Inference via low-dimensional couplings

A Spantini, D Bigoni, Y Marzouk - Journal of Machine Learning Research, 2018 - jmlr.org
We investigate the low-dimensional structure of deterministic transformations between
random variables, ie, transport maps between probability measures. In the context of …

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

L Cao, T O'Leary-Roseberry, PK Jha, JT Oden… - Journal of …, 2023 - Elsevier
We explore using neural operators, or neural network representations of nonlinear maps
between function spaces, to accelerate infinite-dimensional Bayesian inverse problems …

Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy

PC Bürkner, M Scholz, ST Radev - Statistic Surveys, 2023 - projecteuclid.org
Probabilistic (Bayesian) modeling has experienced a surge of applications in almost all
quantitative sciences and industrial areas. This development is driven by a combination of …

An introduction to sampling via measure transport

Y Marzouk, T Moselhy, M Parno, A Spantini - arXiv preprint arXiv …, 2016 - arxiv.org
We present the fundamentals of a measure transport approach to sampling. The idea is to
construct a deterministic coupling---ie, a transport map---between a complex" target" …

Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation

JB Nagel, J Rieckermann, B Sudret - Reliability Engineering & System …, 2020 - Elsevier
This paper presents an efficient surrogate modeling strategy for the uncertainty
quantification and Bayesian calibration of a hydrological model. In particular, a process …

Inverse problems in a Bayesian setting

HG Matthies, E Zander, BV Rosić, A Litvinenko… - … Methods for Solids and …, 2016 - Springer
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the
propagation of uncertainty through a computational (forward) model—are strongly …

Gibbs flow for approximate transport with applications to Bayesian computation

J Heng, A Doucet, Y Pokern - Journal of the Royal Statistical …, 2021 - academic.oup.com
Let π 0 and π 1 be two distributions on the Borel space (R d, B (R d)). Any measurable
function T: R d→ R d such that Y= T (X)∼ π 1 if X∼ π 0 is called a transport map from π 0 to …

Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting

R Morrison, R Baptista… - Advances in neural …, 2017 - proceedings.neurips.cc
We present an algorithm to identify sparse dependence structure in continuous and non-
Gaussian probability distributions, given a corresponding set of data. The conditional …

Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fields

M Katzfuss, F Schäfer - Journal of the American Statistical …, 2024 - Taylor & Francis
A multivariate distribution can be described by a triangular transport map from the target
distribution to a simple reference distribution. We propose Bayesian nonparametric …

Heavy-tailed sampling via transformed unadjusted Langevin algorithm

Y He, K Balasubramanian, MA Erdogdu - arXiv preprint arXiv:2201.08349, 2022 - arxiv.org
We analyze the oracle complexity of sampling from polynomially decaying heavy-tailed
target densities based on running the Unadjusted Langevin Algorithm on certain …