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 Prior”
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.
This work tackles the challenge of Bayesian deep learning by proposing a new framework for matching Gaussian process priors with neural network parameters.
problem The challenge of specifying priors over neural network parameters, which affects the induced functional prior and is uncontrolled.
method The approach involves defining functional priors using Gaussian processes and matching these priors with the functional prior of neural networks through the minimization of Wasserstein distance.
result The proposed framework offers systematic performance improvements over alternative priors and approximate Bayesian deep learning approaches.
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.
Novel prior for orthogonal functions improves functional component estimation.
problem Improving orthogonality in functional principal component analysis.
method Sequential adaptive priors for orthogonal functions using hierarchical conditionally normal distributions.
result Proposed prior leads to nearly orthogonal posterior estimates.
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.
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.
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.
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.
Unified framework for data-driven priors in Bayesian inverse problems
problem Bayesian inverse problems
method Unified framework using score functions
result Evaluation of four data-driven priors
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.
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.
Proposes PE-GP-UCB for time-varying Bayesian optimisation.
problem Time-varying Gaussian process bandits with unknown prior.
method PE-GP-UCB algorithm, relying on consistency of function values with priors.
result Regret bound provided for the proposed algorithm.
Paper presents a robust transfer learning method for active level set estimation.
problem Efficiently identifying regions of a black-box function with limited function evaluations.
method Incorporates prior knowledge from a related function while locally adapting it.
result The method achieves better convergence of level sets compared to standard transfer learning.
The paper explores how prior functions and bootstrapping improve ensemble uncertainty estimation.
problem Improving uncertainty estimation in machine learning models.
method Investigates the benefits of prior functions and bootstrapping in ensemble models.
result Prior functions and bootstrapping enhance ensemble agents' uncertainty estimation across different inputs.
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.
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.
When fitting Bayesian machine learning models on scarce data, the main challenge is to obtain suitable prior knowledge and encode it into the model. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge from data acquired in related tasks. When it comes to meta-learning in Gaussian…
Estimation of response functions is an important task in dynamic medical imaging. This task arises for example in dynamic renal scintigraphy, where impulse response or retention functions are estimated, or in functional magnetic resonance imaging where hemodynamic response functions are required. These functions can no…
Hybrid Bayesian neural networks use function uncertainty for probabilistic inference.
problem Uncertainty in neural network weights is hard to specify and interpret.
method Integrates probabilistic layers with standard deterministic layers for function uncertainty.
result Improves probabilistic inference by encoding function uncertainty.
P-BO reduces black-box adversarial attacks by 10x with Bayesian optimization and function prior.
problem Efficiently generating adversarial examples against black-box models.
method Prior-guided Bayesian Optimization (P-BO) with a function prior initialized from a surrogate model.
result Significantly reduces the number of queries needed for adversarial attacks.
A new method learns priors for Bayesian optimisation to improve performance.
problem Bayesian optimisation tasks often assume strong similarity, which is violated in many cases.
method Replace strong similarity assumption with shape similarity, learn priors for hyperparameters.
result PLeBO and prior transfer find good inputs in fewer evaluations.
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.
Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regressionstat.ME
Functional BART adds shape priors to Bayesian tree regression for better curve fitting.
problem Regression with function-on-scalar data and shape constraints.
method Bayesian tree structure with spline representations, customized Bayesian backfitting algorithm, shape priors.
result Improved estimation and prediction accuracy with shape priors.
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.
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.
New method improves Robbins-Monro algorithm convergence with prior information.
problem Improving convergence speed of Robbins-Monro algorithm.
method Integrates prior information into Robbins-Monro iteration without regression model.
result Prior-information Robbins-Monro sequence converges faster than standard.
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
Two algorithms improve GP bandits by selecting priors and minimizing regret.
problem Selecting appropriate GP priors for unknown functions.
method Developed two algorithms: Prior-Elimination GP-TS and HyperPrior GP-TS.
result Established sublinear regret bound for HyperPrior GP-TS.
In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via estimating prior probabilities from either labeled or unlabeled training data. The erro…
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
problem Difficult inference for multivariate Gaussian Processes with multiple lengthscale parameters.
method Introduces a self-assembled Wishart prior and uses MCMC for Bayesian inference on kernel hyperparameters.
result Demonstrates the effectiveness of the new prior in GP-based learning with empirical results.
Generative model learns functional vector fields for pharmacokinetics.
problem Generating accurate virtual cohorts and forecasting patient trajectories without manual tuning.
method Prior-Fitted Functional Flows model, learning functional vector fields conditioned on sparse, irregular data.
result State-of-the-art predictive accuracy on real-world datasets.
Extends Gaussian Process regression for handling multiple prior distributions.
problem Handling multiple prior distributions in Bayesian Machine Learning models.
method Mixtures of Gaussian Processes with analytical and Sparse Variational approaches.
result Effective in accounting for prior misspecification in functional regression problems.
Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class of priors would represent weights compactly, capture correlations between weigh…
One of the most interesting features of Bayesian optimization for direct policy search is that it can leverage priors (e.g., from simulation or from previous tasks) to accelerate learning on a robot. In this paper, we are interested in situations for which several priors exist but we do not know in advance which one fi…
ColaBO accelerates optimization with user beliefs.
problem Optimizing expensive functions with limited prior knowledge.
method General Bayesian framework for incorporating user beliefs.
result Significant optimization acceleration with accurate prior information.
While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial Basis Function Networks, a novel prior that is able to encode amplitude stationar…
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…
Study proposes learning optimal priors from data for better Bayesian inference.
problem Challenges the use of noninformative uniform priors in Bayesian inference.
method Machine learning approach to learn optimal priors from data using a target function.
result Study models consistently outperformed baseline models in Wikipedia category classification.
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.
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.
Nonparametric Bayesian label prediction on a large graph using truncated Laplacian regularizationstat.CO
This article describes an implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs. We consider a hierarchical Bayesian approach with a prior that is constructed by truncating a series expansion of the soft label function using the graph Laplacian eigenfunctions as basis f…
Study on robust utility maximization with nonconcave utility functions under projective determinacy.
problem Investor's optimal investment strategy under model ambiguity and nonconcave utility.
method Projective functions of the path and sets of priors, upper-semicontinuous utility.
result Existence of optimal investment strategy under PD.
It is well-known that the distribution over functions induced through a zero-mean iid prior distribution over the parameters of a multi-layer perceptron (MLP) converges to a Gaussian process (GP), under mild conditions. We extend this result firstly to independent priors with general zero or non-zero means, and secondl…
We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical s…
Prior-Aligned Meta-RL: Thompson Sampling with Learned Priors and Guarantees in Finite-Horizon MDPscs.LG
New meta-reinforcement learning method improves performance in finite-horizon MDPs.
problem Improving meta-reinforcement learning in finite-horizon MDPs with shared optimal action-value functions.
method Proposes MTSRL and MTSRL+ algorithms with learned priors and covariance, coupled with prior-alignment technique for meta-regret guarantees.
result Achieves meta-regret guarantees with learned priors and covariance, outperforming prior-independent RL and bandit-only meta-baselines.
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.
This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the m…