arXiv research

New diagnostic tool for assessing approximate Bayesian inference.

Fast Bayesian inference with adaptable priors for real-time applications.

We derive and approximate the conjugate prior of Dirichlet and beta distributions.

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model posterior one would simply use this as the prior for the next task.…

Bayesian inverse problems solved with Gaussian models for PDEs.

Derives TAP approximation for Bayesian linear regression.

Bayesian neural networks use ridgelet prior for uncertainty quantification.

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contain…

A new method maps high-dimensional Bayesian inverse problems to lower dimensions.

Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless …

New theory for BNNs with Gaussian priors achieves optimal posterior concentration rates.

GPNs use unlabeled data to estimate uncertainty in Bayesian problems.

Proposes a new method to approximate Bayesian predictive uncertainty.

A new method for Bayesian neural networks using probabilistic backpropagation.

Informative Bayesian priors are often difficult to elicit, and when this is the case, modelers usually turn to noninformative or objective priors. However, objective priors such as the Jeffreys and reference priors are not tractable to derive for many models of interest. We address this issue by proposing techniques fo…

Bayesian inference for deep neural networks using trace-class priors and MLMC.

The explore{exploit dilemma is one of the central challenges in Reinforcement Learning (RL). Bayesian RL solves the dilemma by providing the agent with information in the form of a prior distribution over environments; however, full Bayesian planning is intractable. Planning with the mean MDP is a common myopic approxi…

Transformers can approximate Bayesian inference efficiently.

Study shows prior Lipschitz continuity can improve adversarial robustness of Bayesian Neural Networks.

New MIF architecture improves posterior approximations in Bayesian models.

In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case, where the prior distribution belongs to the exponential family of distributions. The logarithm of the likelihood function is li…

Bayesian neural networks approximate Student-t processes in the infinite-width limit.

The paper proposes a method to improve Bayesian inference for periodic data using data-driven priors.

A new method learns priors for Bayesian optimisation to improve performance.

Unrolled networks learn optimal Bayesian inference for unknown priors.

Proposes DAK model for improved GP computations.

Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.

Enhances RL with function approximation, improving regret bounds.

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…

New method improves BLL models for complex datasets.

New priors improve Bayesian neural networks without cooling.

In the Bayesian approach to structure learning of graphical models, the equivalent sample size (ESS) in the Dirichlet prior over the model parameters was recently shown to have an important effect on the maximum-a-posteriori estimate of the Bayesian network structure. In our first contribution, we theoretically analyze…

This work tackles the challenge of Bayesian deep learning by proposing a new framework for matching Gaussian process priors with neural network parameters.

BI-EqNO improves Bayesian inference with flexible neural operators.

Bayesian deep learning uses function-space priors to improve model uncertainty and robustness.

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…

GABI learns geometry from diverse systems to improve Bayesian inference.

We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Area Under Curve) criterion. We focus initially on the class of linear score functions. We derive PAC-Bayesian non-asymptotic bounds for two types of prior for the score parameters: a Gaussian prior, and a spike-and-slab p…

Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large …

New method for density estimation without approximating posterior distributions.

A new method for sampling complex posterior distributions in DDMs.

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…

Wide BNNs with odd activations fail to approximate data under mean-field inference.

Bayesian Tensor Network combines prior and data likelihood for efficient prediction and parameter estimation.

A new method uses mixture approximations to improve diffusion models for Bayesian inverse problems.

Bayesian neural networks with Mercer priors for interpretable uncertainty quantification.

Bayesian framework calibrates imperfect models using physics-informed priors and Hamiltonian Monte Carlo.

Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian neural networks; several extensions ensued. We show that the log-uniform prior us…