Related papers: Bayesian model reduction
This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…
Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…
Causal Bayesian networks have become a powerful technology for reasoning under uncertainty in areas that require transparency and explainability, by relying on causal assumptions that enable us to simulate hypothetical interventions. The…
A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…
Deep neural networks can obtain impressive performance on various tasks under the assumption that their training domain is identical to their target domain. Performance can drop dramatically when this assumption does not hold. One…
Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems.…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…
Bayesian Networks (BNs) have become increasingly popular over the last few decades as a tool for reasoning under uncertainty in fields as diverse as medicine, biology, epidemiology, economics and the social sciences. This is especially true…
Modelling of inspection data for large scale physical systems is critical to assessment of their integrity. We present a general method for inference about system state and associated model variance structure from spatially distributed time…
We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
Prompt learning has emerged as an effective technique for fine-tuning large-scale foundation models for downstream tasks. However, conventional prompt learning methods are prone to overfitting and can struggle with out-of-distribution…
We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
The traditional two-stage approach to causal inference first identifies a single causal model (or equivalence class of models), which is then used to answer causal queries. However, this neglects any epistemic model uncertainty. In…