BFNs use Bayesian inference and neural networks for generative modeling.
problem Learning from non-stationary data in continual learning.
method Bayesian Flow Networks (BFNs) combining neural network expressiveness and Bayesian inference.
result BFNs effectively model non-stationary data.
We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows…
New framework for Bayesian inference using neural Schrödinger-Föllmer flows.
problem Approximate Bayesian inference in large datasets.
method Stochastic control, Schrödinger bridges, SDE-based models.
result Advocates stochastic control as a finite time and low variance alternative to SGLD.
New method for scalable stochastic neural networks using Kronecker Flow.
problem Scaling stochastic neural networks to high dimensions.
method Kronecker Flow, a scalable parameterization of noise generation.
result Competitive performance on various tasks compared to existing methods.
Bayesian neural flows improve Gaia distance estimates and dust modeling.
problem Improving precision of distance estimates from Gaia DR2 data.
method Normalizing flow for learning flexible color-magnitude diagrams.
result Distance posteriors improved by more than 48% over raw Gaia data.
Finite-width neural networks use non-Gaussian priors, extending Gaussian process theory.
problem Understanding the behavior of neural networks with finite width.
method Perturbative extension of Gaussian process theory to finite-width neural networks, tracking preactivation distributions.
result Non-Gaussian processes as priors in finite-width neural networks.
Paper discovers differential equations from data using neural networks and Bayesian methods.
problem Discovering differential equations from datasets using machine learning.
method Integrates neural network-based surrogates with Sparse Bayesian Learning (SBL).
result Proposes a robust model discovery algorithm and a Physics Informed Normalizing Flow (PINF).
Normalizing flows are shown to be equivalent to Bayesian networks, revealing new insights.
problem Understanding the limitations and capabilities of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models and analyzing their structure.
result Normalizing flows can be reduced to Bayesian networks, revealing new insights into their structure and capabilities.
CoSMIC extends flow-based SVI to transdimensional problems.
problem Bayesian structure learning and model selection with multi-model parameter spaces.
method Normalizing flows with a combined stochastic variational transdimensional inference approach.
result Improved performance on high-cardinality model spaces.
Paper proves CFlows can approximate any diffeomorphism and applies it in Bayesian optimization.
problem Proving the universality of CFlows in approximating diffeomorphisms.
method Deriving the universality of Para-CFlows through affine coupling layers and invertible linear transforms.
result Para-CFlows can approximate any diffeomorphism in C^k-norm.
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
Framework for accelerated gradient flows in Bayesian inverse problems.
problem Design efficient MCMC algorithms for Bayesian inverse problems.
method Nesterov's accelerated gradient flows in probability space, considering various information metrics.
result Proved convergence properties and proposed sampling-efficient algorithms for different metrics.
Bayesian neural networks improve uncertainty estimates and sparsity.
problem Overfitting and lack of uncertainty estimates in neural networks.
method LBBNN with LRT and normalizing flows for more flexible variational posterior.
result Improved predictive power and more sparse networks.
Advances variational Bayesian neural networks using singular learning theory.
problem Discrepancies between predictive performance and variational objective in BNNs.
method Corrected asymptotic form of singular posterior distributions to inform variational family design.
result Improvements in variational free energy and generalization error with proposed normalizing flow.
Posterior refinement improves sample efficiency in Bayesian neural networks.
problem Bayesian neural networks suffer from poor predictive performance due to inaccurate posterior approximations.
method Propose refining Gaussian approximate posteriors with normalizing flows to improve predictive distributions.
result Posterior refinement yields competitive predictive performance with minimal computational overhead.
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
A new method using normalizing flows speeds up Bayesian model comparison.
problem Computational challenges in calculating Bayesian evidence for complex models.
method Savage-Dickey density ratio with normalizing flows.
result The method scales to high-dimensional settings and provides consistent Bayes factors.
A new method infers graph structure and parameters using a single generative flow network.
problem Bayesian Network structure and parameter inference from data.
method Single GFlowNet with two-phase sampling: DAG generation followed by parameter assignment.
result Accurate approximation of joint posterior distribution over graph structure and parameters.
Bayesian Neural Nets improve model stability and fit.
problem Improving model stability and fit in time series prediction.
method Assign Bayesian Neural Nets to drift and diffusion terms of SDE, infer posterior using SGLD.
result Significantly improved stability and better model fit on benchmarks.
Bayesian methods have been successfully applied to sparsify weights of neural networks and to remove structure units from the networks, e. g. neurons. We apply and further develop this approach for gated recurrent architectures. Specifically, in addition to sparsification of individual weights and neurons, we propose t…
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction over deterministic and stochastic functions and allows for scalability via the unde…
Improved NPE with conditional diffusions and summary networks.
problem Approximating complex posterior distributions efficiently and accurately.
method Conditional diffusions coupled with high-capacity summary networks.
result Conditional diffusions offer improved stability, accuracy, and faster training times.
New method speeds up galaxy analysis from hours to seconds.
problem Infeasibility of state-of-the-art SED analyses for large surveys.
method Amortized Neural Posterior Estimation (ANPE) for scalable Bayesian inference.
result Posterior distributions of 12 model parameters estimated in seconds per galaxy.
Paper proposes efficient BNN inference flow to reduce computation and memory costs.
problem High computation complexity in Bayesian Neural Networks (BNNs) limits deployment in power-constrained systems.
method Feature decomposition and memorization strategy to reduce computations and a memory-friendly computing framework to reduce memory overhead.
result Reduces computation by about half and energy consumption by 73% with 14% area overhead.
Bayesian neural networks improve uncertainty in data-driven VFMs for oil and gas wells.
problem Uncertainty and robustness in data-driven VFMs for oil and gas wells.
method Bayesian neural networks with variational inference for uncertainty quantification.
result Variational inference provides more robust predictions on future data.
This paper tackles real-time Bayesian inverse problems using neural networks.
problem Real-time inference of posterior distributions from experimental data.
method Amortized variational inference with Gaussian and Flow guides.
result The approach provides posterior estimates in real-time at the cost of a forward pass.
We present a particle flow realization of Bayes' rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to re…
Generative models improve carbon storage site prediction using Bayesian inversion.
problem Predicting suitable geologic sites for long-term carbon dioxide storage.
method Generative adversarial networks and Bayesian inversion to condition models on physical measurements and historic data.
result Improved resolution of carbon dioxide storage capacity forecasts.
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.
LLEB uses a learned prior to quantify neural network uncertainty.
problem Quantifying uncertainty in neural network predictions.
method LLEB uses a learnable prior as a normalizing flow to maximize the evidence lower bound.
result LLEB performs on par with existing approaches in uncertainty quantification.
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.
New method for variational inference without conjugacy constraints.
problem Efficient variational inference with flexible prior and approximation families.
method Wasserstein gradient flow for mean-field approximation.
result Improved convergence and efficiency of variational inference.
We present Sequential Neural Likelihood (SNL), a new method for Bayesian inference in simulator models, where the likelihood is intractable but simulating data from the model is possible. SNL trains an autoregressive flow on simulated data in order to learn a model of the likelihood in the region of high posterior dens…
Bayesian updating is modeled as a dynamical system, revealing learning rate laws.
problem Modeling Bayesian inference as a dynamical system.
method Formulated Bayesian updating as a continuous dynamical system, solving for trajectories in information geometry.
result Learning rate is governed by a 1/T power-law when the Cramér-Rao bound is saturated. New method reduces variance in Bayesian inverse problems.
problem High variance in Monte Carlo estimates for inverse problems.
method Conditional neural control variates based on Stein's identity.
result Substantial variance reduction across different inverse problems.
ADAVI tackles variational inference for large HBM models in neuroimaging.
problem Large, pyramidally-organized HBM models in neuroimaging studies.
method Automatic dual amortized variational inference using neural networks and attention-based hierarchical encoding.
result Significantly reduced parameterization of the variational family, maintaining expressivity.
Bayesian method finds voids in galaxy surveys with deep neural networks.
problem Finding genuine matter underdensities in sparse galaxy surveys is underconstrained.
method Deep graph neural network evolves 'test particles' to sample from stochastic void definitions.
result Trained model performs well and finds Bayes-optimal void mappings.
This paper shows equivalence between SVGD and BBVI using kernel gradient flows.
problem Bayesian inference methods and their equivalence.
method Formalizes equivalence between SVGD and BBVI using kernel gradient flows.
result BBVI corresponds precisely to SVGD when using the neural tangent kernel.
We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered in deep learning for image-to-image regression tasks. Since normal neural netwo…
SURGIN uses generative models to infer subsurface flow data efficiently.
problem Inefficient and task-specific inversion methods for subsurface multiphase flow.
method SURGIN integrates U-FNO surrogate with SGM for zero-shot conditional generation.
result Decent inference of heterogeneous geological fields and flow dynamics with uncertainty quantification.
Causal Posterior Estimation improves Bayesian inference in complex models.
problem Bayesian inference in models with intractable likelihood functions.
method Normalizing flow-based approximation with conditional dependence structure.
result Improved accuracy in posterior inference through direct incorporation of model structure.
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.
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in practice. This paper employs normalising flows as a flexible likelihood model and …
INP accelerates stochastic simulations using deep Bayesian active learning.
problem Computational expense of stochastic simulations at fine-grained resolution.
method Interactive Neural Process (INP) framework combining spatiotemporal surrogate model and active learning acquisition function.
result STNP outperforms baselines in accelerating stochastic simulations and LIG achieves state-of-the-art for Bayesian active learning.
Paper develops a fast Bayesian method to predict toxic trades in financial transactions.
problem Predicting and managing toxic trades in financial transactions.
method PULSE: an online learning Bayesian procedure for neural networks.
result Neural networks trained with PULSE outperform traditional methods in predicting toxic trades.
Bayesian PINNs solve noisy PDE problems with physics constraints.
problem Uncertainty quantification in noisy PDE problems.
method Bayesian framework combining PINNs and HMC/VI for posterior estimation.
result HMC outperforms VI for noisy data.
StrNN uses neural network structures to learn conditional independencies.
problem Learning conditional independencies in neural networks.
method Designing masks for neural networks based on binary matrix factorization.
result StrNN improves density estimation and causal inference.