Amortized quadrature for posterior expectations in inverse problems
Read the original on arXiv Statistics ML →The Flow has not summarised this story yet — read it at arXiv Statistics ML.
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arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
arXiv:2602. 00387v4 Announce Type: replace-cross Abstract: Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors.
arXiv:2402. 11736v3 Announce Type: replace Abstract: Kernel herding belongs to a family of deterministic quadratures that seek to minimize the maximum mean discrepancy (MMD), that is, the worst-case integration error over a reproducing kernel Hilbert space (RKHS).
This survey article reviews Bayesian quadrature, a probabilistic, model‑based method for numerical integration and expectation estimation. It provides a systematic taxonomy of Bayesian quadrature techniques across modelling, inference, and sampling, presents theoretical guarantees, and includes a controlled numerical study illustrating the impact of different methodological choices. The paper also discusses practical challenges, limitations, and offers an extensive bibliography covering machine learning, statistics, mathematics, and engineering applications.
arXiv:2601. 07094v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function.