TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Dürr, Oliver
A1  - Hörtling, Stefan
A1  - Dold, Daniel
A1  - Kovylov, Ivonne
A1  - Sick, Beate
T1  - Bernstein flows for flexible posteriors in variational Bayes
JF  - AStA Advances in Statistical Analysis
N2  - Black-box variational inference (BBVI) is a technique to approximate the posterior of Bayesian models by optimization. Similar to MCMC, the user only needs to specify the model; then, the inference procedure is done automatically. In contrast to MCMC, BBVI scales to many observations, is faster for some applications, and can take advantage of highly optimized deep learning frameworks since it can be formulated as a minimization task. In the case of complex posteriors, however, other state-of-the-art BBVI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art BBVI methods, including normalizing flow-based BBVI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI compares favorably against other BBVI methods. Further, using BF-VI, we develop a Bayesian model for the semi-structured melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate, for the first time, the use of BBVI in semi-structured models.
KW  - Variational inference
KW  - Deep learning
KW  - Transformation models
KW  - Bayesian neural network
Y1  - 2024
UN  - https://nbn-resolving.org/urn:nbn:de:bsz:kon4-opus4-51564
SN  - 1863-8171
SS  - 1863-8171
U6  - https://doi.org/10.1007/s10182-024-00497-z
DO  - https://doi.org/10.1007/s10182-024-00497-z
N1  - Open Access Publikation finanziert durch Projekt DEAL
N1  - Corresponding author: Oliver Dürr und Beate Sick
SP  - 20 Seiten
S1  - 20 Seiten
PB  - Springer Science and Business Media LLC
CY  - Berlin; Heidelberg
ER  -