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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…

Machine Learning · Statistics 2026-05-25 Shiyi Sun , Geoff K. Nicholls , Jeong Eun Lee

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

Methodology · Statistics 2026-05-18 Jeong Eun Lee , Sitong Liu , Geoff K. Nicholls

Simulation-based inference (SBI) enables amortized Bayesian inference for simulators with implicit likelihoods. But when we are primarily interested in the quality of predictive simulations, or when the model cannot exactly reproduce the…

Machine Learning · Statistics 2023-11-03 Richard Gao , Michael Deistler , Jakob H. Macke

Amortized simulation-based inference (SBI) methods train neural networks on simulated data to perform Bayesian inference. While this strategy avoids the need for tractable likelihoods, it often requires a large number of simulations and has…

Machine Learning · Computer Science 2025-03-04 Manuel Gloeckler , Shoji Toyota , Kenji Fukumizu , Jakob H. Macke

Amortized Bayesian Inference (ABI) enables efficient posterior estimation using generative neural networks trained on simulated data, but often suffers from performance degradation under model misspecification. While self-consistency (SC)…

Machine Learning · Statistics 2026-02-27 Aayush Mishra , Šimon Kucharský , Paul-Christian Bürkner

Graphs arise across diverse domains, from biology and chemistry to social and information networks, as well as in transportation and logistics. Inference on graph-structured data requires methods that are permutation-invariant, scalable…

Machine Learning · Statistics 2026-05-05 Svenja Jedhoff , Elizaveta Semenova , Aura Raulo , Anne Meyer , Paul-Christian Bürkner

Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture…

Machine Learning · Statistics 2026-03-17 Šimon Kucharský , Paul Christian Bürkner

Bayesian statistical inference loses predictive optimality when generative models are misspecified. Working within an existing coherent loss-based generalisation of Bayesian inference, we show existing Modular/Cut-model inference is…

Methodology · Statistics 2026-05-18 Chris U. Carmona , Geoff K. Nicholls

Simulation-based inference (SBI) refers to statistical inference on stochastic models for which we can generate samples, but not compute likelihoods. Like SBI algorithms, generative adversarial networks (GANs) do not require explicit…

Meta-learning is a framework in which machine learning models train over a set of datasets in order to produce predictions on new datasets at test time. Probabilistic meta-learning has received an abundance of attention from the research…

Machine Learning · Statistics 2023-09-07 Tommy Rochussen

We propose a posterior for Bayesian Likelihood-Free Inference (LFI) based on generalized Bayesian inference. To define the posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. In LFI, we can…

Methodology · Statistics 2024-09-24 Lorenzo Pacchiardi , Sherman Khoo , Ritabrata Dutta

Simulation-based Bayesian inference (SBI) can be used to estimate the parameters of complex mechanistic models given observed model outputs without requiring access to explicit likelihood evaluations. A prime example for the application of…

Machine Learning · Computer Science 2022-11-28 Jonas Beck , Michael Deistler , Yves Bernaerts , Jakob Macke , Philipp Berens

Simulation-based inference (SBI) provides a powerful framework for inferring posterior distributions of stochastic simulators in a wide range of domains. In many settings, however, the posterior distribution is not the end goal itself --…

Machine Learning · Computer Science 2023-12-19 Mila Gorecki , Jakob H. Macke , Michael Deistler

Frequently, population studies feature pyramidally-organized data represented using Hierarchical Bayesian Models (HBM) enriched with plates. These models can become prohibitively large in settings such as neuroimaging, where a sample is…

Machine Learning · Computer Science 2022-03-09 Louis Rouillard , Demian Wassermann

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…

Machine Learning · Computer Science 2025-02-11 Sarthak Mittal , Niels Leif Bracher , Guillaume Lajoie , Priyank Jaini , Marcus Brubaker

The global inducing point variational approximation for BNNs is based on using a set of inducing inputs to construct a series of conditional distributions that accurately approximate the conditionals of the true posterior distribution. Our…

Machine Learning · Statistics 2023-10-25 Matthew Ashman , Tommy Rochussen , Adrian Weller

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…

Methodology · Statistics 2025-04-15 Wang Yuyan , Michael Evans , David J. Nott

Bayesian modeling and analysis of the MEG and EEG modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of…

Mathematical Physics · Physics 2008-11-20 Daniela Calvetti , Harri Hakula , Sampsa Pursiainen , Erkki Somersalo

Amortized Bayesian inference (ABI) offers fast, scalable approximations to posterior densities by training neural surrogates on data simulated from the statistical model. However, ABI methods are highly sensitive to model misspecification:…

Machine Learning · Statistics 2026-01-27 Šimon Kucharský , Aayush Mishra , Daniel Habermann , Stefan T. Radev , Paul-Christian Bürkner

Sensitivity analyses reveal the influence of various modeling choices on the outcomes of statistical analyses. While theoretically appealing, they are overwhelmingly inefficient for complex Bayesian models. In this work, we propose…

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