
Bayesian methods enhance deep learning models by improving reliability and uncertainty.
problem Improving reliability and uncertainty awareness in deep learning models.
method Approximate Bayesian inference techniques, including SG-MCMC and VI, applied to deep learning models.
result Enhanced posterior inference for deep learning models, particularly in neural networks and generative models.
Bayesian coresets improve scalable Bayesian inference.
problem Efficiently approximating posterior inference with a subset of data.
method Sparsity constrained optimization and accelerated optimization methods.
result Explicit convergence rate guarantees and superior performance compared to state-of-the-art.
Post-process Bayesian inference speeds up posterior approximation.
problem Leveraging pre-existing model evaluations for quick posterior approximation.
method Variational Sparse Bayesian Quadrature (VSBQ) using sparse Gaussian process (GP) surrogate model.
result VSBQ builds high-quality posterior approximations from existing optimization traces.
BayesFlow trains neural networks for fast Bayesian inference.
problem Fast Bayesian inference for complex models.
method Amortized neural networks for intractable posterior distributions.
result Fast inference through pre-trained neural networks.
Adversarial robustness of amortized Bayesian inference is studied, showing it can be improved.
problem Adversarial robustness of amortized Bayesian inference.
method Simulation-based estimation, regularization scheme based on Fisher information.
result Adversarial robustness can be improved with a regularization scheme.
Bayesian interpolants explain neural network inferences concisely.
problem Understanding neural network inferences.
method Adapting Craig interpolants for neural networks.
result Produces precise, understandable explanations.
Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.
problem Theoretical justification for Bayesian bandit algorithms with approximate inference in stochastic linear bandits.
method Proposed a theoretical framework to analyze approximate inference impact and conducted frequentist regret analysis on LinTS and LinBUCB.
result LinTS and LinBUCB preserve their original regret upper bounds with larger constant terms in approximate inference settings.
BLISS detects and separates astronomical sources quickly and accurately.
problem Detecting and separating overlapping astronomical sources in large images.
method Bayesian Light Source Separator (BLISS) using deep generative models and variational inference.
result BLISS can process megapixel images in seconds and produce highly accurate catalogs.
Improved Bayesian inference for neuronal ensemble inference reduces computational cost.
problem Efficient inference of neuronal ensembles from activity data.
method Modified MCMC algorithm with simulated annealing for hyperparameter control.
result Our method reduces computational cost while maintaining or improving inference accuracy.
Bayesian inference forgetting framework removes influence of single data points.
problem Enforcement of the right to be forgotten in machine learning causes high costs for companies.
method Develops forgetting algorithms for variational and Markov chain Monte Carlo in Bayesian inference.
result Proves removal of influence of single datums on learned models with guaranteed generalizability.
BaMANI uses ensemble learning to improve Bayesian network inference.
problem Bayesian network inference's reliance on specific algorithms can obscure causal relationships.
method Developed an ensemble learning approach to marginalize algorithm impact.
result Improved accuracy and reliability of causal network predictions.
Bayesian methods often misinterpret data and asymptotic concepts.
problem Misunderstandings in Bayesian predictive inference.
method Discussion of two specific misunderstandings.
result Consequences of misinterpretations illustrated through examples.
Bayesian inference using stochastic neural networks ensembles.
problem Approximating Bayesian posterior distributions.
method Formulate stochastic ensembles of neural networks, train with variational inference, and evaluate using Monte Carlo dropout.
result Stochastic ensembles provide more accurate posterior estimates than other methods.
Bayesian nonparametric machine learning improves instrumental variable inference.
problem Estimating causal effects with nonlinear relationships.
method Bayesian Additive Regression Trees (BART) for estimating functions and Dirichlet Process mixtures for error terms.
result Dramatic improvements in inference with nonlinear data, no manual tuning required.
Bayesian method infers contextual bandit policies robustly.
problem Inference of contextual bandit policies in small sample sizes.
method Empirical likelihood for Bayesian inference.
result Accurate uncertainty measurements and policy comparison.
The paper explores how to evaluate Bayesian approximations in neural networks.
problem The difficulty in evaluating Bayesian approximations in neural networks.
method Exploring the interactions between probabilistic models, approximating distributions, optimization algorithms, and datasets.
result The expected utility of the approximate posterior can measure inference quality.
Simformer uses transformer models to perform flexible Bayesian inference.
problem Current simulation-based inference methods are inflexible and require fixed priors.
method Trains a probabilistic diffusion model with transformer architectures.
result Outperforms state-of-the-art methods on various benchmarks.
Method scales Bayesian inference to large datasets and robustifies against outliers.
problem Scalability and robustness to outliers in Bayesian inference.
method Variational inference with β-divergence and Riemannian coresets. result Efficiently constructs cleansed data summaries robust to outliers.
Improved Bayesian neural network inference by selectively removing redundant modes.
problem Redundant modes in Bayesian neural network posteriors complicate approximate inference.
method Structured partial stochasticity and deterministic subset selection of weights.
result Improved performance of approximate inference schemes with simplified posterior distribution.
Bayesian priors and penalties are equivalent in variational inference.
problem Understanding the relationship between Bayesian priors and penalties in variational inference.
method Characterizing the regularizers that can arise in variational inference and providing a systematic way to compute the prior corresponding to a given penalty.
result Equivalence between Bayesian priors and penalties in variational inference.
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.
Develops methods for cooperative Bayesian inference.
problem Cooperation between learning agents.
method Sequential Bayesian inference approaches.
result Theoretical foundation for cooperative inference.
SOLBP extends efficient inference to uncertain Bayesian networks.
problem Inference in uncertain Bayesian networks with second-order probabilities.
method Extends Loopy Belief Propagation to second-order Bayesian networks.
result Generates inferences consistent with sum-product networks, more efficient and scalable.
Proposes TAGI for efficient Gaussian inference in Bayesian neural networks.
problem Efficient inference in Bayesian neural networks with complex architectures.
method Analytical method for tractable approximate Gaussian inference (TAGI).
result Matches performance of gradient-based methods with O(n) computational complexity. We review three algorithms for Latent Dirichlet Allocation (LDA). Two of them are variational inference algorithms: Variational Bayesian inference and Online Variational Bayesian inference and one is Markov Chain Monte Carlo (MCMC) algorithm -- Collapsed Gibbs sampling. We compare their time complexity and performance.…
PIVID infers DAG structures from data using variational inference and permutations.
problem Estimating the structure of Bayesian networks from observational data.
method PIVID uses variational inference and continuous relaxations of discrete distributions to infer a distribution over permutations and DAGs.
result PIVID outperforms deterministic and Bayesian approaches in estimating DAG structures from data.
Stacking improves inference for multimodal Bayesian posterior distributions.
problem Difficulty of MCMC in moving between modes and underestimation of posterior uncertainty.
method Parallel runs of MCMC, variational, or mode-based inference, combined using Bayesian stacking.
result Stacking efficiently samples from multimodal posterior distributions and represents uncertainty better than variational inference.
BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of implementing the variational Bayesian update equations, the user can construct model…
New coin sampling method for Bayesian inference without learning rates.
problem Scalable Bayesian inference with learning rate tuning issues.
method Coin sampling for gradient-based Bayesian inference.
result Comparable performance to other ParVI algorithms without learning rate tuning.
GeoFunFlow tackles inverse problems on complex geometries with efficient learning.
problem Challenges in inverse problems governed by PDEs, especially on irregular geometries.
method Combines geometric function autoencoder and latent diffusion model trained via rectified flow.
result Achieves state-of-the-art reconstruction accuracy and efficient inference.
Bayesian inference engines improve density estimation accuracy and scalability.
problem Constructing accurate and scalable probability density functions.
method Bayesian inference engines (no-U-turn sampling and expectation propagation) with binning strategy.
result Density estimates have excellent comparative performance and scale well to large sample sizes.