Related papers: Bayesian Approaches to Distribution Regression

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

Recent advances in the field of meta-learning have tackled domains consisting of large numbers of small ("few-shot") supervised learning tasks. Meta-learning algorithms must be able to rapidly adapt to any individual few-shot task, fitting…

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model,…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Diffusion models have recently driven significant breakthroughs in generative modeling. While state-of-the-art models produce high-quality samples on average, individual samples can still be low quality. Detecting such samples without human…

Distribution regression, where the goal is to predict a scalar response from a distribution-valued predictor, arises naturally in settings where observations are grouped and outcomes depend on group-level characteristics rather than on…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

Graph neural networks for molecular property prediction are frequently underspecified by data and fail to generalise to new scaffolds at test time. A potential solution is Bayesian learning, which can capture our uncertainty in the model…

We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can…

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…