Related papers: Proximal nested sampling with data-driven priors f…

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…

In recent years, domains such as natural language processing and image recognition have popularized the paradigm of using large datasets to pretrain representations that can be effectively transferred to downstream tasks. In this work we…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Training neural networks on randomly generated artificial datasets yields Bayesian models that capture the prior defined by the dataset-generating distribution. Prior-data Fitted Networks (PFNs) are a class of methods designed to leverage…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

The extensive adoption of Deep Neural Networks has led to their increased utilization in challenging scientific visualization tasks. Recent advancements in building compressed data models using implicit neural representations have shown…

High throughput technologies have become the practice of choice for comparative studies in biomedical applications. Limited number of sample points due to sequencing cost or access to organisms of interest necessitates the development of…

Backward simulation is an approximate inference technique for Bayesian belief networks. It differs from existing simulation methods in that it starts simulation from the known evidence and works backward (i.e., contrary to the direction of…

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection…

Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…

In this paper, we set forth a new vision of reinforcement learning developed by us over the past few years, one that yields mathematically rigorous solutions to longstanding important questions that have remained unresolved: (i) how to…

We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of "live points" varies to allocate samples more efficiently. In empirical tests the new method significantly improves calculation…

This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented…

The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…

The need for function estimation in label-limited settings is common in the natural sciences. At the same time, prior knowledge of function values is often available in these domains. For example, data-free biophysics-based models can be…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…