Hi-fi priors enhance BNNs by learning flexible activations.
problem Challenging to impose function-space priors on BNNs.
method Optimization techniques to learn flexible activations.
result BNNs with flexible activations can achieve desired priors.
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48 results for “function space priors”
Bayesian optimisation is improved by incorporating expert prior through space warping.
problem Cold start phase in expensive function optimisation.
method Prior distribution warps the search space around high probability regions of function optimum.
result Improves optimisation performance through acquisition agnostic approach.
Researchers derive exact priors for finite Bayesian neural networks.
problem Understanding non-Gaussian priors in finite Bayesian neural networks.
method Analytical derivation of function space priors for finite fully-connected feedforward networks.
result Exact solutions for priors of finite networks, including Meijer G-function for linear networks and mixtures for ReLU networks.
Bayesian deep learning uses function-space priors to improve model uncertainty and robustness.
problem Bayesian deep learning struggles with model-specific weight-space priors that are hard to interpret and specify.
method Apply a Dirichlet prior in predictive space and perform approximate function-space variational inference.
result The approach improves uncertainty quantification, scalability, and adversarial robustness in large-scale image classification.
Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networksphysics.geo-ph
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.
Paper addresses variational inference issues in Bayesian neural networks.
problem Negative infinite ELBO for function-space priors in BNNs.
method Regularized KL divergence for well-defined function-space variational inference.
result Method provides competitive uncertainty estimates for BNNs.
New Gaussian priors for neural networks improve scalability and Bayesian inference stability.
problem Scalability and stability issues in Bayesian neural network inference.
method Introduces a new Gaussian neural network prior with decreasing variance in network width, enabling stable MCMC sampling.
result The new prior enables stable MCMC sampling for Bayesian neural network inference, improving scalability and stability.
Bayesian neural network achieves nearly optimal performance in Besov space.
problem Bayesian neural networks in Besov space.
method Spike-and-slab prior and shrinkage prior for posterior convergence rate.
result The posterior convergence rate is nearly minimax and adaptive to unknown smoothness.
Study connects Gaussian processes and regularization for sequence-function mappings.
problem Understanding and interpreting sequence-function maps in biology.
method Relates Gaussian process priors, regularization, and gauge fixing in overparameterized weight space.
result Established the relationship between regularized regression and Gaussian processes in function space.
HyperBO+ pre-trains a universal prior for Bayesian optimization across different domains.
problem Bayesian optimization requires domain-specific priors, limiting its applicability.
method Two-step pre-training method for hierarchical Gaussian processes.
result HyperBO+ achieves lower regrets on unseen search spaces.
MARS meta-learns function scores for improved predictive accuracy and uncertainty.
problem Difficulty in specifying expressive priors for Bayesian meta-learning.
method Meta-learning the score function of data-generating process marginals in the function space.
result State-of-the-art predictive accuracy and improved uncertainty estimates.
Bayesian neural networks with functional priors improve surrogate modeling in mechanics.
problem Challenges in integrating prior knowledge and quantifying uncertainties in high-dimensional NN parameter spaces.
method Anchored ensembling to integrate a priori information and learn low-rank correlations between NN parameters.
result Effective transfer of knowledge between function-space and parameter-space priors improves surrogate model accuracy and uncertainty estimation.
Bayesian neural networks use ridgelet prior for uncertainty quantification.
problem Combining strong predictive performance with uncertainty quantification in Bayesian neural networks.
method Proposes a ridgelet prior that approximates a Gaussian process covariance function in the output space of the network.
result Establishes universality property allowing Bayesian neural networks to approximate any Gaussian process.
Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be in regions of the input space. Output-Constrained BNNs (OC-BNN) represent an int…
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Regularization methods, specifically those which directly alter weights like and , are an integral part of many learning algorithms. Both the regularizers mentioned above are formulated by assuming certain priors in the parameter space and these assumptions, in some cases, induce sparsity in the parameter sp…
This paper introduces hierarchical Gaussian process priors for neural networks to capture weight correlations and inductive biases.
problem Capturing weight correlations and inductive biases in neural networks.
method Hierarchical Gaussian process priors with unit embeddings and input-dependent kernels.
result Hierarchical Gaussian process priors provide competitive predictive performance and desirable uncertainty estimates.
A new method converts neural networks to function space for scalable sequential learning.
problem Challenges in gradient-based deep learning for sequential data.
method Dual parameterization of neural networks from weight to function space.
result Efficient scaling, knowledge retention, and new data incorporation.
Enhances neural networks with prior function values to improve accuracy.
problem Improving neural network accuracy in regions without training data.
method Develops a probabilistic approach to augment BNNs with prior function values.
result Predictions rely more on prior information in uncertain regions.
This paper learns prior models from indirect data efficiently.
problem Learning prior models from indirect data in Bayesian inversion.
method Generative model of prior as pushforward of Gaussian in latent space, learned by minimizing loss function.
result Efficient residual-based neural operator approximation for forward model learning.
FTIP uses normalizing flows to improve posterior inference in function space.
problem Challenges in posterior inference with implicit-process priors.
method FTIP uses normalizing flows to define a richer variational distribution over combination weights.
result FTIP captures asymmetric and multimodal posterior structure better than Gaussian coefficient approximations.
New method tunes prior IP to data for flexible predictive distributions.
problem Challenges in approximate inference for large models with high parameter dependencies.
method Inducing-point representation of prior IP to approximate posterior process.
result Scalable method that tunes prior IP to data and provides accurate non-Gaussian predictive distributions.
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.
Bayesian optimization (BO) is a widely-used method for optimizing expensive (to evaluate) problems. At the core of most BO methods is the modeling of the objective function using a Gaussian Process (GP) whose covariance is selected from a set of standard covariance functions. From a weight-space view, this models the o…
We extend diffusion models to function spaces and introduce a new method for sampling from posterior distributions.
problem Sampling from posterior distributions in infinite-dimensional function spaces using diffusion models.
method Infinite-dimensional extension of Doob's -transform, Supervised Guidance Training for efficient sampling.
result We prove that diffusion models can be conditioned to sample from posterior distributions and introduce a simulation-free score matching objective.
The paper proposes a method for better uncertainty estimation in neural networks.
problem Estimating predictive uncertainty in neural networks is crucial but challenging.
method The paper proposes a function-space variational inference method to infer a posterior distribution over functions.
result The proposed method leads to state-of-the-art uncertainty estimation and predictive performance.
Bayesian Optimization with a Prior for the Optimum (BOPrO) improves efficiency and accuracy.
problem Bayesian Optimization's standard priors are not intuitive for domain experts.
method BOPrO injects expert knowledge into the optimization process using priors about the optimum.
result BOPrO is 6.67x faster than state-of-the-art methods and achieves new state-of-the-art performance.
F-PACOH improves meta-learners' reliability in uncertain regions.
problem Overconfident uncertainty estimates in meta-learning.
method Meta-learning priors as stochastic processes in function space, directly steering predictions towards high epistemic uncertainty.
result Significantly outperforms other meta-learners in Bayesian Optimization.
Drug Discovery under Covariate Shift with Domain-Informed Prior Distributions over Functionsq-bio.BM
Q-SAVI model improves drug discovery accuracy with prior knowledge of chemical space.
problem Challenges in drug discovery due to covariate shift and limited labeled data.
method Probabilistic model with domain-informed prior distributions over functions.
result Q-SAVI outperforms state-of-the-art techniques in predictive accuracy and calibration.
This work extends Gaussian process priors to neural operators for function space mappings.
problem Improving uncertainty quantification in deep neural networks.
method Extending Gaussian process priors to neural operators with conditions for convergence and computation of covariance functions.
result Arbitrary-depth neural operators with Gaussian kernels converge to function-valued GPs, enabling posterior computation in regression scenarios.
Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected improvement is perhaps the most popular method for solving this problem; the algorithm pe…
Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Predictionstat.ML
Bayesian Neural ODEs improve vessel trajectory prediction with better uncertainty estimates.
problem Challenges in predicting vessel trajectories from irregular AIS data.
method Adopted a Gaussian process (GP) kernel-based prior on the vector field evaluated at measurement points, combined with probabilistic multiple shooting for long trajectories.
result Improved accuracy and uncertainty quantification in vessel trajectory predictions.
Study on Bayesian transformers finds issues with weight-space inference and prior specification.
problem Challenges in obtaining meaningful uncertainty estimates for transformer models.
method Proposed a novel method based on implicit reparameterization of the Dirichlet distribution for variational inference on attention weights.
result Proposed method performs competitively with baselines in estimating predictive uncertainty.
An interpretation of the Brownian bridge as a physics-informed prior for the Poisson equationstat.ML
The Brownian bridge serves as a physics-informed prior for solving the Poisson equation.
problem Reconstructing physical fields from limited and noisy data with known governing equations.
method Formalizing inverse problems via Bayesian inference in function spaces using a Brownian bridge Gaussian process.
result The Brownian bridge Gaussian process can be viewed as a physics-constrained prior for the Poisson equation, allowing for a fully Bayesian framework.
Develops a new method for functional regression that works with non-Gaussian data.
problem Limited models for regression in function spaces with Gaussian process priors.
method Introduces Neural Operator Flows (OpFlow) for non-Gaussian function spaces.
result OpFlow enables robust and accurate uncertainty quantification for functional regression.
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibi…
Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defi…
Predictive Complexity Priorsstat.ML
Proposes a new prior for complex models to improve prediction accuracy.
problem Difficulty in specifying priors for complex models like neural networks.
method Predictive complexity priors defined by comparing model predictions to a reference model, transferred to parameters via change of variables.
result Improves model predictions by reducing unintuitive effects of traditional priors.
X-VAE uses data-adaptive Gaussian priors to improve latent space modeling.
problem Limitations of standard Gaussian priors in complex datasets.
method Data-adaptive Gaussian prior derived from pretrained autoencoder latent codes.
result Improved latent space modeling and generation quality.
Empirical Gaussian Processes learn flexible priors from data.
problem Limited effectiveness of standard Gaussian process kernels.
method Estimate mean and covariance functions empirically from data.
result Empirical GPs converge to closest GP to real data generating process.
Bayesian optimization improves with nonstationary covariance functions.
problem Stationary covariance functions fail to capture prior information in high dimensions.
method Proposes nonstationary covariance functions to encode prior information and adaptively promote local exploration.
result Nonstationary covariance functions increase sample efficiency in high dimensions.
Bayesian neural networks fail at out-of-distribution detection, revealing fundamental issues.
problem Out-of-distribution detection with Bayesian neural networks.
method Study of Bayesian inference with function space priors and comparison to Gaussian processes.
result Bayesian inference with function space priors does not lead to good OOD detection.
Efficiently quantifies uncertainty in DeepONets for function spaces.
problem Uncertainty quantification in deep operator networks.
method Randomized prior ensembles for frequentist inference.
result Improved robustness and accuracy, reliable uncertainty estimates, out-of-distribution detection, and model bias quantification.
DVIP improves on IP-based methods by using IPs as priors over latent functions.
problem Limited expressiveness of IP-based models, especially in function space.
method Proposes DVIP, a multi-layer generalization of IPs, and scalable variational inference.
result DVIP outperforms previous IP-based methods and deep GPs in regression and classification tasks.
New method uses trainable activations to make BNNs behave like GPs.
problem Making Bayesian Neural Networks (BNNs) behave like Gaussian Processes (GPs).
method Introduced trainable activations and periodic activations to map GP priors to BNNs. Used 2-Wasserstein distance for optimization.
result Method consistently outperforms existing approaches or matches heuristic methods.
Bayesian optimization improved for high-dimensional outputs using randomized priors.
problem Efficient global optimization of high-dimensional black-box functions.
method Deep learning framework with bootstrapped ensembles of neural architectures with randomized priors.
result Superior performance in tasks with high-dimensional outputs compared to state-of-the-art methods.
Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}. In this paper we address the important class of sum-of-submodular (SoS) function…
We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding th…