Related papers: Bayesian experimental design: grouped geometric po…
We propose a generalised framework for the updating of a prior ensemble to a posterior ensemble, an essential yet challenging part in ensemble-based filtering methods. The proposed framework is based on a generalised and fully Bayesian view…
We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior…
Ensembling can improve the performance of Neural Networks, but existing approaches struggle when the architecture likelihood surface has dispersed, narrow peaks. Furthermore, existing methods construct equally weighted ensembles, and this…
We develop a Bayesian approach called Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from a complex physical system. The calibration parameter and the physical…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting -- a critical component for causal discovery from finite data where interventions can be costly or…
We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This framework differs from classical Bayesian optimal design of experiments (ODE) in the…
Bayesian optimization is an effective method for optimizing expensive-to-evaluate black-box functions. High-dimensional problems are particularly challenging as the surrogate model of the objective suffers from the curse of dimensionality,…
High-dimensional Bayesian optimization (BO) tasks such as molecular design often require 10,000 function evaluations before obtaining meaningful results. While methods like sparse variational Gaussian processes (SVGPs) reduce computational…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian…
We introduce BEDS (Bayesian Emergent Dissipative Structures), a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints. Unlike classical computational models that assume perfect…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
Bayesian models have many desirable properties, most notable is their ability to generalize from limited data and to properly estimate the uncertainty in their predictions. However, these benefits come at a steep computational cost as…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
Generalized Bayesian Inference (GBI) tempers a loss with a temperature $\beta > 0$ to mitigate overconfidence and improve robustness under model misspecification, but existing GBI methods typically rely on costly MCMC or SDE-based samplers…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…
Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates…
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…