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We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
Estimating posteriors and the associated model evidences, with desired accuracy and affordable computational cost, is a core issue of Bayesian model updating, and can be of great challenge given expensive-to-evaluate models and posteriors…
Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic trade-off between cost and speed -- larger batches are more…
We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the…
We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian…
Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and…
Bayesian inference remains one of the most important tool-kits for any scientist, but increasingly expensive likelihood functions are required for ever-more complex experiments, raising the cost of generating a Monte Carlo sample of the…
An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics:…
In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems. The proof techniques that have emerged…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…