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 priors for neural networks are improved by incorporating weight correlations and tail behavior.
problem Improving Bayesian priors for neural networks to better reflect true beliefs and performance.
method Analyzed summary statistics of neural network weights in different architectures and incorporated these observations into new priors.
result Improved performance on image classification datasets by using new priors that account for weight correlations and tail behavior.
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.
Regression Prior Networks improve ensemble performance on regression tasks.
problem Improving ensemble performance on regression tasks.
method Extending Prior Networks and Ensemble Distribution Distillation (EnD2) to regression tasks using the Normal-Wishart distribution. result Regression Prior Networks yield performance competitive with ensemble approaches on regression tasks.
BNNpriors library improves Bayesian neural network inference with various prior distributions.
problem Challenges in choosing good prior distributions for Bayesian neural networks.
method State-of-the-art Markov Chain Monte Carlo inference with a wide range of predefined priors.
result Facilitates foundational discoveries on the nature of the cold posterior effect.
We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by cross validation. Then we formulate network inference as a matrix completion problem…
Variational dropout (VD) is a generalization of Gaussian dropout, which aims at inferring the posterior of network weights based on a log-uniform prior on them to learn these weights as well as dropout rate simultaneously. The log-uniform prior not only interprets the regularization capacity of Gaussian dropout in netw…
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.
Proposes DSM priors for Bayesian neural networks to improve interpretability and robustness.
problem Bayesian neural networks struggle with interpretability, overconfidence, and adversarial attacks.
method Introduces Dirichlet scale mixture (DSM) priors to address these issues.
result DSM priors lead to sparse networks, robustness against adversarial attacks, and competitive predictive performance.
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.
Bayesian weight priors improve neural network learning of identity relations.
problem Neural networks struggle to learn abstract and systematic relations, especially identity relations.
method Extended RBP approach using Bayesian weight priors as a regularization term.
result Bayesian weight priors lead to perfect generalization for identity relations and do not hinder standard neural network learning.
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks. The prior not only favors a desirable global node degree distribution, but also ta…
Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned generative priors they do not require any training over large datasets. However…
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.
Paper improves speech separation by using deep neural networks for more accurate density priors.
problem Improving the accuracy of source priors for independent vector analysis in speech separation.
method Estimating the derivative of speech density using deep neural networks to optimize performance indices.
result Neural network density priors outperform previous ones in convergence speed and SIR.
This work explores how overparametrization and priors affect Bayesian neural network posteriors.
problem Symmetries, non-identifiabilities, and weight-space priors fragment and inflate BNN posteriors.
method We study the interplay between overparametrization and priors in BNN posteriors, deriving key phenomena and validating through experiments.
result Overparametrization induces structured, prior-aligned weight posterior distributions.
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.
Develops methods for constructing likelihoods and priors for Bayesian networks.
problem Learning parameters and structure of Bayesian networks from limited data.
method Introduces assumptions for constructing likelihoods and priors from small assessments.
result Allows construction of likelihoods and priors for a wide range of network structures.
Proposes new priors for neural networks to improve generalization and uncertainty.
problem Improving generalization and uncertainty estimation in neural networks.
method Exploits scalable and structured posteriors as priors with generalization guarantees.
result Improves generalization and uncertainty estimation with non-vacuous bounds.
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.
The paper deals with learning probability distributions of observed data by artificial neural networks. We suggest a so-called gradient conjugate prior (GCP) update appropriate for neural networks, which is a modification of the classical Bayesian update for conjugate priors. We establish a connection between the gradi…
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.
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 …
Ensemble approaches for uncertainty estimation have recently been applied to the tasks of misclassification detection, out-of-distribution input detection and adversarial attack detection. Prior Networks have been proposed as an approach to efficiently \emph{emulate} an ensemble of models for classification by paramete…
Bayesian neural networks incorporate domain knowledge through variational inference.
problem Specifying priors for Bayesian neural networks that capture domain knowledge is challenging.
method Proposes a framework for integrating domain knowledge into BNN priors through variational inference.
result BNNs with proposed domain knowledge priors outperform those with standard priors, achieving better predictive performance.
Bayesian neural networks' performance varies with prior choice, affecting their ability to identify unknowns.
problem The impact of prior choice on Bayesian neural networks' ability to identify unknowns.
method Evaluation of different prior distributions on classification tasks using BNNs and NNs with Monte Carlo dropout.
result Prior choice significantly impacts BNNs' ability to identify unknowns, affecting true and false positive rates.
New method learns priors for Bayesian neural networks from datasets.
problem Lack of prior beliefs in Bayesian deep learning.
method Amortised variational inference to learn priors from datasets.
result Flexible Bayesian neural networks for meta-learning and within-task minibatching.
Bayesian inference is known to provide a general framework for incorporating prior knowledge or specific properties into machine learning models via carefully choosing a prior distribution. In this work, we propose a new type of prior distributions for convolutional neural networks, deep weight prior (DWP), that exploi…
Purpose: Conventional automated segmentation of the head anatomy in MRI distinguishes different brain and non-brain tissues based on image intensities and prior tissue probability maps (TPM). This works well for normal head anatomies, but fails in the presence of unexpected lesions. Deep convolutional neural networks l…
Unrolled networks learn optimal Bayesian inference for unknown priors.
problem Optimizing Bayesian inference when the prior is unknown.
method Unrolling neural networks to simulate iterations of inference algorithms.
result Unrolled networks approximate convergence to optimal denoisers for product priors.
Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dime…
Bayesian neural networks with Mercer priors for interpretable uncertainty quantification.
problem Uncertainty quantification in neural networks, especially for complex input-to-output mappings.
method Introducing Mercer priors for BNNs, which approximate a specified GP and are scalable.
result BNNs with Mercer priors can approximate the uncertainty of a specified GP, making them interpretable and scalable.
Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is suf…
Study shows prior Lipschitz continuity can improve adversarial robustness of Bayesian Neural Networks.
problem Improving adversarial robustness of Bayesian Neural Networks.
method Analysis of i.i.d., zero-mean Gaussian priors and posteriors approximated via mean-field variational inference.
result Adversarial robustness is sensitive to the prior variance.
New theory for BNNs with Gaussian priors achieves optimal posterior concentration rates.
problem Lack of theoretical results for BNNs with Gaussian priors.
method New approximation theory for non-sparse DNNs with bounded parameters.
result BNNs with non-sparse general priors can achieve near-minimax optimal posterior concentration rates.
Review of priors in Bayesian deep learning models.
problem The importance of prior choices in Bayesian deep learning models.
method Overview of different priors and methods of learning priors from data.
result Motivate practitioners to think carefully about prior specification.
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.
The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.
problem Learning semi-parametric relationships in Expert Bayesian Networks with minimal nonlinear components.
method Uses Gaussian Processes and Horseshoe priors to model relationships, prioritizes modifying expert graphs, and generates diverse graphs.
result Models outperform state-of-the-art semi-parametric Bayesian Network models in synthetic and real-world datasets.
Existing Bayesian treatments of neural networks are typically characterized by weak prior and approximate posterior distributions according to which all the weights are drawn independently. Here, we consider a richer prior distribution in which units in the network are represented by latent variables, and the weights b…
Additive Bayesian networks are types of graphical models that extend the usual Bayesian generalized linear model to multiple dependent variables through the factorisation of the joint probability distribution of the underlying variables. When fitting an ABN model, the choice of the prior of the parameters is of crucial…
New priors improve Bayesian neural networks without cooling.
problem Bayesian neural networks underfit on clean datasets.
method Introduce DirClip and confidence priors to replace cooling.
result DirClip and confidence priors outperform cold posterior.
Deep convolutional neural networks are known to specialize in distilling compact and robust prior from a large amount of data. We are interested in applying deep networks in the absence of training dataset. In this paper, we introduce deep audio prior (DAP) which leverages the structure of a network and the temporal in…
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.
We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, "weight decay", regularization. Our results characterize a more intricate regularization effect at the level of the unit activat…
R2D2-Net improves Bayesian neural networks by preventing over-shrinkage of important weights.
problem Bayesian neural networks struggle with choosing appropriate priors, leading to over-shrinkage or poor predictive performance.
method Proposes R2D2-Net with an R^2-induced Dirichlet Decomposition prior and variational Gibbs inference algorithm.
result R2D2-Net effectively shrinks irrelevant coefficients while preventing key features from over-shrinkage.
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…
New method improves causal structure discovery with Prior-Fitted Networks.
problem Errors in likelihood estimation limit proper causal structure discovery.
method Amortized causal discovery with Prior-Fitted Networks.
result Significant gains in structure recovery compared to baselines.
Bayesian neural networks (BNNs) have developed into useful tools for probabilistic modelling due to recent advances in variational inference enabling large scale BNNs. However, BNNs remain brittle and hard to train, especially: (1) when using deep architectures consisting of many hidden layers and (2) in situations wit…