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Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic…
ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi- Monte Carlo) sequences. We show that the resulting ABC…
There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian…
Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…
We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…
Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…
Approximate Bayesian Computation (ABC) is a statistical learning technique to calibrate and select models by comparing observed data to simulated data. This technique bypasses the use of the likelihood and requires only the ability to…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
High dimensional integrals can be approximated well by quasi-Monte Carlo methods. However, determining the number of function values needed to obtain the desired accuracy is difficult without some upper bound on an appropriate semi-norm of…
Approximate Bayesian Computation (ABC) methods are commonly used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Classical ABC methods are based on nearest neighbor type algorithms…
Approximate Bayesian computation (ABC) is one of the most popular "likelihood-free" methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian…
Approximate Bayesian Computation (ABC) is a popular inference method when likelihoods are hard to come by. Practical bottlenecks of ABC applications include selecting statistics that summarize the data without losing too much information or…
Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…
Quasi-Monte Carlo methods are used for numerically integrating multivariate functions. However, the error bounds for these methods typically rely on a priori knowledge of some semi-norm of the integrand, not on the sampled function values.…
Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al.…
Monte Carlo integration becomes prohibitively expensive when each sample requires a high-fidelity model evaluation. Multi-fidelity uncertainty quantification methods mitigate this by combining estimators from high- and low-fidelity models,…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…